Review of Derivatives Research

Publications in this journal

• Article: Calibration risk: Illustrating the impact of calibration risk under the Heston model

  Florence Guillaume, Wim Schoutens
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  ABSTRACT: It is already well documented that model risk is an important issue regarding the pricing of exotics (see Schoutens etal., in A perfect calibration! Now what?, Wilmott Magazine, March 2004: pp 66–78, 2004). Arguments have been made to put this into the perspective of bid-ask pricing using the theory of conic finance and pricing to acceptability (Cherny and Madan Review of Financial Studies, 22: 2571–2606, 2009). In this paper we show also the presence and importance of calibration risk. More particularly, we point out that a variety of plausible calibration methods lead again to serious price differences for exotics and different distributions of the P&L of the delta-hedging strategy. This is illustrated under the popular Heston stochastic volatility model, which is used among practitioners to price all kinds of exotic and structured products. This paper shows that it is prudent to take some additional safety margin into account for the pricing of these structured notes. KeywordsHeston model–Calibration–Model risk–Calibration risk–Exotic options
  Review of Derivatives Research 05/2012; 15(1):57-79.
• Article: The financial crisis and hedge fund returns

  Nicolas P. B. Bollen
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  ABSTRACT: The financial crisis has focused the lens of politicians and regulators on hedge funds as a source of systemic and operational risk in asset markets. We examine the extent to which available data can provide useful information regarding the impact of hedge funds on the financial system. Using data from January 1994 through September 2008, we find dramatic changes in the exposures of hedge funds to risk factors, accompanied by a significant and widespread increase in correlation between hedge fund and factor returns. Lastly, the discontinuity at zero in the cross-sectional distribution of hedge fund returns persists throughout the sample. KeywordsHedge funds–Financial crisis–Systemic risk
  Review of Derivatives Research 04/2012; 14(2):117-135.
• Article: The option CAPM and the performance of hedge funds

  Antonio Diez de los Rios, René Garcia
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  ABSTRACT: We evaluate the investment performance of hedge funds using an asset pricing model that is characterized by a piecewise-linear stochastic discount factor, and which we estimate using the generalized method of moments by minimizing the Hansen–Jagannathan distance. Our results show that, once non-linearities and public information are taken into account, there is only evidence of positive performance for the overall hedge fund index, equity-market neutral strategy and the global macro strategy. KeywordsHedge funds–Non-linear return structure–Performance evaluation
  Review of Derivatives Research 04/2012; 14(2):137-167.
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  Available from: uevora.pt

  Article: American options and callable bonds under stochastic interest rates and endogenous bankruptcy

  João Pedro Vidal Nunes
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  ABSTRACT: A new characterization of the American-style option is proposed under a very general multifactor Markovian and diffusion framework. The efficiency of the proposed pricing solutions is shown to depend only on the use of a viable valuation method for the corresponding European-style option and for the transition density of the model’s state variables. Under a Gauss-Markov stochastic interest rates setup, these new American option pricing solutions are shown to offer a much better accuracy-efficiency trade-off than the approximations already available in the literature. This result is also used to price callable corporate bonds under an endogenous bankruptcy structural approach, by decomposing the option to call or default into a European put on the firm value plus two early exercise premium components. KeywordsAmerican options–Optimal stopping time–Convolutions–Stochastic interest rates–Callable defaultable bonds
  Review of Derivatives Research 04/2012; 14(3):283-332.
• Article: A remark on static hedging of options written on the last exit time

  Yuri Imamura
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  ABSTRACT: In this paper, several different static hedges of the option written on the last exit time are given. One of them was originally presented in Akahori etal. (Methodol Comput Appl Probab 11(4): 661–668, 2009). Another one is derived from an expression in Madan etal. (Asia Pac Financ Mark 15(2): 97–115, 2008d). It is remarked in this paper that these static hedges are also obtained by applying a method in Carr and Chou (Hedging complex barrier options, 2001). KeywordsStatic hedging strategy–Exotic option–Last exit time–Carr-Chou’s symmetry formula
  Review of Derivatives Research 04/2012; 14(3):333-347.
• Article: A binomial approximation for two-state Markovian HJM models

  Massimo Costabile, Ivar Massabó, Emilio Russo
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  ABSTRACT: This article develops a lattice algorithm for pricing interest rate derivatives under the Heath etal. (Econometrica 60:77–105, 1992) paradigm when the volatility structure of forward rates obeys the Ritchken and Sankarasubramanian (Math Financ 5:55–72) condition. In such a framework, the entire term structure of the interest rate may be represented using a two-dimensional Markov process, where one state variable is the spot rate and the other is an accrued variance statistic. Unlike in the usual approach based on the Nelson-Ramaswamy (Rev Financ Stud 3:393–430) transformation, we directly discretize the heteroskedastic spot rate process by a recombining binomial tree. Further, we reduce the computational cost of the pricing problem by associating with each node of the lattice a fixed number of accrued variance values computed on a subset of paths reaching that node. A backward induction scheme coupled with linear interpolation is used to evaluate interest rate contingent claims. KeywordsInterest rate options–Contingent claims–Binomial algorithms–Discrete-time models
  Review of Derivatives Research 04/2012; 14(1):37-65.
• Source

  Available from: SSRN

  Article: The smirk in the S&P500 futures options prices: a linearized factor analysis

  Andrew Carverhill, Terry H. F. Cheuk, Sigurd Dyrting
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  ABSTRACT: In the S&P500 futures options, we identify three factors, corresponding to movements in the underlying, parallel movements, and tilting of the cross section of implied volatilities (the “smirk factor”). We relate these factors non-linearly to movements in the option prices. They seem to be diffusive in nature, have significant associated risk premia, and can account for an overwhelming part of the option price movements. We interpret the options smirk, which is the notion that out-of-the-money (OTM) puts seem expensive relative to OTM calls, in terms of the prices of these risk factors. Going short OTM puts and long OTM calls, corresponding to the third factor, makes a profit on average, but this corresponds to its risk premium, and does not represent a market inefficiency. Our smirk factor is useful for hedging option portfolios, but seems unrelated to movements in the underlying, and does not fit into the framework of the jump-diffusion models.
  Review of Derivatives Research 04/2012; 12(2):109-139.
• Article: Exchange option pricing under stochastic volatility: a correlation expansion

  F. Antonelli, A. Ramponi, S. Scarlatti
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  ABSTRACT: Efficient valuation of exchange options with random volatilities while challenging at analytical level, has strong practical implications: in this paper we present a new approach to the problem which allows for extensions of previous known results. We undertake a route based on a multi-asset generalization of a methodology developed in Antonelli and Scarlatti (Finan Stoch 13:269–303, 2009) to handle simple European one-asset derivatives with volatility paths described by Ito’s diffusive equations. Our method seems to adapt rather smoothly to the evaluation of Exchange options involving correlations among all the financial quantities that specify the model and it is based on expanding and approximating the theoretical evaluation formula with respect to correlation parameters. It applies to a whole range of models and does not require any particular distributional property. In order to test the quality of our approximation numerical simulations are provided in the last part of the paper. KeywordsOptions-Stochastic volatility-SDE’s-PDE’s-Margrabe’s formula Mathematical Subject Classification (2002)60H10-91B24 JEL Classification (2007)C020-G130
  Review of Derivatives Research 04/2012; 13(1):45-73.
• Article: Foreign currency bubbles

  Robert A. Jarrow, Philip Protter
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  ABSTRACT: This paper develops a new model for studying foreign currency exchange rate bubbles. The model constructed is a modification of the martingale based bubble approach of Jarrow etal. (Adv Math Finance 105–130, 2006; Math Finance 20(2):145–185, 2008). This model generates some new insights into our understanding of exchange rate bubbles and it can be utilized empirically to test for their existence. The new insights are: (1) exchange rate bubbles can be negative, in contrast to asset price bubbles, (2) exchange rate bubbles are caused by price level bubbles in either or both of the relevant countries’ currencies, and (3) price level bubbles decrease the expected inflation rate in the domestic economy. KeywordsPrice bubbles–Foreign currencies–Inflation–Martingale measures–Arbitrage
  Review of Derivatives Research 04/2012; 14(1):67-83.
• Article: A recombining lattice option pricing model that relaxes the assumption of lognormality

  Dasheng Ji, B. Wade Brorsen
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  ABSTRACT: Option pricing models based on an underlying lognormal distribution typically exhibit volatility smiles or smirks where the implied volatility varies by strike price. To adequately model the underlying distribution, a less restrictive model is needed. A relaxed binomial model is developed here that can account for the skewness of the underlying distribution and a relaxed trinomial model is developed that can account for the skewness and kurtosis of the underlying distribution. The new model incorporates the usual binomial and trinomial tree models as restricted special cases. Unlike previous flexible tree models, the size and probability of jumps are held constant at each node so only minor modifications in existing code for lattice models are needed to implement the new approach. Also, the new approach allows calculating implied skewness and implied kurtosis. Numerical results show that the relaxed binomial and trinomial tree models developed in this study are at least as accurate as tree models based on lognormality when the true underlying distribution is lognormal and substantially more accurate when the underlying distribution is not lognormal. KeywordsBinomial trees–Gaussian quadrature–Option pricing
  Review of Derivatives Research 04/2012; 14(3):349-367.
• Article: An empirical analysis of alternative recovery risk models and implied recovery rates

  Frank Xiaoling Zhang
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  ABSTRACT: This article studies the role of recovery on defaultable debt prices in alternative recovery risk models. The empirical results suggest two central findings. First, the recovery concept that specifies recovery as a fraction of the discounted par value has broader empirical support. Second, parametric debt valuation models can provide a useful assessment of recovery rates embedded in bond prices. KeywordsRecovery-Default risk-Defaultable bonds-Corporate bond pricing-Recovery payout as a fraction of face-Recovery as a fraction of pre-default debt values-Recovery as a fraction of the present value of face-Implied recovery JEL ClassificationG0-G10-G11-G12-G13-C5
  Review of Derivatives Research 04/2012; 13(2):101-124.
• Article: Dynamic programming and mean-variance hedging with partial execution risk

  Koichi Matsumoto
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  ABSTRACT: In this paper I consider a hedging problem in an illiquid market where there is a risk that the hedger’s order to buy or sell the underlying asset may be executed only partially. In this setting, I find a mean-variance optimal hedging strategy by the dynamic programming method. The solution contains a new endogenous state variable representing the current position in the underlying. The exogenous coefficients in the solution are given by recursive formulas which can be calculated efficiently in Markov models. I illustrate effects of the partial execution risk in several examples.
  Review of Derivatives Research 04/2012; 12(1):29-53.
• Article: The cross-section of average delta-hedge option returns under stochastic volatility

  Alfredo Ibáñez
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  ABSTRACT: Existing evidence indicates that average returns of purchased market-hedge S&P 500 index calls, puts, and straddles are non-zero but large and negative, which implies that options are expensive. This result is intuitively explained by means of volatility risk and a negative volatility risk premium, but there is a recent surge of empirical and analytical studies which also attempt to find the sources of this premium. An important question in the line of a priced volatility explanation is if a standard stochastic volatility model can also explain the cross-sectional findings of these empirical studies. The answer is fairly positive. The volatility elasticity of calls and puts is several times the level of market volatility, depending on moneyness and maturity, and implies a rich cross-section of negative average option returns—even if volatility risk is not priced heavily, albeit negative. We introduce and calibrate a new measure of option overprice to explain these results. This measure is robust to jump risk if jumps are not priced.
  Review of Derivatives Research 04/2012; 11(3):205-244.
• Article: Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields

  Carl Chiarella, Oh Kang Kwon
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  ABSTRACT: Finite dimensional Markovian HJM term structure models provide ideal settings for the study of term structure dynamics and interest rate derivatives where the flexibility of the HJM framework and the tractability of Markovian models coexist. Consequently, these models became the focus of a series of papers including Carverhill (1994), Ritchken and Sankarasubramanian (1995), Bhar and Chiarella (1997), Inui and Kijima (1998), de Jong and Santa-Clara (1999), Björk and Svensson (2001) and Chiarella and Kwon (2001a). However, these models usually required the introduction of a large number of state variables which, at first sight, did not appear to have clear links to the market observed quantities, and the explicit realisations of the forward rate curve in terms of the state variables were unclear. In this paper, it is shown that the forward rate curves for these models are affine functions of the state variables, and conversely that the state variables in these models can be expressed as affine functions of a finite number of forward rates or yields. This property is useful, for example, in the estimation of model parameters. The paper also provides explicit formulae for the bond prices in terms of the state variables that generalise the formulae given in Inui and Kijima (1998), and applies the framework to obtain affine representations for a number of popular interest rate models.
  Review of Derivatives Research 04/2012; 6(2):129-155.
• Article: The β-variance gamma model

  Wim Schoutens, Geert Van Damme
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  ABSTRACT: Kuznetsov (Ann Appl Prob, 2009) introduces a 10-parameter family of Lévy processes for which the Wiener-Hopf factors and the distribution of the running supremum (infimum) can be determined semi-analytically. In this text we will examine the numerical performance of this so-called β-family, both in the equity world and in the field of credit risk. In order to do this, we will calibrate a particular member of this family to a vanilla option surface (by means of the Fast Fourier Transform-technique due to Carr and Madan (J Comput Fin 2(4):61–73, 1999) and use the resulting parameters to determine the prices of a digital down-and-out barrier (DDOB) option, written on the same underlying. In a second experiment, we will try and calibrate the model to some real-life credit default swap (CDS) term structures. The parameters of the model under investigation are chosen such that its Lévy density is approximately equal to that of the famous Variance Gamma (VG) process, which will serve as a benchmark. Hence, the former will be referred to as the β-VG model. The option prices will be determined both semi-analytically [using the formulas derived by Kuznetsov (Ann Appl Prob, 2009)] and through a Monte-Carlo simulation. However, the CDS spreads will only be determined semi-analytically, due to the very close relation between pricing DDOB options and determining the par spread of a CDS. Furthermore, in both cases, the results will be compared with the ones obtained using the VG model [Cf. Schoutens (Lévy processes in finance: pricing financial derivatives, Wiley , Chichester, 2003) and, Cariboni and Schoutens (Levy processes in credit risk, Wiley, Chichester, 2009)]. It will turn out that, w.r.t. vanilla option prices, the β-VG model performs almost identically as the VG model, whereas the semi-analytical expressions by Kuznetsov (Ann Appl Prob, 2009) lead to a (fast and) accurate pricing of DDOB options and CDSs. KeywordsLevy processes–Hitting probability–Barrier options
  Review of Derivatives Research 04/2012; 14(3):263-282.
• Source

  Available from: SSRN

  Article: Equilibrium preference free pricing of derivatives under the generalized beta distributions

  Masayuki Ikeda
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  ABSTRACT: This paper demonstrates that the risk neutral valuation relationship (RNVR) exists when the aggregate wealth and the underlying variable for derivatives follow a distribution from the family of transformed beta distributions. Specifically, the asset specific pricing kernel (ASPK) is solved for the generalized beta (GB) distribution class, which is extremely flexible to describe various shapes of underlying distributions. With the ASPK in hand, preference free call option formulas are obtained for rescaled and shifted beta distribution of the first kind (RSB1) and for the second kind (RSB2). These distributions include many well known important distributions as special cases. If the preference free formula does not exist under the GB distribution class, then the call price is shown to be numerically calculated without information of preference parameters once the spot price of the underlying is given. KeywordsGeneralized beta distribution-Risk neutral valuation relationship-Asset specific pricing kernel-Implied volatility JEL ClassificationG12-G13
  Review of Derivatives Research 04/2012; 13(3):297-332.
• Source

  Available from: SSRN

  Article: A forward started jump-diffusion model and pricing of cliquet style exotics

  Gabriel G. Drimus
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  ABSTRACT: In this paper we present an alternative model for pricing exotic options and structured products with forward-starting components. As presented in the recent study by Eberlein and Madan (Quantitative Finance 9(1):27–42, 2009), the pricing of such exotic products (which consist primarily of different variations of locally/globally, capped/floored, arithmetic/geometric etc. cliquets) depends critically on the modeling of the forward–return distributions. Therefore, in our approach, we directly take up the modeling of forward variances corresponding to the tenor structure of the product to be priced. We propose a two factor forward variance market model with jumps in returns and volatility. It allows the model user to directly control the behavior of future smiles and hence properly price forward smile risk of cliquet-style exotic products. The key idea, in order to achieve consistency between the dynamics of forward variance swaps and the underlying stock, is to adopt a forward starting model for the stock dynamics over each reset period of the tenor structure. We also present in detail the calibration steps for our proposed model. KeywordsExotic options-Forward volatility smiles-Variance swaps-Cliquets JEL ClassificationG12-G13-C63
  Review of Derivatives Research 04/2012; 13(2):125-140.
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  Available from: SSRN

  Article: The cost of operational risk loss insurance

  Robert A. Jarrow, Jeff Oxman, Yildiray Yildirim
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  ABSTRACT: Using the Algo FIRST operational risk database, this paper computes the cost of operational risk loss insurance for a sample of banks over a 1-year horizon. The estimated cost of 1-year operational risk loss insurance for an average bank is 1.24% as a percentage of firm value on December 31, 2006, while an average AA bank is 0.24%. These estimates far exceed the typical 1-year default insurance premiums as reflected in market CDS rates for similarly rated banks. These insurance premiums confirm the economic importance of operational risk in the management of financial institutions. KeywordsOperational risk-Loss severity-Multinomial logit JEL ClassificationG21-G28-G13
  Review of Derivatives Research 04/2012; 13(3):273-295.
• Article: A fast Fourier transform technique for pricing American options under stochastic volatility

  Oleksandr Zhylyevskyy
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  ABSTRACT: This paper develops a non-finite-difference-based method of American option pricing under stochastic volatility by extending the Geske-Johnson compound option scheme. The characteristic function of the underlying state vector is inverted to obtain the vector’s density using a kernel-smoothed fast Fourier transform technique. The method produces option values that are closely in line with the values obtained by finite-difference schemes. It also performs well in an empirical application with traded S&P 100 index options. The method is especially well suited to price a set of options with different strikes on the same underlying asset, which is a task often encountered by practitioners. KeywordsAmerican option-Stochastic volatility-Heston model-Geske-Johnson scheme-Fast Fourier transform-Characteristic function inversion
  Review of Derivatives Research 04/2012; 13(1):1-24.
• Article: Static versus dynamic hedges: an empirical comparison for barrier options

  Bernd Engelmann, Matthias R. Fengler, Morten Nalholm, Peter Schwendner
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  ABSTRACT: We conduct an empirical comparison of static versus dynamic hedges of barrier options. Using more than five years of data, we compare a number of static hedges from the literature with dynamic hedges based on the local volatility model. The main result is that the variability of profit-and-loss distributions from certain static hedges is significantly smaller than that of dynamic hedges and robust to changing market scenarios. Furthermore, these static hedges are able to provide a robust tracking of barrier options’ sensitivities.
  Review of Derivatives Research 04/2012; 9(3):239-264.