Conference PaperPDF Available

Price Probability Predictor. Capital investments assisted by a probability field

Authors:
  • Algorithm Invest

Abstract and Figures

Capital investment is a sustained activity nowadays. After the worldwide release of the electronic trading systems, automated decision-making investment software is the new trend in financial speculation. A significant part of capital trading is fully computerized today. The buying and selling orders are made and sent automatically, almost in real-time. The price evolution is analyzed by servers using advanced mathematical algorithms. This paper will present one of these models named Price Probability Predictor. It is a method to build a probability field based on the price history and the real-time price action. The revealed function will generate the current probability of a price growth in the next time intervals. Automated entry and exit signals and market limit conditions will be built using the new indicator, in order to automate the whole investment process. Capital investment results will also be included in the current paper to qualify the presented trading methodology and to compare it with other similar models. In conclusion, it was found that the Price Probability Predictor is a reliable mathematical algorithm that can assist any trading decisions, in both ways, manual or automatic capital investments.
Content may be subject to copyright.
DOI:
Price Probability Predictor.
Capital investments assisted by a probability field.
Cristian PĂUNA1
Economic Informatics Doctoral School, Academy of Economic Studies, Bucharest, Romania
cristian.pauna@ie.ase.ro
Abstract. Capital investment is a sustained activity nowadays. After the worldwide release of the
electronic trading systems, automated decision-making investment software is the new trend in
financial speculation. A significant part of capital trading is fully computerized today. The buying and
selling orders are made and sent automatically, almost in real-time. The price evolution is analyzed by
servers using advanced mathematical algorithms. This paper will present one of these models named
Price Probability Predictor. It is a method to build a probability field based on the price history and the
real-time price action. The revealed function will generate the current probability of a price growth in
the next time intervals. Automated entry and exit signals and market limit conditions will be built
using the new indicator, in order to automate the whole investment process. Capital investment results
will also be included in the current paper to qualify the presented trading methodology and to
compare it with other similar models. In conclusion, it was found that the Price Probability Predictor is
a reliable mathematical algorithm that can assist any trading decisions, in both ways, manual or
automatic capital investments.
Keywords: capital investment, price action, price probability field, investment decision, trading
signals, limit conditions, automated investment software
Introduction
Capital investment has become a sustained and collective activity nowadays. An impressive
number of market participants are buying and selling every day to make a profit. Private or
public investment funds, financial companies, professional investors, traders, or just
speculating people, all are part of an unstopped dispute with the price action. Using
different strategies, everyone tries to predict the price evolution in order to buy cheap and
sell more expensive. After the global scale of the electronic trading systems
implementation, access to the capital markets is at a couple of clicks distance. This fact has
increased the liquidity in all markets and also has grown the price volatility once the
psychological factors can influence the market price behavior in seconds.
The question this paper will answer to is: how much is the current probability for
price growth in the next period of time? The interest in an accurate answer at this question
is huge. Studying a probability field for price growth in a specific market will permit us to
exit investments when the probability is low, and to initiate new positions when the
probability is high. Moreover, a lower price growth probability can avoid buying near the
maximal price levels and will inform investors to wait until the market presents a
significant decrease. The evolution of a price probability field will also give us additional
information about market behavior. The Ph.D. research behind this paper has found a
probability prediction function, based only on the price time series that will give us the
answer to the formulated question. It is called here as the Price Probability Predictor.
1 This paper was financed by Algorithm Invest company (https://algoinvest.biz).
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 2
In the electronic trading environment, a significant part of the investment orders is
made and sent today by automated decision-making computer software. The online price
quotes transmission permits today a real-time price analysis through advanced
mathematical algorithms to fundament the investment decisions. A simple trading strategy
is not useful today if it can not be set in the algorithmic trading environment. One of the
highest advantages of the Price Probability Predictor is the fact that it can be automated.
Based on the revealed function, automated trading signals and limit conditions can be built
and incorporate in any algorithmic trading software system, for any market.
In the last part of this paper, real capital investment results will be included, in order
to qualify the presented trading methodology and to compare it with other similar
mathematical models. At the end of this paper has found that the Price Probability Predictor
is a reliable probability field for a price growth that can be used with excellent results to
build a stable investment strategy and also to optimize the capital efficiency of any other
strategy. Any reader will find the originality and universality of the presented method.
Literature review
There are few studies in the literature about price growth probability even the probability
term appears in many titles of trading books. The most are trying to estimate the
probability that the price will touch a precise level in the future. The author of the current
research has decided not to cite any of these studies. During the research conducted behind
this paper, it was found that in more than 2200 trading books and papers read, no
probability field method with sustained and repetitive characteristics when it is about the
algorithmic capital investment was found. Several studies indicate entry points in the
market based on probability estimate but have no criteria for a technical exit decision.
Other studies are made for particular markets, having no proved possible generalization.
There are no reasons to cite uncompleted strategies or unproved price probability models.
This will be the gap filled by the current paper.
Regarding the subject of capital investment strategies that can be automated,
working and proved models for the stock markets can be found in (Connors, 1999),
(Connors & Sen, 2004), (Bernstein & Bernstein, 2008), (Connors & Alvarez, 2009a), or
(Connors & Alvarez, 2009b). Even these papers are not presenting the ways to automate the
included strategies; it remains excellent references for stock markets investment strategies.
The currency market trading strategies are also a very actual subject. Effective and proved
strategies that can be automated can be found in (Cheng, 2007), (Lien, 2009), (Lien, 2011),
or (Volman, 2011). Particular approaches for the commodity markets can be found in
(Kleinman, 2009), (Jagerson & Hanson, 2011). Important psychological strategies that can
be easily adapted with any technical analysis investment strategy can be found in (Pring,
1992), (Kiev, 2008), and (Ward, 2010). Some working mathematical models that can be
adapted for algorithmic trading can be found in (Focardi & Fabozzi, 2004). A particular
approach for risk management techniques that can be used in automated decision-making
systems for capital investments can be found in (Vince, 1992). Mathematical models
especially designed and optimized for algorithmic trading with proved and sustained
results in real capital investments can be found in (Păuna & Lungu, 2018), (Păuna, 2018a),
(Păuna, 2018b), (Păuna, 2018c), (Păuna, 2019a), (Păuna, 2019b), (Păuna, 2019c), (Păuna,
2019d), (Păuna, 2019e), (Păuna, 2019f), and (Păuna, 2020).
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 3
Price probability field
In this paper, we will call a price probability field an analytical function that will give us a
measure for price growth in the next time periods. The current research will present how a
price probability field can be built, how it can be optimized to estimate a precise price
growth, and how three different types of price probability fields can be combined in order
to obtain a more accurate mathematical model. Besides, in the second part of this paper,
automated trading signals and limit conditions will be built using the price probability field
introduced to present how this model can be used in automated capital investment
software systems.
To clarify the notion of the price probability growth, we will say that a price presents
zero probability for growth with an established value in the future if the price never riches
that value before to decrease with at least the double of that value. Similarly, a price has a
100% probability for increase with a specified value if it will touch that value in the future
time before to decrease with the double of value considered. The definitions above are the
hypothesis for this study. The probability field can be defined in different other modes. The
current research has established that comparing a price increase with the double of his
decrease gives us the best capital efficiency in the model that will be presented further. An
additional requirement for a price probability field is to be continuously defined in all the
time price series definition intervals. In other words, the price probability field has to give
us the probability value for price growth at any moment of time.
Probability through Price Cyclicality Function
The Price Probability function was introduced in (Păuna & Lungu, 2018). It was proved that
a very strong and direct correlation exists between this function and the price movement.
The function is defined in [0;100] intervals and has minimal points near the minimal price
levels, and maximal values correlated with the maximal price levels. We will define the
probability field through Price Cyclicality Function the next function:
 
100/100 PCYPROPCY
(1)
where PCY is the Price Probability Function, and φ is a functional parameter that will be
optimized for each capital market analyzed, depending on the way of how the price
probability field is defined, as we will see. Once the PCY function is defined in [0;100], the
PROPCY function will be defined in [0;1] and will be inversely proportional to the price
evolution. When PROPCY has a minimal point, this means the probability for a price increase
is at a minimum, and the price will not make significant up movements. Similarly, when the
PROPCY makes a maximum, the probability for price growth is at maximum, a significant
price increase being expected in that market.
For each market, depending on the price probability field definition, the φ factor will
be computed using the historical price evolution. For example, the probability for a 200
points price increase after a maximal value of the probability field, using the PCY function
with 20 time intervals period, and 20 and 50 periods for the weighted moving averages
used, on a daily time price series of DAX30 Index market, is 98.75%. This means, for the
specified market, the 200 point growth price probability field is defined by φ=0.9875.
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 4
Figure 1. Price probability field using the Price Cyclicality Function for DAX30 Index market.
The value φ=0.9875 was found computing the PCY function and analyzing the price
evolution for the historical time price series of the DAX30 Index market between 2010 and
2019. Considering all the cases when the PCY function made a minimal point lower than 10,
1.25% of cases were not true. In 1,25% of cases, after a minimum point of the PCY function,
the price made a lower movement with more than 400 points before to rich an up value
with 200 points. In this way can be computed the φ parameter for any type of probability
field using any kind of function. To compute the formula (1), the PCY function with n period
will be defined by the recurrence formula:
 
11 iiii PCYPCYPCY
for
0i
with
0
0PCY
(2)
where α defines the gradient of the PCY function, and
ii
ii
iminmax
max
,
(3)
 
kk
ni
ik
imaMamax
max
,
 
kk
ni
ik
imaMamax
max
(4)
using Mak and mak as two weighted moving averages with different periods (Cox, 1969).
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 5
Probability through price Smoothed Heikin-Ashi transform
Smoothed Heikin-Ashi price transform is analytically defined in (Păuna, 2018c):
 
 
4/
),,max(
),,min(
2/
11
i
ii
ii
ii
i
i
ii
i
i
iii
CLHOCha
COHHha
COLLha
COOha
(5)
in which
i
O
,
i
H
,
i
L
and
i
C
are the averages values of open, high, low, respectively close
price levels into a specified M number of time intervals. During this research, it was found
that this price function has a direct and positive correlation with the price evolution.
Measuring the price evolution after the moment when
ii OH
, a significant price growth
probability was found.
The probability field through the Smoothed Heikin-Ashi price transform will be
defined analyzing the cyclicality of
i
O
and
i
H
price series:
 
100/100 SAHPROSHA
(6)
where
 
11 iiii SAHSHASHA
for
0i
with
0
0SHA
(7)
where β defines the gradient of the SHA function with m period, and
ii
ii
iminmax
max
,
iii maMa
(8)
and the maximal and minimal functions are computed using
i
O
and
i
H
:
 
kk
mi
ik
iOHmax
max
,
 
kk
mi
ik
iOHmax
max
(9)
The price probability field measuring the chances for 200 point price increase after
ii OH
on a daily time price series of DAX30 Index market is presented in figure 2. The
functional parameters β and ψ can be found using the historical time price series of any
market. β will define the gradient of the probability field, and ψ will define the maximal
probability value measured in the historical time price series.
As a first observation, the probability variation in figure 1 and the probability field in
figure 2 have significantly different evolutions. There are some time intervals when both
series take maximal or minimal probability values. An important note is that the two
functions are measuring the same phenomenon, which is the price increase with 200
points, but using different methods. Later in this paper, we will see how two or more
probability fields can be combined in order to obtain a better capital efficiency.
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 6
Figure 2. Price probability field using the Smoothed Heikin-Ashi for DAX30 Index market.
Probability through Price Prediction Line and Trigonometric Price Line
The Price Prediction Line is a function introduced in (Păuna, 2019d). It represents the back
transformation into the price space of the Price Cyclicality Function, using the formula:
 
iiiii PminPminPmaxPCYPPL 100/
(10)
where the terms
i
Pmin
and
i
Pmax
represent the minimum and respectively maximum price
values on the current monotony interval of the Price Cyclicality Function. The Price
Prediction Line is figured with a dotted line in figure 3.
The Trigonometric Price Line is a price interpolation line using trigonometric
functions, presented in (Păuna, 2020). The analytical function is given by the form:
 
 
N
k
N
kikiki Nitktktp 1 1
0,1),sin()cos()(
(11)
where
k
and
k
coefficients are computed solving the N equation system, based on the
fact that the values
)( i
tp
are known for the last time moment
i
t
in the price history series.
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 7
Figure 3. Price probability field through Price prediction Line and trigonometric Price Line.
The Trigonometric Price Line is figured in the above picture over the price evolution
with continuous red and blue lines. During the Ph.D. research behind this paper, it was
found that the intersections between the Price Prediction Line and trigonometric Price Line
have an important significance. Once the Trigonometric Price Line values exceed the Price
Prediction Lines values and both functions are increasing, the price will make a significant
up evolution. To define a price probability grow field we will apply the same technique
presented above, considering the cyclicality between the two functions:
 
100/100 PPLTPLPROPPLTPL
(12)
where
 
11 iiii PPLTPLPPLTPLPPLTPL
for
0i
with
0
0PPLTPL
(13)
where γ defines the gradient of the PPLTPL function with p period, and
ii
ii
iminmax
max
,
iii PPLTPL
(14)
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 8
and the maximal and minimal functions are computed this time using PPL and TPL:
 
kk
pi
ik
iPPLTPLmax
max
,
 
kk
pi
ik
iPPLTPLmax
max
(15)
The price probability field through Price Prediction Line and trigonometric Price
Line is presented in figure 3 for the same example of the DAX30 Index market.
Price Probability Predictor
This research has found that a simple average of the three probability field presented
above, will produce a more stable probability function that is giving us a better capital
efficiency when trading signals are computed using it. This is called the Price Probability
Predictor (PPP) and it is given by the relation:
 
3/
PPLTPLSHAPCY PROPROPROPPP
(16)
The results of the Price Predictor Probability function for a 200 points chance of price
increase on a daily time price series of DAX30 Index market are presented in figure 3. The n,
m, and p periods of PCY, SHA and PPLTPL functions are also at our disposal to be optimized
for each analyzed market. In figure 4 was used n=m=p=5.
Figure 4. Price probability predictor for DAX30 Index market.
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 9
To prove that the Price Probability Predictor is in a inverse and strong correlation with the
price action, the Paerson correlation coefficient (Andrei, 2003) was computed for a
significant number of capital markets. Values between (-0.999) and (-0.537) were obtaind
for 4-hours and daily timeframes for the next markets: Frankfurt Stock Exchange Deutscher
Aktienindex DAX30, New York Stock Exchange Dow Jones Industrial Average Index DJIA30,
Financial Times London Stock Exchange Index FTSE100, Cotation Assistée en Continu Paris
Stock Exchange Index CAC40, Swiss Market Index SMI20, Standard & Poor’s Index S&P500,
National Association of Securities Dealers Automated Quotations NASDAQ100, Tokyo Stock
Exchange index NIKKEI225, and Australian Security Exchange Index ASX200, spot price of
gold XAUUSD, and brent crude oil. For currency pairs markets, values between (-0.972) and
(-0.518) were obtaind for 4-hours and daily timeframes for all major currencies pairs.
These results confirm that the Price Probability Predictor is in a inverse and strong
correlation with the price tendency. Based on this fact, after a maximum point of the Price
Probability predictor, the price will make a significant up movement.
Automated trading signals and limit conditions
Two types of entry automated trading signals can be built using the Probability Price
Predictor. The first type follows the maximal points made by the PPP function and will
generate one market entry after a maximal point if the PPP values are higher than a
profitability limit level:
   
iiiiii PPPPPPPPPPPPPPPBuySignal 211
(17)
where λ filter the signals in order to ignore entries when the price growth probability is
lower, in case the PPP function makes a local maximal point at lower values; usually λ=0.5.
The second type of automated trading signals that can be built with the PPP function
is adapted for more volatile markets, initiating multiple entries each time when the price
decrease with a specific δ value:
   
11 kkiiiik ppPPPPPPPPPBuySignal
for
Nk 1
(18)
where i denotes the time interval, and k denotes the number of opened trade. In formula
(17), the first price entry
1
p
is made for
i
PPP
, hen the market probability riches for the
first time θ value on an ascending probability interval:
 
iiii PPPPPPPPPBuySignal 11
(19)
In formula (17), N is the maximal number of simultaneously opened trades, having
the purpose of limiting capital exposure; N will make possible risk management. The θ, δ,
and N factors are at the investors' disposal; all can be optimized depending on the traded
market and on the timeframe used for price analysis.
The exit conditions using the Price Probability Predictor function must be related
with the probability field definition considered in the built model. If the probability field
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 10
was computed for a price growth of 200 points, a target higher that this value will have no
sense. Moreover, to be safe of the unpredictable market behavior, using a target lower than
the target considered building the probability field is recommended. As conclusion, the first
exit criteria is a price increase with a Δ distance than the price level met in the maximal
interval of the PPP function, noted here as Ω:
 
ii pnalExitBuySig
(20)
The exit condition made with formula (20) can be used for one entry made with (17) or for
multiple market entries by formula (18). During this research was found that a better exit
condition is met using the Average True Range (ATR) function introduced in (Wilder,
1978). This will take into consideration the market volatility change during the investment
process. The exit decision can be automated using the relation:
 
iii ATRpnalExitBuySig
(21)
if ATR value is less than the target considered for the price probability field definition.
Formula (21) will generate exit decisions faster that (20), the capital will stay shorter
allocated in the trades, and the investment efficiency will be significantly improved.
Limit conditions built using the PPP functions can be used to improve any other
investment strategy. Entries made by any mathematical or empirical trading model can be
filtered using the Price Probability Predictor. The capital efficiency can be improved
allowing only entries when the price growth probability is higher than a minimal limit:
 
ii PPPtionLimitCondi
(22)
Moreover, an increase in the price probability field values will be a positive condition:
 
iiii PPPPPPPPPtionLimitCondi 1
(23)
In the same idea, exit conditions applied to trades opened with any other trading
strategy can be built when the price growth probability is decreasing under a specific level:
 
iiii PPPPPPPPPionExitCondit 1
(24)
where the parameters Θ and Ξ can be optimized for each traded market and for each
timeframe used for the price analysis.
Results
In this section, trading results obtained with the signals presented in the last part will be
presented in order to prove the functionality of the method introduces in this paper and to
get the possibility to compare the results with other investment strategies.
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 11
The automated signals made by relation (17) were traded for Frankfurt Stock
exchange Deutscher Aktienindex DAX30 market between 1 January 2019 and 31 December
2019. The Price probability predictor was optimized for a price increase with 200 points
after a maximal probability evolution, using the DAX30 historical time price series between
1 January 2010 and 31 December 2018. The cross-over validation is used in this example,
once the optimization interval does not contain the time interval in which the results are. In
figure 5 is presented the capital evolution due to signals (17), for a particular value of λ=0.5,
using a 4-hours timeframe.
Figure 5. Trading results obtained with (17) automated signals for DAX30 Index market.
In 12 months, signals (17) have obtained a risk to reward ratio of 1:2.64 in a total
number of 39 profitable trades. There was no losing trade, and the most extended trade last
475 hours. The results were obtained with DaxTrader (Păuna, 2010), an automated capital
investment software using the Price Probability Predictor to build automated capital
investment signals. The risk and capital management were assured using the “Global Stop
Loss” method (Păuna, 2018d) with a maximal risk level of 1%.
A significantly large number of trades were made by the signals built with (18)
formula for θ=0.75 and δ=100 points. The results obtained with the same automated
trading software are presented in figure 6. In this case, it was obtained a risk to reward
ratio of 1:2.32, and the longest trade last 522 hours. In this second case, a maximal risk level
of 2% of the available capital was used. In this case, two positions were closed with losses, 2
from 117 trades made, meaning a percentage of success equal with 98,29%.
Figure 6. Trading results obtained with (18) automated signals for DAX30 Index market.
The results above are better understood is both signals are used together. Using the
(17) and (18) automated trading signals for the 2019 period applied for the DAX30 Index
market, with a maximal risk level of 2% of the available capital, a risk to reward ratio of
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 12
1:4.96 was obtained. This is an excellent result, proving that the Price Probability Predictor
is a reliable and profitable model to build trading signals on the capital market.
Another important observation is regarding the specificity of the trades opened with
signals built with Price Probability Predictor. The Quality Trading Coefficient (Păuna,
2018e) of 98% of trades above has a positive and higher value in the interval [0.52;0.96].
This means the trades opened when the probability for a price increase is higher are trades
that are evolving fast and constant to the designed target. The values obtained for the
Quality Trading Coefficient classify the investment methodology using price Probability
predictor in the top trading strategies presented in the Ph.D. research behind this paper.
Conclusions
Price Probability Predictor is a technical indicator built using the time price series and
several particular functions as Price Cyclicality Function, Smoothed Heikin-Ashi price
transformation, Price Prediction Line, and Trigonometric Price Line. An analytical
mathematical model links all of these functions into a continuous probability field,
measuring the chance for price growth in the next time intervals. The model includes
several functional parameters that can be optimized for each market in order to define the
function to indicate the probability of price increase with a specified value.
The Price Probability Predictor can be used to build reliable trading signals and limit
conditions to automate the investment activity. It can be optimized for any analyzed capital
market and for any timeframe used. During this research, the model was tested with
excellent results for a considerable number of financial markets: Frankfurt Stock Exchange
Deutscher Aktienindex DAX30, New York Stock Exchange Dow Jones Industrial Average
Index DJIA30, Financial Times London Stock Exchange Index FTSE100, Cotation Assistée en
Continu Paris Stock Exchange Index CAC40, Swiss Market Index SMI20, Standard & Poor’s
Index S&P500, National Association of Securities Dealers Automated Quotations
NASDAQ100, Tokyo Stock Exchange index NIKKEI225, and Australian Security Exchange
Index ASX200. For more volatile markets as spot gold (XAUUSD) and currency markets, the
signals built with the PPP function must be filtered by additional limit conditions imposed
with the Price Cyclicality Function (Păuna & Lungu, 2018).
Due to how the Price Probability Predictor function is defined and optimized, it
measures the price increase chance. The presented function is also an excellent tool for
educational purposes. When the values of the PPP field are high, the function indicates a
higher price growth probability. Besides, when the PPP function has lower values, it will
mean a lower chance for price growth, but not a higher chance for a price decrease. Based
on this particular observation, any capital trading or investment strategy can be filtered and
improved using the Price Probability Predictors to reduce the allocated risk, to reduce the
time spent into a trade, and, consequently, to increase the capital efficiency.
The Price Probability Predictor function was designed for automated trading
systems. Even the mathematical model is a complex one, the computational power needed
to build the function is a reasonable one. It can be built-in real-time with low latency and
can be included in any automated capital investment software system.
The Price Probability Predictor function has a high degree of efficiency in improving
the results of any other trading strategy. Due to this fact, in the research behind this article,
the PPP function assists any automated capital investment decision. Also, it can be used for
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 13
manual investment decisions. Any investor using the PPP function can simply choose to
invest in a market with an 85% price increase probability and to exit from markets
indicating only a 20% price growth chance or a decreasing probability evolution. With all
the facts presented, the Price Probability Predictor is a reliable investment indicator, giving
us the possibility to measure the chance to record a profit in any market on the next time
interval.
References
Andrei T., Statistică și econometrie, Romania: Editura Economică, București, 2003. ISBN: 973-
590-764-X
Bernstein, J, Bernstein, E. (2008). Stock market strategies that work. McGraw Hill. ISBN: 0-
07-140633-6 DOI: 10.1036/0071406336
Cheng, G. (2007). 7 Winning Strategies for Trading Forex. Real and actionable techniques for
profiting from the currency markets. GB: Hariman Trading. ISBN: 978-0-857190-90-1
Connors, L.A. (1999). Best Trading Patterns. The Best of the Professional Traders Journal. US:
M. Gordon Publishing Group. ISBN: 0-9650461-0-2
Connors, L., Alvarez, C. (2009a). Short Term Trading Strategies That Work. A Quantitative
Guide to Trading Stocks and ETFs. , US: TradingMarkets Publishing Group, ISBN: 978-
0-0919239-0-1
Connors, L., Alvarez, C. (2009b). High Probability ETF Trading 7 Professional Strategies to
Improve Your ETF Trading. US: Connors Research. ISBN: 978-0-615-29741-5
Connors, L., Sen, C. (2004). How Markets Really Work A Quantitative Guide to Stock Market
Behavior. US: Connors Research Group. ISBN 978-0-9755513-1-8
Cox, Sir, D.R. (1969). Prediction by Exponentially Weighted Moving Averages and Related
Methods. Journal of the Royal Statistical Society. Series B, Volume 23, No. 2.
Focardi, S.M, Fabozi, F.J. (2004). The mathematics of financial modeling and Investment
Management. John Wiley & Sons. ISBN: 0-471-46599-2
Jagerson, J, Hansen, S.W. (2011). All about investing in gold. McGraw Hill, ISBN: 978-0-07-
176834-4
Kiev, A. (2008). Mastering Trading Stress. John Wiley & Sons. ISBN: 978-0-470-18168-3
Kleinman, G. (2009). The new commodity trading guide. Breakthrough strategies for
capturing market profits. Pearson Education. ISBN: 978-0-13-714529-4
Lien, K. (2009). Day Trading and Swing Trading the Currency Market. Technical and
Fundamental Strategies to Profit the Market Moves. US: John Wiley & Sons. ISBN: 978-
0-470-37736-0
Lien, K. (2011). The Little Book of Currency Trading. How to Make Big Profits in the World of
Forex. US: John Wiley & Sons. ISBN: 978-0-470-77035-1
Păuna, C. (2010), DaxTrader automated trading system, online software presentation.
Available at: https://pauna.biz/daxtrader
Păuna, C. (2018a). Reliable Signals Based on Fisher Transform for Algorithmic Trading.
Timișoara, Romania: Timișoara Journal of Economics and Business. Volume 11, Issue
1/2018 ISSN: 2286-0991. West University of Timișoara. DOI: 10.2478/tjeb-2018-
0006 Available at: https://tjeb.ro
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 14
Păuna, C. (2018b). Reliable Signals and Limit Conditions for Automated Trading Systems.
Iași, Romania: Review of Economic and Business Studies. Volume XI, Issue 2/2018.
ISSN: 1843-763X. Alexandru Ioan Cuza University Press. DOI: 10.1515/rebs-2018-
0070 Available at: http://rebs.feaa.uaic.ro
Păuna, C. (2018c) Smoothed Heikin-Ashi Algorithms Optimized for Automated Trading
Systems. Graz, Austria: Proceeding of the 2nd International Scientific Conference on IT,
Tourism, Economics, Management, and Agriculture, ITEMA 2018. Graz University of
Technology. Available at: https://itema-conference.com
Păuna, C.. (2018d). Capital and Risk Management for Automated Trading Systems, Romania:
Proceedings of the 17th International Conference on Informatics in Economy, pp 183-
188. Available at: https://pauna.biz/ideas
Păuna, C. (2018e). The Quality Trading Coefficient. General Formula to Qualify a Trade and
a Trading Methodology. Bucharest, Romania: Informatică Economica Journal.
Volume 22. Issue 3/2018. ISSN: 1453-1305 DOI: 10.12948/issn14531305/
22.2.2018.04 Available at: https://revistaie.ase.ro
Păuna, C. (2019a). Low risk trading algorithm based on the price cyclicality function for
capital markets. Bucharest, Romania: 13th International Conference on Business
Excellence. DOI: 10.2478/mmcks-2019-0006
Păuna, C. (2019b). Additional Limit Conditions for Breakout Trading Strategies. Bucharest,
Romania: Informatica Economica Journal. Volume 23, Issue 2/2019. DOI:
10.12948/issn14531305/23.2.2019.03 Available at: http://revistaie.ase.ro
Păuna, C. (2019c). A prediction model using price cyclicality function optimized for
Algorithmic trading in financial markets. International Journal of Computer and
Information Engineering. Volume 13, No. 4/2019. Athens, Greece: World Academy of
Science, Engineering and Technology. Available at: https://publications.waset.org/
author/cristian-pauna
Păuna, C. (2019d). Price Prediction Line. Investment Signals and Limit Conditions Applied
for the German Financial Market. International Journal of Computer and Information
Engineering. Volume 13, No. 9/2019. Rome, Italy: World Academy of Science,
Engineering and Technology. Available at: https://publications.waset.org/
author/cristian-pauna
Păuna, C. (2019e). Data mining methods on time price series for algorithmic trading
systems. Bucharest, Romania: Informatica Economica Journal. Volume 23. Issue
1/2019. ISSN: 1453-1305. DOI: 10.12948/issn14531305/23.1.2019.03. Available at:
https://revistaie.ase.ro
Păuna, C. (2019f). Silent Market Indicator. Methodology to avoid the risk in no significant
price movements. Timișoara, Romania: Timișoara Journal of Economics and Business.
Volume 12. Issue 1/2019. ISSN: 2286-0991. DOI: 10.2478/tjeb-2018-0009 Available
at https://tjeb.ro
Păuna, C. (2020). Reliable Signals and Limit Conditions using Trigonometric Interpolation
for Algorithmic Capital Investments. Alicante, Spain: Proceedings of 7th Business
Systems Laboratory International Symposia Conference, BSLAB 2020. Available at:
https://pauna.biz/ideas
Păuna, C., Lungu, I. (2018). Price cyclicality model for financial markets. Reliable limit
conditions for algorithmic trading. Bucharest, Romania: Economic Computation and
DOI:, pp. , ISSN 2558-9652| Proceedings of the 14th International Conference on Business Excellence 2020
PICBE | 15
Economic Cybernetics Studies and Research Journal. Volume 52. Issue 4/2018. ISSN:
1842-3264. DOI: 10.24818/18423264/52.4.18.10 Available at: https://ecocyb.ase.ro
Pring, M.J. (1992). Investment psychology explained. John Wiley & Sons. ISBN:
9780471557210
Vince, R. (1992). The mathematics of money management: risk analysis techniques for
traders. John Wiley & Sons. ISBN: 0-471-54738-7
Volman, B. (2011). Forex price action scalping. An in-deep look into the field of professional
scalping. Light Tower Publishing. ISBN: 978-90-9026411-0
Ward, S. (2010). High Performance Trading. 35 Practical Strategies and Techniques to
enhance Your Trading Psychology and Performance. GB: Hariman House. ISBN: 978-1-
905641-61-1
Wilder, J.W., 1978. New Concepts in Technical Trading Systems. Greensboro, Trend Research.
ISBN 978-0-89459-027-6
---
... This research has identified a reliable function to estimate the price growth probability. Using the Price Probability predictor (PPP) introduced in [22], the limit conditions can be build using the next formulas: (9) where the index (i) denotes the current day price interval, and (i-1) the previous day interval. ...
Conference Paper
Full-text available
Using automated capital investment software systems is a common task today. At the beginning of the third millennium, modern investors are using artificial intelligence resources and methods to find the best investment opportunities on capital markets and to process the trading orders. One of the most important aspects of this activity, besides the buying and selling decisions, is to stay away from the market risk in specific conditions. For this purpose, in the current doctoral research, the notion of limit conditions in capital markets was introduced by the authors. On the high price volatility markets, when the economic or geopolitical background is changing fast, real-time decisions for earlier investment closing, or filtering decision not to open new positions in specific market states, will contribute together to the risk reduction and will provide a higher capital efficiency a the long time run. In the real-time investment software systems, the limit conditions method's implementation presumes particular aspects in order not to introduce additional time delays for the trading orders. This paper will present the way how to include additional limit conditions procedures into automated algorithmic trading software systems. It was found that any investment strategy can be improved by using the limit conditions methods presented in this paper. Based on particular data-mining methods applied to real-time price series of any market, these methods can be automated and included in any capital investment informatics systems in order to improve the results and to reduce the allocated capital risk.
... This research has identified a reliable function to estimate the price growth probability. Using the Price Probability predictor (PPP) introduced in [22], the limit conditions can be build using the next formulas: ...
Thesis
Full-text available
After several attempts to publish my Ph.D. thesis with different prestigious publishers, I have decided to make this work public and free of charge for anyone. Enjoy! Cristian Păuna
Conference Paper
Full-text available
ABSTRACT Algorithmic capital investment procedures became the essential tools to make a profit in the volatile price markets of the 21st century. A large number of market participants, private traders, companies, or investment funds are buying and selling on thousands of markets every day to make a profit. After the 2010 year, algorithmic trading systems became a significant part of the capital investment environment. The price evolution is analyzed today in real-time by powerful computers. To buy cheap and to sell more expensive is a simple idea, but to put it on practice is not easy today in very volatile price markets. The orders are built and set almost instantly today by artificial intelligence software using special mathematical algorithms. These procedures automatically decide the best moments to buy and to sell on different financial markets depending on the price real-time movements. This paper will present a specific methodology to analyze the time price series of any capital market. The model will build reliable trading signals to enter and to exit the market to make a profit. The presented method uses trigonometric interpolation of the price evolution to build a significant trend line called here the Trigonometric Trend Line. It will be mathematically proved that this function is in a positive and direct correlation with the price evolution. The Trigonometric Trend Line will be used to build and automate capital investment signals. Besides, the introduced function will be used in order to qualify the actual price trend and to measure the trend power in order to decide if the price makes an important evolution or not. Limit conditions will be imposed in the financial market to avoid trading in non-significant price movement and to reduce the risk and capital exposure. Comparative trading results obtained with the presented methodology will be included in the last part of this paper to qualify the model. Each trading signal type presented in the paper was traded separately to have a qualitative image. Also, all capital trading signals built with the Trigonometric Trend Line were traded together in order to obtain a better risk to reward ratio. To classify the presented methodology, the presented results were compared with real trading profits obtained with the other three well-known capital investment strategies. With all of these, it was found that using the Trigonometric Trend Line reliable automated trading procedures can 7 th International Symposium "SOCIO-ECONOMIC ECOSYSTEMS " January 22-24, 2020 University of Alicante , Spain Please send to: abstract-submission@bslab-symposium.net be made and optimized for each financial market to obtain good results in the capital investment. Being exclusively a mathematical model, the Trigonometric Trend Line methodology presented in this paper can be applied with good results for any algorithmic trading and high-frequency trading software. The functional parameters can be optimized for each capital market and for each timeframe used in order to optimize the capital efficiency and to reduce the risk. The optimization methods will use the historical time price series in order to catch the price behavior and specificity of each market. The reduced number of parameters and the simplicity of the presented method recommend the Trigonometric Trend Line model to be used in any advanced algorithmic trading software.
Article
Full-text available
In the first decades of the 21st century, in the electronic trading environment, algorithmic capital investments became the primary tool to make a profit by speculations in financial markets. A significant number of traders, private or institutional investors are participating in the capital markets every day using automated algorithms. The autonomous trading software is today a considerable part in the business intelligence system of any modern financial activity. The trading decisions and orders are made automatically by computers using different mathematical models. This paper will present one of these models called Price Prediction Line. A mathematical algorithm will be revealed to build a reliable trend line, which is the base for limit conditions and automated investment signals, the core for a computerized investment system. The paper will guide how to apply these tools to generate entry and exit investment signals, limit conditions to build a mathematical filter for the investment opportunities, and the methodology to integrate all of these in automated investment software. The paper will also present trading results obtained for the leading German financial market index with the presented methods to analyze and to compare different automated investment algorithms. It was found that a specific mathematical algorithm can be optimized and integrated into an automated trading system with good and sustained results for the leading German Market. Investment results will be compared in order to qualify the presented model. In conclusion, a 1:6.12 risk was obtained to reward ratio applying the trigonometric method to the DAX Deutscher Aktienindex on 24 months investment. These results are superior to those obtained with other similar models as this paper reveal. The general idea sustained by this paper is that the Price Prediction Line model presented is a reliable capital investment methodology that can be successfully applied to build an automated investment system with excellent results.
Article
Full-text available
After the widespread release of electronic trading, automated trading systems have become a significant part of the business intelligence system of any modern financial investment company. An important part of the trades is made completely automatically today by computers using mathematical algorithms. The trading decisions are taken almost instantly by logical models and the orders are sent by low-latency automatic systems. This paper will present a real-time price prediction methodology designed especially for algorithmic trading. Based on the price cyclicality function, the methodology revealed will generate price cyclicality bands to predict the optimal levels for the entries and exits. In order to automate the trading decisions, the cyclicality bands will generate automated trading signals. We have found that the model can be used with good results to predict the changes in market behavior. Using these predictions, the model can automatically adapt the trading signals in real-time to maximize the trading results. The paper will reveal the methodology to optimize and implement this model in automated trading systems. After tests, it is proved that this methodology can be applied with good efficiency in different timeframes. Real trading results will be also displayed and analyzed in order to qualify the methodology and to compare it with other models. As a conclusion, it was found that the price prediction model using the price cyclicality function is a reliable trading methodology for algorithmic trading in the financial market.
Article
Full-text available
One of the most popular trading methods used in financial markets is the Turtle strategy. Long-time passed since the middle of 1983 when Richard Dennis and Bill Eckhardt disputed about whether great traders were born or made. To decide the matter, they recruited and trained some traders (the Turtles) and give them real accounts and a complete trading strategy to see which idea is right. That was a breakout trading strategy, meaning they bought when the price exceeded the maximum 20 or 50 days value and sold when the price fell below the minimum of the same interval. Since then many changes have occurred in financial markets. Electronic trading was widespread released and financial trading has become accessible to everyone. Algorithmic trading became the significant part of the trading decision systems and high-frequency trading pushed the volatility of the financial markets to new and incredible limits nowadays. The orders are built and sent almost instantly by smart computers using advanced mathematical algorithms. With all these changes there are many questions today regarding the breakouts strategies. Are the Turtle rules still functional? How can the Turtle strategy be automated for algorithmic trading? Are the results comparable with other modern trading strategies? After a short display of the history and the system's rules, this paper will find some answers to all these questions. We will reveal a method to automate a breakout strategy. More different trading strategies originating from the Turtle rules will be presented. A mathematical model to build the trading signals will be described in order to automate the trading process. It was found that all of these rules have a positive expectancy when they are combined with modern limit conditions. The paper will also include trading results obtained with the methods presented in order to compare and to analyze this capital investment methodology adapted especially for algorithmic trading.
Article
Full-text available
Investing in capital markets is a common task today. An impressive number of traders and investors, companies, private or public funds are buying and selling every day on the free markets. The current high price volatility in the financial markets gives everyone a tremendous number of speculative opportunities to make a profit. Sometimes the price makes no significant movement, however. The majority of the trades initiated in those periods will conclude to losses or will need a very long time to become profitable. To avoid these cases, a mathematical algorithm was developed in this paper: The Silent Market Indicator. This article will present the general principles and the mathematics behind the indicator and how it can be applied in financial trading to improve capital investment efficiency. It was found that the model generates a very reliable filter to avoid entry into the silent markets intervals, when the price action conducts to small amplitude price movements and when the profit expectation is lower. In order to reveal the efficiency of the Silent Market Indicator usage, some comparable trading results will be presented in the last part of this article together with the functional parameters optimized for several known capital markets. As a conclusion, it will be proved that the presented methodology is an excellent method to stay away from the market risk. In addition, being exclusively a mathematical model, it can be applied in any algorithmic trading system, combined with any other trading strategy in order to improve capital efficiency
Conference Paper
Full-text available
Buy cheap and sell more expensive is one of the basic ideas of trading the capital markets for hundreds of years. To apply it in practice has become difficult nowadays due to the high price volatility. The uncertainty in the price movements often leads to high-risk allocation. One main question is when the price is low enough for a low-risk entry? Once established an entry point, the second question is how long to keep the open trades in order to optimize the investment efficiency? This article will answer these questions. A general trading algorithm based on the price cyclical behavior will be revealed. The mathematical model is developed using the Price Cyclicality Function combined with other computational techniques in order to establish low-risk intervals. The algorithm will use multiple entry points in order to catch the best price opportunities. A simple empirical exit algorithm will be optimized in order to maximize the profit for a certain capital exposure level. The presented model uses a low number of functional parameters which can be optimized with a reasonable computational effort for any financial market. Trading results obtained for several markets will also be included in this paper in order to reveal the efficiency of the presented methodology. It was found that the Low-Risk Trading Algorithm can be used with good results for algorithmic trading in any financial market. With the right parameters set, this methodology can be wide range applied in the stock markets, currency and cryptocurrency markets, commodities and raw materials markets and even for the real estate investments. The simplicity of the presented model and the good efficiency level obtained will recommend it. This methodology can be used by any investor in order to manage the investment plan with multiple capital markets.
Article
Full-text available
Buy cheap and sell more expensive. This is the main principle to make a profit on capital markets for hundreds of years. The rule is simple but to apply it in practice has become a very difficult task nowadays, with very high price volatility in the financial markets. Once electronic trading was widespread released, reliable solutions can be found using algorithmic trading systems. This paper presents a data mining method applied to the time price series in order to generate buy and sell decisions using computational algorithms. It was found that an original data mining method based on the price cyclicality function gives us an important profit edge when it is about the capital investments on the short and medium term. The Cyclical Trading Method will be presented together with the main principles and practices to design and optimize trading software. Test results are also included in this article in order to compare the presented method with other known methodologies to trade the capital markets.
Article
Full-text available
Trading and investment on financial markets are common activities today. A very high number of investors, companies, public or private funds are buying and selling every day with a single purpose: the profit. The common questions for any market participant are: when to buy, when to sell and when is better to stay away from the market risk. In order to answer all these questions, many trading strategies are used to establish the best moments to entry or to exit the trades. Due to the large price volatility, a significant part of the trades is set up automatically today by computers using algorithmic trading procedures. For this particular field, special aspects must be met in order to automate the trading process. This paper presents one of these mathematical models used in automated trading systems, a method based on the Fisher transform. A general form of this method will be presented, the functional parameters and the way to optimize them in order to reduce the risk. It will be also suggested a method to build reliable trading signals with the Fisher function in order to be automated. Three different trading signal types will be explained together with the significance of the functional parameters in the price field. A code sample will be included in this paper to prove the simplicity of this method. Real results obtained with the Fisher trading signals will be also presented, compared and analyzed in order to show how this method can be implemented in algorithmic trading.
Article
Full-text available
Automated trading software is a significant part of the business intelligence system in a modern investment company today. The buy and sell orders are built and sent almost instantly by computers using special trading and computational strategies. The trading decisions are made by automated algorithms. In this paper it will be presented one of these mathematical models which generate trading signals based only on the time price series. The algorithm combines several known computing techniques to build a trading indicator to automate the trades. With this method, buy decisions on oversold intervals and sell decisions on overbought price values can be built. Limit conditions in order to close the long and short trades can be also automatically generated. More trading signal types based on this model will be revealed. Trading results obtained with all these signals will be presented in order to qualify this methodology developed especially for algorithmic trading.
Article
Full-text available
Trading the financial markets is a common idea nowadays. Millions of market participants, individuals, companies or public funds are buying and selling different equities in order to obtain profit from the buy and sell price difference. Once the equity was established, the main question marks are when to buy, when to sell and how long to keep the opened positions. This paper will present a mathematical model for the cyclicality of the price evolution. The model can be applied for any equity in any financial market, using any timeframe. The method will gives us information about when is good to buy and when is better to sell. The price cyclicality model is also a method to establish when the price is approaching to change its behavior in order to build limit conditions to stay away the market and to minimize the risk. The fundamental news is already included in the price behavior. Being exclusively a mathematical model based on the price evolution, this method can be easily implemented in algorithmic trading. The paper will also reveal how the cyclicality model can be applied in automated trading systems and will present comparative results obtained in real-time trading environment.