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Foreign Exchange Option and Returns Based Correlation Forecasts: Evaluation and Two Applications

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We compare option-implied correlation forecasts from a dataset consisting of over 10 years of daily data on over-the-counter (OTC) currency option prices to a set of return-based correlation measures and assess the relative quality of the correlation forecasts. We find that while the predictive power of implied correlation is not always superior to that of returns based correlations measures, it tends to provide the most consistent results across currencies. Predictions that use both implied and returns-based correlations generate the highest adjusted R2s, explaining up to 42 per cent of the realised correlations. We then apply the correlation forecasts to two policyrelevant topics, to produce scenario analyses for the euro effective exchange rate index, and to analyse the impact on cross-currency co-movement of interventions on the JPY/USD exchange rate.
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WORKING PAPER SERIES
NO. 447 / FEBRUARY 2005
FOREIGN EXCHANGE
OPTION AND RETURNS
BASED CORRELATION
FORECASTS
EVALUATION AND
TWO APPLICATIONS
by Olli Castrén
and Stefano Mazzotta
In 2005 all ECB
publications
will feature
a motif taken
from the
50 banknote.
W ORKING PAPER SERIES
NO. 447 / FEBRUARY 2005
This paper can be downloaded without charge from
http://www.ecb.int or from the Social Science Research Network
electronic library at http://ssrn.com/abstract_id=668247.
FOREIGN EXCHANGE
OPTION AND RETURNS
BASED CORRELATION
FORECASTS
EVALUATION AND
TWO APPLICATIONS
1
by Olli Castrén
2
and Stefano Mazzotta
3
1 The OTC volatilities used in this paper were provided by Citibank N.A.We are grateful to Peter Christoffersen and Lorenzo Cappiello
who provided many ideas and suggestions to this work, and Stelios Makrydakis and participants in an internal ECB seminar
for useful comments.The usual disclaimer applies.
2 Corresponding author: DG-Economics, European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany;
e-mail: Olli.Castren@ecb.int
3 McGill University - Faculty of Management, 1001 Sherbrooke St.West, Montreal, Quebec H3A1G5, Canada;
e-mail: stefano.mazzotta@mail.mcgill.ca
© European Central Bank, 2005
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The views expressed in this paper do not
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Central Bank.
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Working Paper Series is available from
the ECB website, http://www.ecb.int.
ISSN 1561-0810 (print)
ISSN 1725-2806 (online)
3
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Working Paper Series No. 447
February 2005
CONTENTS
Abstract 4
Non-technical summary 5
1. Introduction 7
2. Correlation forecast evaluation 10
2.1. Data issues 10
2.2. The forecasting object of interest 11
2.3. The measures of correlation 13
3. Correlation forecast evaluation
methodology and results
3.1. Efficiency and bias 18
4. Two applications of correlation forecasts 19
4.1. Scenario analysis for the euro nominal
effective exchange rate index 19
and correlation among cross-rates 23
5. Concluding remarks 26
References 27
Appendices 1-2 30
33
41
European Central Bank working paper series 46
4.2. Exchange rate intervention
16
Appendix 3 Charts
Appendix 4 Tables
Abstract: We compare option-implied correlation forecasts from a dataset consisting
of over 10 years of daily data on over-the-counter (OTC) currency option prices to a
set of return-based correlation measures and assess the relative quality of the
correlation forecasts. We find that while the predictive power of implied correlation is
not always superior to that of returns based correlations measures, it tends to provide
the most consistent results across currencies. Predictions that use both implied and
returns-based correlations generate the highest adjusted R
2
s, explaining up to 42 per
cent of the realised correlations. We then apply the correlation forecasts to two policy-
relevant topics, to produce scenario analyses for the euro effective exchange rate
index, and to analyse the impact on cross-currency co-movement of interventions on
the JPY/USD exchange rate.
Keywords: Correlation forecasts, currency options data, effective exchange rate.
JEL classification: F31, F37, G15.
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Working Paper Series No. 447
February 2005
Non-technical summary
The purpose of this study is to investigate the extent to which it is possible to use
returns based measures and foreign exchange options based measures to predict the
correlation between bilateral exchange rates. In particular, we study whether the
forward-looking information contained in the OTC currency options data can provide
good forecasts of the future realised correlation between exchange rates by
themselves or in addition to various correlation forecasts derived from returns based
measures. Armed with the results from the correlation forecast analysis, we then
illustrate two different applications of the methodology for policy related purposes.
There is ample anecdotal evidence that over time, certain currency pairs tend to move
in tandem. In other words, when one of the two exchange rates appreciates
(depreciates), the other tends to follow a similar pattern. In economic terms, these
patterns are interesting from several points of view. First, the reason why two
currency pairs show a positive correlation over time could be that their dynamics is
driven by the same economic fundamentals. Second, a sudden fall in an otherwise
relatively steady degree of correlation could be indicative of attempts by
policymakers to try to influence the dynamics of some particular exchange rate. Third,
a set of correlations among several exchange rates could provide an idea about which
currencies are facing excess demand in the foreign exchange market. And fourth, if
we have a reliable forecast of the correlation relationship between, say, the euro and
the currencies of two or more euro area major trading partner economies, then the
impact of an assumed future movement in one of the bilateral exchange rates on the
future movements in the other bilateral exchange rates can be assessed using these
correlation forecasts. For a central bank that uses exchange rates mainly as an
indicator for future inflationary risks, it is important to have a forecast of as many of
the bilateral exchange rates entering into the effective exchange rate basket as
possible. Forecasts of correlation provide one way of expanding the information on
future developments received from individual bilateral exchange rates.
We find that the implied correlation calculated from currency options prices shows
predictive power for the future realised correlation among most major currency pairs.
However, for the exchange rate pairs that show correlation predictability, implied
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February 2005
correlation is not the only one that produces good forecasts. Both GARCH and
RiskMetrics correlation forecasts show substantial predictive power. In substance, the
two types of correlations forecasts seem to nicely complement each other in that the
best forecasts are often produced when implied and return-based correlations are used
jointly. The highest adjusted R
2
is almost invariably obtained from the encompassing
(multivariate) regressions. The total predictability obtained using a combination of
forecasts ranges from 18 to 38 per cent for the entire sample and from 20 to 42 per
cent for the post-January 1999 sample.
After assessing the relative forecasting properties of the various methodologies, we
apply the correlations measures on two policy relevant cases. In the first study, the
correlation forecasts are employed to generate scenario analysis for the euro effective
exchange rate conditional on assumptions on the future evolution of the JPY/USD
exchange rate. In the second case, we study whether the interventions by the Japanese
authorities on the JPY/USD exchange rate in the 1990s and 2000s have affected the
patterns of co-movement among the JPY/EUR and USD/EUR exchange rates. We
find that when included as an additional explanatory variable in the correlation
forecast regressions, interventions improve upon the explanatory power of the model.
Therefore, it cannot be excluded that interventions on the JPY/USD rate tend to
increase the co-movement among the euro cross rates (JPY/EUR and USD/EUR).
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February 2005
1. Introduction
The purpose of this study is to investigate the extent to which it is possible to use
returns based measures and foreign exchange options based measures to predict the
correlation between bilateral exchange rates. In particular, we study whether the
forward-looking information contained in the OTC currency options data can provide
good forecasts of the future realised correlation between exchange rates by
themselves or in addition to various correlation forecasts derived from returns based
measures. Armed with the results from the correlation forecast analysis, we then
illustrate two different applications of the methodology for policy related purposes.
There is ample anecdotal evidence that over time, certain currency pairs tend to move
in tandem. In other words, when one of the two exchange rates appreciates
(depreciates), the other tends to follow a similar pattern. In economic terms, these
patterns are interesting from several points of view. First, the reason why two
currency pairs show a positive correlation over time could be that their dynamics is
driven by the same economic fundamentals. Second, a sudden fall in a historically
stable correlation relationship could be indicative of attempts by policymakers to try
to influence the dynamics of some particular exchange rate. Third, a set of
correlations among several exchange rates could provide an idea about which
currencies are facing excess demand in the foreign exchange market. And fourth, if
we have a reliable forecast of the correlation relationship between, say, the euro and
the currencies of two or more euro area major trading partner economies, then the
impact of an assumed future movement in one of the bilateral exchange rates on the
future movements in the other bilateral exchange rates can be assessed using these
correlation forecasts. For a central bank that uses exchange rates mainly as an
indicator for future inflationary risks, it is important to have a forecast of as many of
the bilateral exchange rates entering into the effective exchange rate basket as
possible. Forecasts of correlation provide one way of expanding the information on
future developments received from individual bilateral exchange rates.
There is a substantial literature investigating the informational content of options in
relation to asset price returns. Several early contributions use market-based options
data with mixed results to investigate conditional second moments, but they almost
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Working Paper Series No. 447
February 2005
invariably concentrate on volatility rather than correlation. Beckers (1981) finds that
not all available information is reflected in the current option price and questions the
efficiency of the option markets. Canina and Figlewski (1993) find
that implied
volatility is a poor forecast of subsequent realized
volatility. Lamoureux and Lastrapes
(1993) provide evidence against restrictions of option pricing models which assume
that variance risk is not priced. However,
Jorion (1995) finds that statistical models of
volatility based on returns are dominated by implied volatility forecasts even when the
former are given the advantage of ex post in sample parameter estimation. He also
finds evidence of bias. More recently,
Christensen and Prabhala (1998) use longer
time series and non-overlapping data and find that implied volatility outperforms past
volatility in forecasting future volatility. Fleming (1998) finds that implied volatility
dominates historical volatility in terms of ex ante forecasting power and suggests that
a linear model which corrects for the bias present in implied volatility forecasts can
provide a useful market-based estimator of conditional volatility. Blair, Poon, and
Taylor (2001), find that nearly all relevant information is provided by the VIX index
and there is not much incremental information in high-frequency index returns. Neely
(2003) finds that econometric projections supplement implied volatility in out-of-
sample forecasting and delta hedging. He also provides some explanations for the bias
and inefficiency pointing to autocorrelation and measurement errors in implied
volatility. Pong, Shackleton, Taylor and Xu (2004) find that high-frequency historical
forecasts are superior to implied volatilities using OTC data for horizons up to one
week. Covrig and Low (2003) use OTC data to find that quoted implied volatility
subsumes the information content of historically based forecasts at shorter horizons,
while the former is as good as the latter at longer horizons. Finally, Christoffersen and
Mazzotta (2004) systematically assess the quality of option based volatility, interval
and density forecasts for the major currencies 1992-2003. They find that implied
volatilities explain a large share of the variation in realized volatility and that wide-
range interval and density forecasts are often misspecified whereas narrow-range
interval forecasts are well specified.
It is of course striking that all of the above studies investigate options informational
content with regard to volatility forecasts. Studies investigating exchange rate
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February 2005
correlations implied by market data are, on the contrary, rather sparse.
1
The
contributions perhaps closest related to our work are Siegel (1997), Campa and Chang
(1998) and Lopez and Walter (2000), who specifically focus on exchange rate
correlations. Campa and Chang find that implied correlation among the DEM/USD,
USD/JPY and DEM/JPY currency pairs from January 1989 to May 1995 outperform
alternative forecasts at one- and three month horizons. In addition, they find that when
included in joint forecast regressions, implied correlation always incrementally
improves the performance of other forecasts.
In this study, we extend upon the results by Campa and Chang by looking at several
other currencies in a larger sample that also covers the first five years of the single
European currency. In particular, we focus our attention on the correlations between
the following exchange rate pairs: USD/EUR-JPY/EUR; USD/EUR-GBP/EUR;
GBP/EUR-JPY/EUR; USD/GBP-JPY/GBP; USD/JPY-GBP/JPY; USD/EUR-
PLN/EUR; and USD/EUR-CZK/EUR.
2
Our sample starts in January 1992 and ends in
March 2004, except for the Polish zloty and the Czech koruna currency pairs for
which the sample period commences at January 2001. Prior to the launch of the euro
in January 1999, we use data on D-mark currency pairs. This is reflected in our
estimations in that all regressions are run in two samples, the full sample and the post-
January 1999 sample. In the case of the full sample the notation, for simplicity, refers
only to the euro.
We find that the implied correlation calculated from currency options prices shows
predictive power for the future realised correlation among all currency pairs except
the GBP/EUR-JPY/EUR. However, for the exchange rate pairs that show correlation
predictability, implied correlation is not the only one that produces good forecasts.
Both GARCH and RiskMetrics correlation forecasts show substantial predictive
power. In substance, the two types of correlations forecasts seem to nicely
complement each other in that the best forecasts are often produced when implied and
return-based correlations are used jointly. The highest adjusted R
2
is almost invariably
1
However, there exists a more generous literature in correlations among stock and bond markets. Good
reviews of such studies are provided Kroner and Ng (1998) and Cappiello, Engle and Sheppard (2003).
2
The choice of the particular correlation pairs is partially dictated by data availability on the currency
options, as will be discussed in more detail below.
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February 2005
obtained from the encompassing (multivariate) regressions. The total predictability
obtained using a combination of forecasts ranges from 18 to 38 per cent for the entire
sample and from 20 to 42 per cent for the post-January 1999 sample.
After assessing the relative forecasting properties of the various methodologies, we
apply the correlations measures on two policy relevant cases. In the first study, the
correlation forecasts are employed to generate scenario analysis for the euro effective
exchange rate conditional on assumptions on the future evolution of the JPY/USD
exchange rate. In the second case, we study whether the interventions by the Japanese
authorities on the JPY/USD exchange rate in the 1990s and 2000s have affected the
patterns of co-movement among the JPY/EUR and USD/EUR exchange rates.
The rest of this study is organised as follows. Section 2 introduces the framework in
which the various correlation measures will be analysed. Section 3 specifies the
estimated equations and the reports the results. Section 4 presents the two applications
and Section 5 concludes.
2. Correlation Forecast Evaluation
2.1. Data issues
The currency options data used in this study consists of 1-month implied volatilities
on a large number of exchange rates, obtained from Citigroup. Traditionally, the bulk
of trading in options is on OTC basis and not at centralised futures/options exchanges.
Christensen, Hansen and Prabhala (2001) argue that in terms of forecasting properties,
OTC options data could be of superior quality relative to exchange traded options.
This is because OTC prices are quoted daily with fixed “moneyness“ (the distance
between the forward rate and the option’s strike price) in contrast with market-traded
options, which have fixed strike prices and thus time-varying moneyness as the
forward exchange rate changes. Moreover, the trading volume in OTC options is often
much larger than in the corresponding market traded contracts. The underlying
liquidity on OTC quotes is therefore deeper, which makes the OTC quotes a more
reliable source for information extraction. The fact that the currency options market is
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February 2005
heavily concentrated on a few global players does that the liquidity problems can be
reduced further if data from these institutions is available. Citigroup has a significant
market share both in options on major exchange rates as well as on the emerging
currencies.
2.2. The Forecasting Object of Interest
The methodologies we adopt for this study are in several ways similar to those used to
investigate volatility predictability from OTC currency options in Christoffersen and
Mazzotta (2004), with some major differences. The particular object of interest of our
study is forecasting the realised future sample correlation of an exchange rate pair
over the horizon of the following h = 21 trading days.
There exists substantial literature regarding the use of realized volatility as a measure
of equity and foreign exchange variability (see e.g. Andersen and Bollerslev (1998)
and Andersen et al. (2001a, 2001b, 2003)). The common thread of this literature is the
idea that one can sum squared log returns at a frequency higher than that of interest to
obtain a measure of the realized quadratic variation over the frequency of interest. For
instance, one can compute the monthly variance as the sum of squared daily log
returns or the daily variance as the sum of intraday squared log returns. In this
theoretical framework, by increasing the sampling frequency it is possible to construct
ex post realized volatility measures for the integrated latent volatilities that are
asymptotically free of measurement error. In practice, the benefit of increasing the
frequency is offset by the microstructure noise which is invariably included in the
observed market quotes.
One approach commonly taken is to strike a balance between the horizon of interest
and the number of sub-periods in which such horizon is divided for the purpose of
computing the squared returns. In the case of daily variance estimates, whereas early
work suggests using 5-minute returns more recent contributions indicate that 30-
minute returns (i.e. about 16-18 data points per trading day) provide a measure of
daily volatility relatively robust to microstructure noise. In our case, since we want a
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measure of monthly correlation, the sum of own and cross products of demeaned
3
daily log return over the 21 trading days can be considered a sufficiently robust
measure of monthly realized co-variation. The measure of correlation we obtain is
nothing but the ex-post sample correlation over the next 21 trading days. Following
the conventions established in the above mentioned literature, we call this measure
“realised correlation”, henceforth RC. We define RC for the next h days as follows
1, 1, 1, 2, 2, 1,
1
12,
12
1
()(
(, )
h
ti t th ti t th
i
RC
th
RR
RR RR
h
RR
ρ
σσ
++++ ++
=
−−
=
)
, (2.1)
where
2
,
1
1 h
Rj jt i
i
R
h
σ
,
+
=
=
(2.2)
and
1, 1, 1, 1
ln( / )
ti ti ti
RSS
+++
=
(2.3)
are the FX spot return of exchange rate S
1
on day t+i.
The plots of all correlation measures are illustrated in Appendix 3 (note that we have
labelled the realised correlation as “historical correlation” as the latter is simply a
lagged realised correlation as will be explained in more detail below). The charts
show that on daily basis, the measures are very volatile. In particular, it seems that the
correlations between the USD/EUR and JPY/EUR currency pairs, between the
USD/EUR and GBP/EUR currency pairs, between the USD/GBP and JPY/GBP
currency pairs, and between the USD/JPY and GBP/JPY currency pairs have
fluctuated in the positive territory most of the time. Moreover, the positive correlation
seems to be higher in the post-euro subsample.
3
Although asymptotically the mean should be irrelevant and in practice is very close to zero almost
always in the case of correlation it is a good empirical practice to subtract the sample mean from each
21-day sample to constrain the realised correlation to be between minus one and one.
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February 2005
2.3. The Measures of Correlation
To forecast future realised correlation, four alternative correlation measures are
applied. First, we calculate the implied correlation from options implied volatility. To
do so it is necessary to assume that in addition to the Black and Scholes model also
the triangular parity condition between exchange rate cross rates holds.
Being based on options data, implied correlation provides a forward-looking
perspective to the analysis of co-movements between currency pairs. Because
exchange rate options provide information on the currency options market’s
uncertainty about the price of one currency in terms of another, with three currencies
and options on each of the possible exchange rate pairings we can derive an estimate
of the market’s expected future, or implied, correlation between any two of the
exchange rates. To put it in another way, implied correlation represents the degree of
co-movement between two currencies using a third currency as a numeraire.
The implied correlations are derived using the well-known Black-Scholes pricing
formula as well as exploiting the arbitrage condition on currencies. The Black-Scholes
formula allows one to derive implied volatilities for the underlying asset. The no-
arbitrage condition provides, given the proportional changes in returns of two
exchange rates, R
1
and R
2
, the proportional change in the return of a third exchange
rate R
3
simply as R
3
= R
1
– R
2
. It then follows that
()
(
)
(
)
(
)
312 1
2,VarR VarR VarR CovRR=+
2
, (2.4)
whereby it is straightforward to derive the implied correlation (IC) between R
1
and R
2
knowing Var(R
1
), Var (R
2
), and Var (R
3
).
4
The implied correlation is then defined as
22 2
1, 2, 3,
12,
1, 2,
(, )
2
tt
IC
th
tt
RR
t
σσ
ρ
σσ
+−
=
. (2.5)
4
See Malz (1997), Butler and Cooper (1997) and Brandt and Diebold (2003) for further details.
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February 2005
In (2.5), σ
2
1,t
=Var
t
(R
1
) and σ
2
2,t
= Var
t
(R
2
), can be measured by the square of the
implied volatility on each of the currency pairs. The implied correlation for a
particular date can then be calculated simply by inserting values for the implied
volatilities in the equation.
Bollerslev and Zhou (2003)
5
point out that if the volatility risk is priced in the options
markets then implied volatility is a biased predictor of realized volatility. In fact,
implied volatilities are often empirically found to be upward biased estimates of the
objective volatility. In a standard stochastic volatility set up, it can be shown that if
the price of volatility risk is zero, the process followed by the volatility is identical
under the objective and the risk neutral measures. In such a case there would be no
bias. However, the volatility risk premium is generally estimated to be negative which
in turn implies that the volatility process under the risk neutral measure will have
higher drift. These theoretical arguments do apply to the computation of implied
correlation as well. However, because such a potential bias could affect all variances
used in the computation of the implied correlation in (2.5), it is not clear a priori that
the bias for implied correlations is a problem as severe as it is for volatilities. We will
show below that bias is indeed present in correlations computed from options.
The other three volatility forecasts are derived from historical FX returns only. The
simplest possible forecast is the historical h-day volatility, defined as
,
tt
. (2.6)
(1,2) (1,2)
,
HC RC
th t hh
ρρ
=
The historical correlation is simply the lagged realized correlation. Alternatively, we
can consider second moments that apply an exponential weighting scheme putting
progressively less weight on distant observations. The simplest measure using such a
scheme is the Exponential Smoother or RiskMetrics correlation. Daily variance and
covariance then evolve as
() ()
() ()
21222
(1), 1 1, 1 (1), 1,
1
212
(1,2), 1 1, 1 2, 1 (1,2), 1, 2,
1
11
11
i
ttitt
i
i
ttitit
i
RR
R
RR
σλλλσλ
σλλ λσλ
+−+
=
+−++
=
=− = +
=− = +
%%
%%
R
. (2.7)
5
See also Bandi and Perron (2003), Chernov (2003), and Bates (2002).
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February 2005
Following JP Morgan we simply fix λ=0.94 for all the daily FX returns. The forecast
for h-day correlation is therefore
2
(,), 1
(,)
1
,1 ,1
jk t
RM j k
t
jt kt
σ
ρ
σσ
+
+
+
+
=
%
%%
. (2.8)
The third estimate for correlation based on past exchange rate returns that is
considered here is the GARCH correlation. The GARCH methodology permits the
calculation of time-varying second moments for the universe of assets that are
considered by the researcher. According to this approach, variances and correlations
are conditional on a time-varying information set that allows one to update the
estimated second moments at each point in time when new information becomes
available. We have adopted a bivariate GARCH model where R
t
is defined as the
vector of returns
(
)
1, 2,
,
ttt
R
RR=
. (2.9)
We assume that R
t
follows a GARCH process
12
tt
RH
t
ε
=
. (2.10)
In (2.10) ε
t
is an identical and independently distributed vector sequence with mean
zero and unit variance. The conditional covariance H
t
evolves according to a diagonal
BEKK GARCH process
6
(2.11)
11,12,1
'' '
where
H = 2 x 2, A, = 2 x 2 diagonal, = 2 x 2 lower triangular
H(1,1) = variance of exchange rate 1
H(2,2) = variance of exchange rate 2
H(1,2) = covariance
tttt
HHRR
−−
=Ω+Β Β Α
ΒΩ
of currency 1 and currency 2
6
See Engle and Kroner (1995) for further details.
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February 2005
The next day GARCH correlation is thus defined as
1
121
11
H(1,2)
(, )
H(1,1) H(2,2)
GARCH
t
t
tt
RR
ρ
+
+
+
+
=
. (2.12)
In contrast to the RiskMetrics model, which implies a random walk volatility process,
to forecast the 21 days ahead correlation with GARCH it is necessary to consider the
mean reversion of the model and iteratively forecast variances and covariances. The
computations to obtain the GARCH correlation forecasts are detailed in Appendix 1.
The plots of the GARCH correlations (GC) for the various exchange rate pairs are
found in Appendix 3. The plots are substantially smoother than those obtained from
historical correlations.
3. Correlation Forecast Evaluation Methodology and Results
To compare the forecasting capability of the different correlation measures, we run
simple linear predictability regressions. These are carried out in-sample, by using
different windows for the realised correlation (the left-hand side variable) and for the
right-hand side variables. In other words, we assess how various estimates of monthly
exchange rate correlations have in the past predicted realised correlation one month
ahead in time. More specifically, the following univariate regressions are first run for
each correlation
,,
RC j j
th th th
ab
,
ρ
ρε
=+ +
(3.1)
for j = IC, HC, GC.
These univariate regressions
7
serve to assess the fit through the adjusted R
2
and to
check how close the estimates of a are to 0 and how close the estimates of b are to 1.
In addition, bivariate regressions are performed, including the implied correlation and
the two return-based forecasts in turn, as follows
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February 2005
(3.2)
jIC
ht
j
ht
IC
ht
RC
ht
cba
,
,,,,
ερρρ
+++=
for j = HC, GC.
These bivariate regressions shed some light into whether the return-based correlation
forecasts add anything to the market-based forecast implied from currency options.
Finally, a regression will be run including all three correlation forecasts in the same
equation, in order to asses the relative merits of the different correlation forecasts.
The results are reported in Tables 1 and 2 of Appendix 4 where both regression point
estimates as well as standard errors corrected for heteroskedasticity and
autocorrelation, using GMM, are included. The robust Newey-West weighting matrix
with a pre-specified bandwidth equal to 21 days is applied. The regression fit is
reported using adjusted R
2
. Table 2 of Appendix 4 includes the same regressions than
Table 1, but now using the sample period beginning from January 1999.
We find that correlation between foreign exchange pairs is predictable to a substantial
extent. The adjusted R
2
of the GMM regressions
8
ranges from 18 to 38 per cent for
the entire sample and from 20 to 42 per cent for the post-January 1999 sample.
However, for the exchange rate pairs that show correlation predictability, implied
correlation is only in a few cases the best univariate forecast. Both GARCH and
RiskMetrics correlation forecasts show considerable predictive power, too.
When comparing these results with predictability regressions for volatility forecasts,
one difference we find is, therefore, that information from currency options prices
does not always seem to be as helpful in predicting correlation as it is in predicting
volatility. Returns based measures sometimes perform better than correlation
measures based on options data. We note however that the return based measures also
sometimes perform very poorly. This is in contrast with the implied correlation, which
seems to be more consistent as it shows less variability in the predictive power from
one pair of exchange rates to the other. In substance, the two types of correlations
forecasts seem to nicely complement each other. The best forecasts obtain when
7
See e.g. Fleming et al (1995)
8
For the technicalities regarding the GMM implementation refer to Christoffersen Mazzotta (2004).
17
ECB
Working Paper Series No. 447
February 2005
return based measures are used jointly with market based measures, as the highest
adjusted R
2
is almost invariably obtained from the encompassing (multivariate)
regressions.
For the entire sample implied correlation and GARCH correlation generally show
good predictive power and typically outperform historical correlations. Implied and
GARCH correlations between the most important currency pairs from the euro area
perspective, i.e. the correlations between the USD/EUR; GBP/EUR and the
USD/EUR; JPY/EUR exchange rates, provide reliable forecasts of future correlation.
They can thus be useful in assessing near-term future inflationary risks that originate
from exchange rate movements. Perhaps surprisingly, in the post-1999 sample the
best forecasts are RiskMetrics and implied correlation, both winning the race in 3 out
of 7 cases. It is possible that RiskMetrics displays a better ability to model the
extremely high persistence of typical forex correlations. However, we conjecture that
the fact that RiskMetrics outperform GARCH may be due to the choice of the
adjusted R
2
as the metric to determine the best forecast.
9
We leave an in-depth
analysis of this and related issues for future research.
3.1. Efficiency and Bias
To study the merit of each correlation forecasts with regard to the relative efficiency
and bias we perform a Mincer-Zarnowitz (1969) decomposition of the MSE into bias
squared, ineciency and random variation.
10
The decomposition is as follows: MSE
= [E[y] E[ŷ]]
2
+ (1 β)
2
Var(ŷ) + (1 R
2
) Var(y), where y is the variable of
interest, in our case the realised correlation, and ŷ is each correlation forecast in turn.
From the regression of y on ŷ and a constant, we obtain the slope coecient β and the
regression fit, R
2
. The Mincer-Zarnowitz regressions are run for each of the currency
pairs and for each of the currency forecasts. Table 3 in Appendix 4 reports the MSEs
in absolute value and their decomposition into bias squared, inefficiency, and residual
variation, in percentage of the total MSE. It appears that bias is generally higher for
the implied correlation than is for all the other correlation forecasts, with the only
exception of the RiskMetrics correlation for the USD/EUR-JPY/EUR pair for the
entire sample. In the same sample, historical correlation is shown to be the least
9
For the importance of the loss function see e.g. Christoffersen and Jacobs (2004)
10
We thank an anonymous referee for pointing us in this direction.
18
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February 2005
efficient of the correlation forecasts. In the post 1999 sample however, implied
correlation bias becomes less of an issue, almost disappearing for the USD/EUR-
GBP/EUR and GBP/EUR-JPY/EUR pairs. A notable exception to this pattern is the
USD/JPY-GBP/JPY implied correlation bias which almost doubles to 47.29 per cent.
In the post 1999 sample the historical correlation is shown to be rather inefficient but
substantially unbiased. RiskMetrics correlation appears to be somewhat inefficient
for some currency pair and biased for others. GARCH often perform better than the
other forecasts under one measure but not the other.
In summary, although in general implied correlation from options is more efficient
but biased and return based measures are less biased but also less efficient, the
ranking does not hold for all the currency pairs in both sample periods. In other
words, the decomposition reinforces the idea that different measures of correlation
may have different informational content and therefore they may contribute to provide
the best forecasts when used jointly.
4. Two applications of correlation forecasts
Measures of correlation were above shown to provide effective forecasts of future
realised correlation. A question that arises from the practical perspective is then
whether such measures can contribute to enhance our understanding on exchange rate
developments beyond the simple co-movement among various bilateral exchange
rates. In this section we propose and illustrate two applications where correlation
forecasts can be useful when monitoring and assessing exchange rate developments.
4.1. Scenario analysis for the euro nominal effective exchange rate index
The nominal effective exchange rate (NEER) index of a currency is commonly
calculated as a weighed average whereby the various bilateral exchange rates of the
most important trading partner currencies are aggregated using the respective trade
shares as weights. The resulting index would then better reflect the possible future
inflationary risks originating from exchange rate movements in so far as diverging
movements of bilateral exchange rates would partially cancel each other out. Many
central banks therefore use the NEER among indicators of medium-term risks to price
19
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Working Paper Series No. 447
February 2005
stability. In addition, the price-deflated real effective exchange rates (REERs) provide
an insight to the economy’s overall price competitiveness in the medium to long term.
In the context of forward-looking monetary policy, various scenarios for the likely
future developments of the NEER index could prove useful in assessing the risks to a
given baseline model. Due to the known near-impossibility of forecasting bilateral
exchange rates it should be clear that assessing the future level of an index that
consists of a large number of bilateral rates should, if anything, multiply the difficulty
of the task. However, by using measures of correlation it is, in principle, possible to
construct consistent scenarios for future movements in a NEER index conditional on
an assumption of a future change in one bilateral exchange rate only.
As an example, we take the euro nominal effective exchange rate index with the
narrow group of trading partner currencies, calculated by the ECB.
11
Since the
weights in the euro NEER are rather concentrated on the currencies of the three
largest trading partner countries of the euro area (the United States, the UK and
Japan), we analyse how the changes in these currencies, conditional on an assumed
movement in another major world exchange rate, the Japanese yen-US dollar rate, are
reflected in the NEER index. We consider here the sample period starting from
January 1999 only. To this end, we exploit the property of conditional expectation
under bivariate normal distribution that can be written as follows.
))(()()(
1
,
,
,,1,11, ++++
+==
tt
tY
tXi
tYXititttit
YEXEYXE
ϑ
σ
σ
ρϑ
(4.1)
i= USD/EUR, JPY/EUR, GBP/EUR
In (4.1), the left-hand side captures the level expected to be realised at time t+1 of the
bilateral exchange rate of the euro against the dollar, the pound or the yen (X
i
), given
an assumption
ϑ
made at time t about the level of the JPY/USD exchange rate (Y) to
be realised at t+1. The right-hand side of (4.1) shows how this conditional expectation
on X
i
differs from the unconditional expectation of that exchange rate that is provided
at time t by the t+1 horizon forward exchange rate E
t
(X
i,t+1
). In particular, under the
11
A detailed overview of the methodology used to calculate the euro effective exchange rate indices is
provided by Buldorini, Makrydakis and Thimann (2002).
20
ECB
Working Paper Series No. 447
February 2005
horizon of 1 month, the spread between the assumed future level
ϑ
of the JPY/USD
exchange rate and the 1-month forward JPY/USD rate E
t
(Y
t+1
) is multiplied by the
forecast correlation between the JPY/USD and the relevant bilateral euro exchange
rate, scaled by the ratio of forecast volatilities. After having calculated the conditional
expectations for the three main euro bilateral exchange rates, the conditional
expectation of the NEER index can be calculated by multiplying the former with the
relevant trade weights, and aggregating across currencies.
12
In Appendix 2, we run regressions à la Fama and find that the conditional
expectations on the bilateral USD/EUR, JPY/EUR or GBP/EUR exchange rates as
calculated using equation 4.1 produce estimates that outperform the forecasts
provided by the forward exchange rates. We can now construct a framework for
scenario analysis on the euro NEER index. To this end, the particular question we
want to ask is the following. What is the impact on the expectation of the euro NEER
one-month ahead, given that today the Japanese yen is expected to appreciate by 10%
against the US dollar over one month’s horizon? Clearly, since the measures of
correlation are time-varying the impact on the euro NEER of an expected yen
appreciation against the US dollar vary across different dates. For instance, a scenario
where the euro NEER would be expected to move significantly following an expected
10% move in the JPY/USD rate would presuppose that the euro would be expected to
move in the same direction against all three major currencies. In that case, the
USD/JPY rate would need to be positively correlated against all three major bilateral
euro exchange rates.
13
Table A illustrates the scenarios on the bilateral euro exchange
rates and on the euro NEER for four selected dates using GARCH correlation
forecasts.
12
Note that since the calculation of the expectation of the euro NEER requires as input the correlation
between the GBP/EUR and the JPY/USD exchange rates, which do not enter the same exchange rate
“triangle”, the correlation forecasts using the implied correlation approach cannot be used for this
exercise.
13
The results have to be qualified in so far as the three main currencies “only” represent some 70% of
the weight in euro NEER basket. In the calculations it is assumed that the other bilateral rates do not
change, although some of them could be rather sensitive to movements in the JPY/USD rate.
21
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February 2005
Table A: Scenarios for the euro exchange rates one month ahead (GARCH correlation)
Assumption: 10% JPY appreciation against US dollar in 1 month’s
time
USD/EUR GBP/EUR JPY/EUR Euro NEER
27 Sep 2000 -7.21% -2.95% -22.6% -6.24%
21 Jan 2002 0.47% -1.01% -11.88% -2.01%
22 Jul 2002 6.89% 0.67% -0.85% 1.71%
12 Dec 2003 2.48% 1.58% -1.37% 0.76%
Positive (negative) reading denotes euro appreciation (depreciation).
The forecast co-movements of the various bilateral euro exchange rates conditional on
the assumed 10% appreciation of the yen vis-à-vis the US dollar vary substantially
across episodes. This is also reflected by the fact that the euro NEER depreciates in
some occasions, while it appreciates in others. Therefore, expectations on a stronger
yen against the US dollar could contribute to higher or lower expected import prices
and inflationary pressures in the euro area, depending on the particular correlation
configuration in the FX market at the time when the scenario is conducted.
Looking at the conditional expectations of the bilateral rates, a general observation is
that the conditional expectations on the movements in the euro bilateral exchange
rates have changed over time. In particular, there is a tendency from expected euro
weakness against the US dollar and the pound towards expected euro strength as a
response to the assumed 10% appreciation of the yen against the US dollar. Moreover,
there is a tendency from a sharp towards more moderate projected future euro
depreciation against the yen. What could be the factors contributing to the
constellation during the early years of the single currency whereby an appreciation of
the yen against the dollar would have contributed to a stronger dollar against the euro,
rather than to a general weakness of the US currency? Soon after its launch in January
1999, the euro entered a protracted period of broad-based depreciation that by fall of
2000 was considered to have brought the single currency out of line of the underlying
fundamentals. The euro exchange rates subsequently stabilised but remained weak
throughout 2001. From 2002 Q2 onwards the US dollar started depreciating against
all major currencies amid growing concerns regarding the large US current account
deficit. This seems to have changed also the correlations that measure the interplay
22
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Working Paper Series No. 447
February 2005
among the various bilateral exchange rates and, consequently, the conditional
expectations regarding future movements in the euro NEER as a response to a
hypothetical yen appreciation vis-à-vis the US currency. Finally, throughout 2003 the
Japanese authorities markedly increased the intervention activity to retard the pace of
yen appreciation against the US dollar. In that context, a sudden switch in policy to
“tolerate” a 10% appreciation of the yen could have been seen as reducing the
pressure on the euro to appreciate against the US currency. This would explain the
conditional expectation indicating a more moderate appreciation of the euro relative
to the US dollar than was the case in mid-2002.
In the 1990s and in the early 2000s, the attempts by Japanese authorities to counter
the pressures of yen appreciation against the US dollar were often seen as a potential
factor affecting G3 exchange rate dynamics.
14
How is foreign exchange market intervention supposed to affect exchange rates and
their cross-rates? According to the standard monetary or portfolio balance approach to
interventions, an increased supply of a currency (or bonds denominated in that
currency) in the context of an open market operation should imply a depreciation of
that currency against all other currencies in the market until the equilibrium is
restored. For example, an intervention operation by the Japanese authorities where the
yen is sold against the US dollar should imply a depreciation of the yen not only
against the US dollar but also against the euro, the pound and so on. Conversely, the
purchase of US dollars should exert a general upward pressure on the US currency in
the market. Therefore, a yen-selling intervention against the US dollar should, ceteris
paribus, contribute to a weaker yen and a stronger US dollar also against the euro.
However, as argued by Sarno and Taylor (20001), the daily trading volumes in the
foreign exchange markets are so large that even relatively sizeable interventions are
unlikely to affect the levels of major currencies through the monetary or the portfolio
channels. On the other hand, if the interventions are repeated and follow a systematic
14
See Castrén (2004) and Ito (2002) for analyses of the Japanese interventions using official Japanese
intervention data.
23
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Working Paper Series No. 447
February 2005
4.2. Exchange rate intervention and correlation among cross-rates
strategy, possibly combined with oral communication, they are likely to affect the
market’s expectations regarding the “desired” level of the USD/JPY rate. In such a
constellation, the adjustment pressures in the FX market are likely to be channelled
increasingly through currency pairs that are not actively managed.
15
Following the
previous example, with the USD/JPY rate “managed” by systematic intervention any
pressure on the US dollar to depreciate – for instance due to the large US current
account deficit – would imply that the euro would be expected to appreciate over time
both against the dollar and, due to the interventions on the JPY/USD rate, against the
yen. If this hypothesis were correct, the implications of interventions should
demonstrate themselves in increased correlation between the euro cross rates.
We will augment our earlier correlation forecast regressions by incorporating a
variable that measures the daily purchases of Japanese yen carried out by the Bank of
Japan in the FX market between April 1992 and March 2004. Our goal is to analyse
whether data on the interventions on the JPY/USD exchange rate can improve the
forecasts of correlation between the USD/EUR and JPY/EUR exchange rates. In other
words, we want to find out whether interventions can work as an additional
explanatory factor for realised correlation between the two cross rates of the particular
exchange rate that is the focus of the market operation. The particular equation we
estimate is
,
,,
RC j j
th th t th
ab cINT
ρ
ρ
=+ + +
ε
(4.2)
for j = HC, RMC, GC, IC
The regressions serve to assess whether the coefficients of the intervention variable
are positive and significant and whether the adjusted R
2
improves relative to standard
correlation forecast equations.
The results are summarized in Table B. The regressions show that the variable
measuring the BoJ yen-purchasing interventions receives the negative and statistically
15
BIS (2004) reports evidence from Reuters and EBS trading systems suggests that in 2002-2004, there
was a marked reduction in absolute trading volumes in the JPY/USD exchange rate while the absolute
volumes on the USD/EUR and the USD/GBP exchange rates sharply increased. The period
incorporates some of the most pronounced episodes of interventions by the BoJ that could have
reduced the traders’ appetite to take large yen positions.
24
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Working Paper Series No. 447
February 2005
significant coefficient in all regressions. The interpretation of the negative coefficient
is that yen-selling interventions (almost all observations in the data set were yen sales)
have a positive impact on the forecasts of future realised correlation. In all cases, the
adjusted R
2
s improve; the increase is particularly marked in the case of implied
correlation forecast (15% in the full sample). Hence, an intervention strategy that aims
at systematically stabilising a particular exchange rate over time could increase the
expected future co-movement among its cross exchange rates as reflected in particular
by the currency options prices.
Table B: Japanese interventions on JPY/USD and forecasts of correlation
between USD/EUR and JPY/EUR (standard errors in parenthesis)
Full sample Post euro sample
Correlation
(b)
Intervention
(c)
R
2
Correlation
(b)
Intervention
(c)
R
2
Implied 0.747*
(0.105)
0.745*
(0.067)
-0.28*
(0.053)
0.205
0.220
0.924*
(0.113)
0.920*
(0.069)
-0.013*
(0.044)
0.359
0.365
Historical
0.564*
(0.053)
0.561*
(0.037)
-0.197*
(0.045)
0.314
0.326
0.583*
(0.076)
0.581*
(0.050)
-0.013*
(0.044)
0.343
0.349
RiskMetri
cs
0.874*
(0.112)
0.871*
(0.079)
-0.022*
(0.046)
0.235
0.242
1.168*
(0.143)
1.163*
(0.093)
-0.011*
(0.044)
0.382
0.387
GARCH
0.858*
(0.066)
0.854*
(0.049)
-0.020*
(0.045)
0.329
0.341
0.834*
(0.094)
0.832*
(0.094)
-0.014*
(0.045)
0.362
0.370
*Denotes a significant estimate at 5% level
25
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Working Paper Series No. 447
February 2005
5. Concluding remarks
The various estimations of correlation between the major bilateral exchange rates
show distinctive fluctuations over time. The correlations generally increased soon
after the introduction of the euro, but have more recently returned closer to their
longer-term average levels. This development reflects the episode of broad-based euro
depreciation 1999-2000, followed in 2002-early 2003 by euro appreciation that was
somewhat more prominent against the US dollar than against the pound sterling and
the Japanese yen.
Regarding the ability to forecast future correlation, implied correlation can predict up
to 36% of future realized correlation. Nevertheless, it is not univocally the best
predictor of future correlation as GARCH and RiskMetrics correlations yield
occasionally very good predictive power, too. When used together, implied
correlation, GARCH correlation and RiskMetrics correlation are particularly useful in
predicting future correlation between the major euro currency pairs at the one-month
horizon. The predictive power seems to have strengthened after the introduction of the
euro.
When applying the estimated correlation measures, we found that using correlation
forecasts to analyse scenarios for effective exchange rates is useful as an expected
movement in one currency pair seems to indicate a very different impact on the
effective exchange rate in various points in time. The time-varying correlation
forecasts take into account the market’s current perception of the relative adjustment
of various exchange rates as a response to a sudden movement in one major exchange
rate. Mapping these bilateral movements into the NEER index provides conditional
forecasts that could be a useful input in analysing scenarios for future inflationary
risks. Furthermore, we show that data on interventions on the JPY/USD exchange rate
improve the ability of implied correlation in particular to forecast future realised
correlation. This effect, that is not consistent with the monetary or portfolio channels
of interventions, suggests that systematic intervention might be capable of affecting
the options market’s perception about future co-movement among the cross-rates of
the currency pair that is on the focus of the market operation.
26
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Working Paper Series No. 447
February 2005
References
Andersen, T.G. and T. Bollerslev, 1998, Answering the Skeptics: Yes, Standard
Volatility Models do Provide Accurate Forecasts. International Economic Review 39
Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys, 2001a, The Distribution of
Realised Stock Return Volatility, Journal of Financial Economics, 61
Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys, 2001b, The Distribution of
Realised Exchange Rate Volatility, Journal of the American Statistical Association,
96
Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys, 2003, Modelling and
Forecasting Realised Volatility, Econometrica 71
Bandi, F., and B. Perron, 2003, Long Memory and the Relation Between Implied and
Realized Volatility, Manuscript, University of Chicago
Bank of International Settlements, 2004, Annual Report, Basel, Switzerland
Bates, D., 2003, Empirical Option Pricing: A Retrospection, Journal of Econometrics
116:1/2, September/October, 387-404.
Beckers, S., 1981, Standard Deviations Implied in Options Prices as Predictors of
Future Stock Price Volatility, Journal of Banking and Finance 5, 363-81.
Blair, B., S.-H. Poon, and S. Taylor, 2001, Forecasting S&P 100 volatility: The
Incremental Information Content of Implied Volatilities and High-Frequency Index
Returns, Journal of Econometrics 105, 5–26.
Bollerslev, T., and H. Zhou, 2003, Volatility Puzzles: A Unified Framework for
Gauging Return-volatility Regressions, Working paper, Duke University, Department
of Economics.
Brandt, M., and F. Diebold, 2003, A No-Arbitrage Approach to Range-Based
Estimation of Return Covariances and Correlations, Journal of Business, forthcoming.
Buldorini, L, S. Makrydakis and C. Thimann, 2002, The Effective Exchange Rates of
the Euro, European Central Bank Occasional Paper No 2.
Butler and Cooper, 1997, Implied Exchange Rate Correlations and Market
Perceptions of European Monetary Union, Bank of England Quarterly Bulletin,
November 1997
Campa J. M. and K. Chang, 1998, The Forecasting Ability of Correlations Implied in
Foreign Exchange Options, Journal of International Money and Finance, Vol. 17, No.
5.
Canina, L., and S. Figlewski, 1993, The Informational Content of Implied Volatility,
Review of Financial Studies 6, 659-81.
27
ECB
Working Paper Series No. 447
February 2005
Cappiello, L., R. Engle and K. Sheppard, 2003, Asymmetric Dynamics in the
Correlation of Global Bond and Equity Returns, ECB Working Paper No204.
Castrén, O., 2004, Do Options-Implied RND Functions on G3 Currencies Move
around the Times of Interventions on the JPY/USD Exchange Rate? ECB Working
Paper No. 410
Chernov, M., 2003, Implied Volatilities as Forecasts of Future Volatility, Time-
Varying Risk Premia, and Returns Variability, Manuscript, Columbia University
Christensen, B. J., and N.R. Prabhala, 1998, The Relation Between Implied and
Realized Volatility, Journal of Financial Economics 50, 125-50
Christensen, B.J., C.S. Hansen, and N.R. Prabhala, 2001, The Telescoping Overlap
Problem in Options Data, Manuscript, School of Economics and Management,
University of Aarhus, Denmark.
Christoffersen, P. and Mazzotta S., 2004, The Informational Content of Over-the-
Counter Currency Options, ECB Working Paper No 366.
Christoffersen, P. and K. Jacobs, 2004, The Importance of the Loss Function in
Option Valuation, Journal of Financial Economics, 72, 291-318.
Covrig, V. and B. S. Low, 2003, The Quality of Volatility Traded on the Over-the-
Counter Currency Market: A Multiple Horizons Study, Journal of Futures Markets
23, 261-285.
Diebold, F.X., J. Hahn, and A. S. Tay, 1999, Multivariate Density Forecast Evaluation
and Calibration in Financial Risk Management: High Frequency Returns on Foreign
Exchange, Review of Economics and Statistics 81, 661-673
Engle, R. and K. Kroner, 1995, Multivariate Simultaneous GARCH, Econometric
Theory Vol 11.
Fleming, J., 1998, The Quality of Market Volatility Forecasts Implied by S&P 100
Index Option Prices, Journal of Empirical Finance 5, 317-45.
Fleming, J., B. Ostdiek, and R.E. Whaley. 1995. Predicting stock market volatility: A
new measure, Journal of Futures Markets, Vol 15, 265-302
Ito, T., 2002, Is Foreign Exchange Intervention Effective? The Japanese Experience
in the 1990s, NBER Working Paper No8914
Jorion, P., 1995, Predicting Volatility in the Foreign Exchange Market, Journal of
Finance 50, 507-528
Kroner, K. and V. Ng, 1998, Modelling Asymmetric co-movement of Asset Returns,
Review of Financial Studies, Vol 11
28
ECB
Working Paper Series No. 447
February 2005
Lamoureux, C., and W. Lastrapes, 1993, Forecasting Stock-Return Variance: Toward
an Understanding of Stochastic Implied Volatilities, Review of Financial Studies 6,
293-326
Lopez, J.A. and C. Walter, 2000, Is Implied Correlation Worth Calculating? Evidence
from Foreign Exchange Options and Historical Data, Journal of Derivatives 7
Malz, A., 1997, Option-Implied Probability Distributions and Currency Excess
Returns, Federal Reserve Bank of New York Staff Reports
Mincer, J., Zarnowitz, V. 1969. The evaluation of economic forecasts. In J. Mincer,
Zarnowitz, V., eds.: Economic Forecasts and Expectations Columbia University
Press, New York.
Neely, C., 2003, Forecasting Foreign Exchange Volatility: Is Implied Volatility the
Best We Can Do? Manuscript, Federal Reserve Bank of St. Louis
Newey, Whitney and Kenneth West, 1987, "A Simple Positive Semi-Definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,"
Econometrica, 55, 703-708
Pong, S.-Y., M. Shackleton, S. J. Taylor, and X. Xu, 2004, Forecasting Currency
Volatility: A Comparison of Implied Volatilities and AR(FI)MA Models, Journal of
Banking and Finance, forthcoming.
Sarno, L. and M. Taylor, 2001, Official Intervention in the Foreign Exchange Market:
Is it Effective, and if so, How Does it Work? Journal of Economic Literature, 39.
Siegel, A., 1997, International Currency Relationship Information Revealed by Cross-
Option Prices, Journal of Futures Markets 17.
29
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Appendix 1
In contrast with the RiskMetrics model, the GARCH model implies a non-constant
term structure of variance and covariance. To compute the GRACH forecast it is
necessary to take into account the mean reverting nature of the process.
In particular, the persistence of currency 1 is A(1,1)
2
+ B(1,1)
2
; similarly, the
persistence of currency 2 = A(2,2)
2
+ B(2,2)
2
; the persistence of the covariance is =
A(1,1)*A(2,2) + B(1,1)*B(2,2).
The unconditional second moment for forex rates can be computes as:
Ucvar(1) = (1,1)
2
/(1 – persistence(1))
Ucvar(2) = ( (2,2)
2
+ (2,1)
2
)/(1 –persistence(2))
Ucovar(1,2) = (1,1)* (2,1)/(1 – persistence(1,2))
The term structures are:
21
(i-1)
i=1
21
(i-1)
i=1
21
(i-1)
i=1
Term(1) = Persistence(j)
Term (2) = Persistence(k)
Term (1,2) = Persistence(j,k)
The variance 21 days ahead forecasts are:
GARCHterm(1) = (21*Ucvar(1) – Ucvar(1)*Term(1) + H(1,1)*Term(1));
GARCHterm(2) = (21*Ucvar(2) – Ucvar(2)*Term(2) + H(2,2)*Term(2));
GARCHterm(1,1) = (21*Ucvar(1,2) – Ucvar(1,2)*Term(1,2) + H(1,2)*Term(1,2).
Finally, the 21 days ahead GARCH correlation forecast is
121,21
GARCHterm(1,2)
(, ) =
GARCHterm(1) GARCHterm(2)
GARCH
t
RR
ρ
+
.
30
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Working Paper Series No. 447
February 2005
Appendix 2
In this appendix, we assess the relative forecasting performance of the conditional
expectations, as calculated using equation 4.1, against the forward exchange rates. To
this end, we run regressions à la Fama for all three currency pairs, where the realised
change in the exchange rate over 1-month horizon is regressed on a constant and a
forecast error. The forecast future rate is either the forward exchange rate E
t
(X
i,t+1
) or
the conditional expectation
)(
11,
ϑ
=
++ ttit
YXE
, where
ϑ
is chosen to be the realised
value of the JPY/EUR exchange rate 1 month ahead in time:
16
eXYXEXX
eXXEXX
tittittiti
titittiti
+=+=
+
+=
+++
++
))((
))((
,11,,1,
,1,,1,
ϑβα
β
α
(A2.1)
The null hypothesis is that
α
is equal to a possibly non-zero constant (including
Jensen’s inequality term) and
β
equals positive unity. The sample period covers the
period of euro exchange rates only, i.e. it stretches from 4 January 1999 to 31 March
2004.
Table C summarises the results of the Fama regressions for the forward exchange
rates and for the conditional expectations where three different correlation forecasts
are applied (historical, RiskMetrics and GARCH correlation).
Table C: Results from the regressions of equation
Conditional expectation based on correlation
Forward rate
Historical RiskMetrics GARCH
USD/EUR -0.553*
(0.058)
0.085*
(0.037)
0.121*
(0.013)
0.125*
(0.041)
GBP/EUR 0.204*
(0.095)
0.264*
(0.054)
0.193*
(0.023)
0.397*
(0.070)
JPY/EUR 0.593*
(0.003)
0.616*
(0.029)
0.035*
(0.008)
0.779*
(0.037)
*Denotes a significant estimate at 5% level
16
We make this choice purely arbitrarily; alternatively, we also used today’s spot exchange rates as a
proxy for υ and found that the results were little changed.
31
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The results show that, in line with several earlier studies, for the USD/EUR the
β
coefficient is significant and negative in the forward rate regression, amounting to the
familiar forward bias puzzle. However, the coefficients from the regressions including
conditional expectations are all correctly signed (positive) indicating that the
estimators do not suffer from the bias. Regarding the GBP/EUR and the JPY/EUR
exchange rates, the coefficients are also all correctly signed (positive) and significant.
Moreover, apart from the RiskMetrics correlation, the coefficients from the
regressions using conditional expectations are higher than from the regressions that
use forward exchange rates. The constant terms were small and significant for most of
the regressions involving the USD/EUR and JPY/EUR rates, and significant in some
cases for the GBP/EUR rate. The R
2
s were generally higher for the regressions that
use conditional expectations.
All in all, it cannot be excluded that expectations conditional on future developments
in the JPY/USD exchange rate, that use the information on correlation forecasts, can
improve upon the forecasting power of forward exchange rates in the case of the
bilateral euro exchange rates.
32
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Appendix 3 Charts
1: Correlations pre-January 1999
17
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_gbpeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
gbpeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdgbp_jpyg bp
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdjpy_gbpjpy
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_plzeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_czkeur
Chart 1. Historical Correlation. Pre 1999.
17
For all the pre-1999 period or the full sample period the DEM proxies for the EUR.
33
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-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_gbpeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
gbpeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdgbp_jpyg bp
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdjpy_gbpjpy
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_plzeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_czkeur
Chart 2. Implied Correlation. Pre 1999.
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-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_gbpeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
gbpeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdgbp_jpyg bp
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdjpy_gbpjpy
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_plzeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_czkeur
Chart 3. RiskMetrics Correlation. Pre 1999.
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-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_gbpeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
gbpeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdgbp_jpyg bp
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdjpy_gbpjpy
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_plzeur
-0.8
-0.4
0.0
0.4
0.8
1992 1993 1994 1995 1996 1997 1998
usdeur_czkeur
Chart 4. GARCH correlation. Pre 1999.
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2: Correlations post-January 1999
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_gbpeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
gbpeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdgbp_jpyg bp
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdjpy_gbpjpy
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_plzeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_czkeur
Chart 5. Historical Correlation. Post 1999.
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-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_gbpeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
gbpeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdgbp_jpyg bp
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdjpy_gbpjpy
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_plzeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_czkeur
Chart 6: Implied Correlation. Post 1999.
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-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_gbpeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
gbpeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdgbp_jpyg bp
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdjpy_gbpjpy
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_plzeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_czkeur
Chart 7. RiskMetrics Correlation. Post 1999.
39
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-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_gbpeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
gbpeur_jpyeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdgbp_jpyg bp
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdjpy_gbpjpy
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_plzeur
-0.8
-0.4
0.0
0.4
0.8
1999 2000 2001 2002 2003
usdeur_czkeur
Chart 8. GARCH Correlation. Post 1999.
40
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Appendix 4 Tables (coefficient estimates above; standard errors below)
Table 1. Correlation Predicatability Regressions. All sample: January 1992 - March 2003
USD/EUR-JPY/EUR USD/EUR-GBP/EUR
Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2
0.045 0.747 0.205 0.009 0.79 0.207
0.052 0.105 0.073 0.124
0.178 0.564 0.314 0.209 0.548 0.295
0.027 0.053 0.034 0.058
0.174 0.874 0.229 0.257 0.563 0.125
0.03 0.112 0.048 0.12
0.095 0.858 0.329 0.093 0.875 0.324
0.029 0.066 0.04 0.079
0.053 0.356 0.446 0.346 0.045 0.384 0.426 0.33
0.04 0.095 0.059 0.065 0.12 0.059
0.028 0.452 0.602 0.282 0.009 0.653 0.216 0.219
0.044 0.103 0.115 0.07 0.126 0.113
0.022 0.263 0.706 0.343 -0.022 0.323 0.708 0.347
0.038 0.096 0.085 0.062 0.12 0.086
0.048 0.29 0.367 -0.55 0.59 0.366 -0.008 0.425 0.182 -0.493 0.765 0.383
0.037 0.094 0.105 0.167 0.165 0.062 0.123 0.11 0.137 0.164
GBP/EUR-JPY/EUR USD/GBP-JPY/GBP
Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2
0.021 0.661 0.136 -0.02 0.751 0.203
0.039 0.117 0.049 0.101
0.14 0.351 0.123 0.211 0.315 0.099
0.021 0.063 0.031 0.068
0.133 0.43 0.101 0.166 0.46 0.156
0.022 0.091 0.033 0.075
0.109 0.584 0.171 0.078 0.745 0.174
0.021 0.077 0.042 0.107
0.027 0.47 0.232 0.179 -0.011 0.662 0.097 0.209
0.035 0.112 0.063 0.048 0.113 0.067
0.017 0.506 0.259 0.166 0.001 0.56 0.204 0.221
0.036 0.115 0.089 0.046 0.12 0.084
0.024 0.385 0.43 0.206 -0.033 0.517 0.372 0.227
0.033 0.108 0.084 0.047 0.125 0.132
0.034 0.376 -0.044 -0.476 0.945 0.227 -0.059 0.491 -0.19 0.012 0.669 0.234
0.032 0.103 0.096 0.127 0.173 0.05 0.126 0.102 0.141 0.279
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USD/JPY-GBP/JPY USD/EUR-PLZ/EUR
Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2
0.075 0.698 0.337 -0.101 1.316 0.285
0.068 0.093 0.139 0.261
0.316 0.406 0.161 0.237 0.496 0.234
0.048 0.075 0.085 0.12
0.221 0.565 0.222 0.143 0.69 0.296
0.057 0.091 0.091 0.143
-0.008 0.982 0.228 -0.409 1.786 0.187
0.095 0.16 0.278 0.519
0.075 0.674 0.031 0.338 -0.047 0.955 0.215 0.306
0.067 0.111 0.075 0.113 0.252 0.149
0.07 0.629 0.092 0.34 -0.016 0.675 0.405 0.318
0.068 0.117 0.097 0.109 0.328 0.236
0.016 0.604 0.219 0.342 -0.324 1.065 0.672 0.3
0.083 0.108 0.158 0.299 0.283 0.67
-0.057 0.603 -0.145 -0.013 0.507 0.346 -0.125 0.647 -0.032 0.388 0.293 0.319
0.107 0.114 0.135 0.154 0.275 0.245 0.342 0.125 0.232 0.595
USD/EUR-CZK/EUR
Intercept Implied Historical RiskMetrics GARCH Adj-rbar2
-0.132 0.906 0.186
0.082 0.217
0.175 0.109 0.012
0.047 0.116
0.177 0.114 0.007
0.051 0.154
0.16 0.238 0.002
0.081 0.423
-0.134 0.888 0.039 0.186
0.084 0.202 0.086
-0.134 0.897 0.025 0.185
0.087 0.204 0.121
-0.144 0.897 0.089 0.184
0.108 0.209 0.305
-0.131 0.889 0.074 -0.054 -0.008 0.183
0.104 0.205 0.113 0.233 0.568
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Table 2. Correlation Predicatability Regressions. Sample: March 1999 - March 2004
USD/EUR-JPY/EUR USD/EUR-GBP/EUR
Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2
0.1 0.924 0.359 -0.085 1.139 0.217
0.075 0.113 0.188 0.274
0.254 0.583 0.343 0.34 0.473 0.206
0.052 0.076 0.071 0.096
0.189 1.168 0.382 0.253 0.979 0.218
0.056 0.143 0.088 0.198
0.19 0.834 0.362 0.272 0.692 0.206
0.056 0.094 0.1 0.164
0.097 0.577 0.32 0.411 -0.012 0.728 0.294 0.27
0.062 0.139 0.107 0.145 0.205 0.082
0.091 0.473 0.717 0.417 -0.023 0.661 0.608 0.265
0.062 0.17 0.254 0.14 0.191 0.196
0.088 0.512 0.477 0.406 -0.035 0.713 0.412 0.261
0.062 0.14 0.151 0.151 0.211 0.149
0.093 0.485 0.106 0.55 -0.025 0.418 -0.013 0.67 0.185 0.169 0.075 0.27
0.062 0.154 0.123 0.557 0.307 0.144 0.186 0.173 0.386 0.317
GBP/EUR-JPY/EUR USD/GBP-JPY/GBP
Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2
0.222 0.467 0.067 0.077 0.682 0.198
0.069 0.141 0.054 0.119
0.251 0.387 0.146 0.274 0.252 0.063
0.038 0.081 0.043 0.094
0.217 0.581 0.152 0.224 0.382 0.1
0.044 0.127 0.047 0.108
0.218 0.586 0.193 0.153 0.612 0.09
0.041 0.095 0.068 0.18
0.179 0.229 0.334 0.158 0.077 0.67 0.014 0.197
0.057 0.13 0.087 0.054 0.129 0.094
0.167 0.178 0.513 0.16 0.076 0.646 0.041 0.198
0.057 0.138 0.147 0.054 0.139 0.12
0.177 0.131 0.543 0.199 0.08 0.696 -0.026 0.197
0.053 0.117 0.107 0.065 0.144 0.207
0.191 0.147 -0.049 -0.309 0.855 0.204 0.149 0.697 0.026 0.335 -0.61 0.204
0.05 0.12 0.14 0.471 0.423 0.064 0.139 0.109 0.157 0.314
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USD/JPY-GBP/JPY USD/EUR-PLZ/EUR
Intercept Implied Historical RiskMetrics GARCH Adj-rbar2 Intercept Implied Historical RiskMetrics GARCH Adj-rbar2
-0.075 0.856 0.242 -0.128 1.368 0.314
0.106 0.144 0.131 0.248
0.412 0.213 0.043 0.225 0.514 0.267
0.061 0.097 0.075 0.105
0.305 0.404 0.103 0.14 0.694 0.329
0.071 0.115 0.078 0.123
0.105 0.771 0.112 -0.456 1.872 0.219
0.118 0.203 0.244 0.458
-0.087 0.943 -0.092 0.247 -0.06 0.965 0.228 0.338
0.108 0.179 0.107 0.107 0.254 0.134
-0.077 0.876 -0.022 0.242 -0.024 0.677 0.416 0.351
0.107 0.201 0.152 0.104 0.316 0.203
-0.068 0.878 -0.042 0.242 -0.358 1.083 0.719 0.332
0.118 0.213 0.289 0.262 0.28 0.611
-0.167 0.79 -0.337 0.192 0.39 0.258 -0.135 0.649 -0.03 0.392 0.302 0.351
0.138 0.216 0.147 0.187 0.425 0.229 0.328 0.125 0.21 0.571
USD/EUR-CZK/EUR
Intercept Implied Historical RiskMetrics GARCH Adj-rbar2
-0.156 0.956 0.206
0.077 0.21
0.166 0.114 0.012
0.046 0.115
0.166 0.126 0.008
0.05 0.151
0.152 0.233 0.002
0.08 0.423
-0.158 0.94 0.037 0.205
0.079 0.196 0.085
-0.158 0.947 0.027 0.205
0.081 0.197 0.118
-0.165 0.948 0.074 0.204
0.103 0.203 0.304
-0.145 0.937 0.068 -0.02 -0.095 0.203
0.1 0.2 0.114 0.227 0.558
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Table 3. Mincer Zarnowitz Decomposition of MSE in Percentage
MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual
Implied 0.077 16.379 1.513 82.108 0.030 0.061 0.411 99.528
Historical 0.073 0.008 22.189 77.803 0.042 0.040 24.315 75.645
RiskMetrics 0.085 10.684 7.093 82.223 0.091 65.952 0.005 34.043
GARCH 0.056 2.789 0.936 96.275 0.044 24.434 3.717 71.848
MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual
Implied 0.078 7.778 2.656 89.566 0.044 8.144 0.347 91.509
Historical 0.077 0.005 21.491 78.504 0.052 0.089 21.072 78.839
RiskMetrics 0.088 22.581 0.476 76.943 0.101 61.291 0.489 38.220
GARCH 0.062 3.089 1.294 95.618 0.052 22.414 1.704 75.882
MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual
Implied 0.071 2.171 2.200 95.629 0.070 1.565 3.166 95.269
Historical 0.095 0.136 23.985 75.878 0.094 0.041 24.650 75.310
RiskMetrics 0.072 0.133 7.875 91.991 0.071 0.049 8.714 91.237
GARCH 0.080 0.358 4.284 95.358 0.081 0.738 5.730 93.532
MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual
Implied 0.082 33.949 0.165 65.885 0.083 35.371 0.035 64.593
Historical 0.124 0.132 46.572 53.295 0.123 0.324 45.211 54.465
RiskMetrics 0.099 0.029 33.026 66.945 0.099 0.001 31.743 68.256
GARCH 0.070 1.932 3.623 94.445 0.071 1.124 3.553 95.323
MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual
Implied 0.088 7.151 3.708 89.141 0.065 0.084 8.620 91.296
Historical 0.118 0.001 32.415 67.584 0.077 0.013 29.989 69.998
RiskMetrics 0.099 0.537 16.411 83.052 0.065 9.191 7.749 83.060
GARCH 0.085 1.299 9.349 89.352 0.064 10.222 9.597 80.182
MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual
Implied 0.091 18.372 2.238 79.390 0.051 6.521 4.774 88.705
Historical 0.124 0.007 34.097 65.896 0.085 0.000 37.359 62.641
RiskMetrics 0.096 0.001 20.289 79.711 0.066 0.040 22.535 77.425
GARCH 0.077 0.000 2.405 97.595 0.054 0.612 3.863 95.525
MSE Bias Inefficiency Residual MSE Bias Inefficiency Residual
Implied 0.061 24.794 6.556 68.650 0.065 47.291 0.475 52.235
Historical 0.074 0.009 29.115 70.875 0.070 0.047 38.557 61.396
RiskMetrics 0.057 0.691 14.431 84.877 0.051 0.885 19.967 79.148
GARCH 0.049 0.677 0.010 99.313 0.041 0.901 1.095 98.004
USD/GBP-JPY/GBP USD/GBP-JPY/GBP
USD/JPY-GBP/JPY USD/JPY-GBP/JPY
USD/EUR-CZK/EUR USD/EUR-CZK/EUR
GBP/EUR-JPY/EUR GBP/EUR-JPY/EUR
USD/EUR-PLZ/EUR USD/EUR-PLZ/EUR
USD/EUR-JPY/EUR USD/EUR-JPY/EUR
All sample Post 1999
USD/EUR-GBP/EUR USD/EUR-GBP/EUR
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European Central Bank working paper series
For a complete list of Working Papers published by the ECB, please visit the ECB’s website
(http://www.ecb.int)
402 “Forecasting euro area inflation using dynamic factor measures of underlying inflation”
by G. Camba-Méndez and G. Kapetanios, November 2004.
403 “Financial market integration and loan competition: when is entry deregulation socially beneficial?”
by L. Kaas, November 2004.
404 “An analysis of systemic risk in alternative securities settlement architectures” by G. Iori,
November 2004.
405 “A joint econometric model of macroeconomic and term structure dynamics” by P. Hördahl,
O. Tristani and D. Vestin, November 2004.
406 “Labour market reform and the sustainability of exchange rate pegs” by O. Castrén, T. Takalo and
G. Wood, November 2004.
407 “Banking consolidation and small business lending” by E. Takáts, November 2004.
408 “The great inflation, limited asset markets participation and aggregate demand: FED policy was better
than you think” by F. O. Bilbiie, November 2004.
409 “Currency mismatch, uncertainty and debt maturity structure” by M. Bussière, M. Fratzscher
and W. Koeniger, November 2004.
410 “Do options-implied RND functions on G3 currencies move around the times of interventions
on the JPY/USD exchange rate? by O. Castrén, November 2004.
411 “Fiscal discipline and the cost of public debt service: some estimates for OECD countries”
by S. Ardagna, F. Caselli and T. Lane, November 2004.
412 “The real effects of money growth in dynamic general equilibrium” by L. Graham and
D. J. Snower, November 2004.
413 “An empirical analysis of price setting behaviour in the Netherlands in the period
1998-2003 using micro data” by N. Jonker, C. Folkertsma and H. Blijenberg, November 2004.
414 “Inflation persistence in the European Union, the euro area, and the United States”
by G. Gadzinski and F. Orlandi, November 2004.
415 “How persistent is disaggregate inflation? An analysis across EU15 countries and
HICP sub-indices” by P. Lünnemann and T. Y. Mathä, November 2004.
416 “Price setting behaviour in Spain: stylised facts using consumer price micro data”
by L. J. Álvarez and I. Hernando, November 2004.
417 “Staggered price contracts and inflation persistence: some general results”
by K. Whelan, November 2004.
418 “Identifying the influences of nominal and real rigidities in aggregate price-setting behavior”
by G. Coenen and A. T. Levin, November 2004.
419 “The design of fiscal rules and forms of governance in European Union countries”
by M. Hallerberg, R. Strauch and J. von Hagen, December 2004.
420 “On prosperity and posterity: the need for fiscal discipline in a monetary union” by C. Detken, V. Gaspar
and B. Winkler, December 2004.
47
ECB
Working Paper Series No. 447
February 2005
421 “EU fiscal rules: issues and lessons from political economy” by L. Schuknecht, December 2004.
422 “What determines fiscal balances? An empirical investigation in determinants of changes in OECD
budget balances” by M. Tujula and G. Wolswijk, December 2004.
423 “Price setting in France: new evidence from survey data” by C. Loupias and R. Ricart,
December 2004.
424 “An empirical study of liquidity and information effects of order flow on exchange rates”
by F. Breedon and P. Vitale, December 2004.
425 “Geographic versus industry diversification: constraints matter” by P. Ehling and S. B. Ramos,
January 2005.
426 “Security fungibility and the cost of capital: evidence from global bonds” by D. P. Miller
and J. J. Puthenpurackal, January 2005.
427 “Interlinking securities settlement systems: a strategic commitment?” by K. Kauko, January 2005.
428 “Who benefits from IPO underpricing? Evidence form hybrid bookbuilding offerings”
by V. Pons-Sanz, January 2005.
429 “Cross-border diversification in bank asset portfolios” by C. M. Buch, J. C. Driscoll
and C. Ostergaard, January 2005.
430 “Public policy and the creation of active venture capital markets” by M. Da Rin,
G. Nicodano and A. Sembenelli, January 2005.
431 “Regulation of multinational banks: a theoretical inquiry” by G. Calzolari and G. Loranth, January 2005.
432 “Trading european sovereign bonds: the microstructure of the MTS trading platforms”
by Y. C. Cheung, F. de Jong and B. Rindi, January 2005.
433 “Implementing the stability and growth pact: enforcement and procedural flexibility”
by R. M. W. J. Beetsma and X. Debrun, January 2005.
434 “Interest rates and output in the long-run” by Y. Aksoy and M. A. León-Ledesma, January 2005.
435 “Reforming public expenditure in industrialised countries: are there trade-offs?”
by L. Schuknecht and V. Tanzi, February 2005.
436 “Measuring market and inflation risk premia in France and in Germany”
by L. Cappiello and S. Guéné, February 2005.
437 “What drives international bank flows? Politics, institutions and other determinants”
by E. Papaioannou, February 2005.
438 “Quality of public finances and growth” by A. Afonso, W. Ebert, L. Schuknecht and M. Thöne,
February 2005.
439 “A look at intraday frictions in the euro area overnight deposit market”
by V. Brousseau and A. Manzanares, February 2005.
440 “Estimating and analysing currency options implied risk-neutral density functions for the largest
new EU member states” by O. Castrén, February 2005.
441
442
443
by S. Rosati and S. Secola, February 2005.
“Explaining cross-border large-value payment flows: evidence from TARGET and EURO1 data”
“The Phillips curve and long-term unemployment” by R. Llaudes, February 2005.
“Why do financial systems differ? History matters” by C. Monnet and E. Quintin, February 2005.
48
ECB
Working Paper Series No. 447
February 2005
444
445
February 2005.
446
February 2005.
447
by O. Castrén and S. Mazzotta, February 2005.
and A. al-Nowaihi, February 2005.
“Welfare implications of joining a common currency” by M. Ca’ Zorzi, R. A. De Santis and F. Zampolli,
“Trade effects of the euro: evidence from sectoral data” by R. Baldwin, F. Skudelny and D. Taglioni,
“Foreign exchange option and returns based correlation forecasts: evaluation and two applications”
“Keeping up with the Joneses, reference dependence, and equilibrium indeterminacy” by L. Stracca
... Previous research (see e.g. Campa andChang 1998, Castrén, andMazzotta 2005) conclude that implied correlation adds to the forecasting accuracy of time-series based forecasts. These results are however based on evaluation criteria (mainly Diebold-Mariano statistics and encompassing regressions) which differ markedly from those we have used in this study. ...
... where IV p,t is the annualised implied 22-day-ahead standard deviation of the index, w i is the portfolio weight given to asset i, and s i is the annualised implied 22-day-ahead standard deviation of asset i. (2008) calculate the IC for the S&P500 index and show that it closely matches the fitted equicorrelation from both the cDCC-DECO and LDECO models, although they do not use the IC directly in model estimation or forecasting. Further, the IC has been used previously by Castren and Mazzotta (2005) in a bivariate setting of exchange rates and they find that a combination forecast of IC and an MGARCH model is preferred, these conclusions are based on the in-sample adjusted R 2 only as they do not conduct a forecasting exercise. These results, and the publishing of IC for the S&P 500 Index by the CBOE 11 , motivate an investigation of the incremental information content of the IC relative to the various proposed measures of the equicorrelation, X t . ...
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