Valuing Options in Regime-Switching Models

Abstract:We develop a flexible discrete-time hedging methodology that minimizes the expected value of any desired penalty function of the hedging error within a general regimeswitching framework. A numerical algorithm based on backward recursion allows for the sequential construction of an optimal hedging strategy. Numerical experiments comparing this and other methodologies show a relative expected penalty reduction ranging between 0.9% and 12.6% with respect to the best benchmark.

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“…5 To ease notation, V n (v 0 , Y 0:n , θ 1:n ) is denoted by V n . 6 Or a weaker version of it asking for V n to be positive.…”

Section: 2mentioning

confidence: 99%

Optimal hedging when the underlying asset follows a regime-switching Markov process

François

Gauthier

Godin

2014

European Journal of Operational Research

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“…Campa andChang (1995, 1998) and Campa, Chang, and Reider (1998) study the empirical properties of the OTC currency options. Bollen (1998) and Bollen, Gray, and Whaley (2000) propose regime-switching models for currency option pricing. Nevertheless, Bollen and Raisel (2003) find that the jump-diffusion stochastic volatility model of Bates (1996b) outperforms regime-switching and GARCH-type models in matching the observed behaviors of OTC currency options.…”

Section: Stochastic Skew In Currency Optionsmentioning

confidence: 99%

Stochastic Skew in Currency Options

Carr

2004

SSRN Journal

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Verma, and participants at Baruch College, UC Riverside, and Columbia University for comments. Any remaining errors are ours. We welcome comments, including references to related papers we have inadvertently overlooked. † Stochastic Skew in Currency Options ABSTRACTWe document the behavior of over-the-counter currency option prices across moneyness, maturity, and calendar time on two of the most actively traded currency pairs over the past eight years. We find that the risk-neutral distribution of currency returns is relatively symmetric on average. However, on any given date, the conditional currency return distribution can show strong asymmetry.This asymmetry varies greatly over time and often switch directions. We design and estimate a class of models that capture these unique features of the currency options prices and perform much better than traditional jump-diffusion stochastic volatility models. Stochastic Skew in Currency OptionsOptions markets have enjoyed tremendous growth during the past decade. In conjunction with this growth, researchers have developed numerous new option pricing models to account for the various pricing biases in the classic Black and Scholes (1973) model. Most recently, a series of papers synthesize and test the performance of a number of different models for pricing equity index options, e.g., Chen (1997, 2000a,b), Bates (2000), Andersen, Benzoni, and Lund (2002), Pan (2002), Eraker (2003), and Huang and Wu (2004). However, studies on currency option pricing have been relatively sparse.At first glance, this relative paucity of study is surprising since foreign exchange is the largest of the global financial markets. Currently, daily trading volume in the currency markets stands at over 1.5 trillion U.S. dollars. It is widely appreciated that the dynamic behavior of foreign exchange rates has important economic repercussions. It is also widely appreciated that currency option prices reveal important information about the conditional risk-neutral distribution of the underlying currency returns over different horizons.The most likely reason for the relative scarcity of research on currency options is the absence of a publicly available database for currency option prices. Currency options trade on the PhiladelphiaOptions Exchange (PHLX), but volume in this market has thinned during the past five years as trading activity has shifted to the over-the-counter (OTC) market. The OTC currency options market is very liquid and deep. The bid-ask spreads for major currency options are narrower than those on equity index options, and trading volume is measured in trillions of U.S. dollars per year. Hence, the over-thecounter currency options market constitutes an economically important market for academic research.We obtain a data set of OTC option quotes on two of the most actively traded currency pairs during the past eight-year span from January 1996 to January 2004. The two currency pairs are the U.S. dollar price of Japanese yen (JPYUSD) and the U.S. dollar price of the British po...

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“…This should lead to the transition of volatilities of both the underlying stock and the option issuer's asset. The financial events are often modeled by the regime switching model to capture the changes of the market environment by the unanticipated events (see, e.g., Hamilton [8], Bollen [2], Buffington and Ellott [4], Boyle and Draviam [3], Zhang et al [15], Zhu et al [16], Elliott et al [7]). Based on this approach, we model the business cycle by a continuous-time two-state regime switching.…”

Section: Introductionmentioning

confidence: 99%

Probability for transition of business cycle and pricing of options with correlated credit risk

Kim

2018

HJMS

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In this paper we propose the transition probability of business cycle for the pricing of options with credit risk. In order to describe business cycles of markets, the regime switching model is considered. We provide the probability density functions of the occupation time of the high volatility regime via Laplace transforms. Using these functions we derive the analytic valuation formulae for options with correlated credit risk and business cycle. We also illustrate the important properties of options with numerical graphs.

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Valuing Options in Regime-Switching Models

Cited by 212 publications

References 17 publications

Optimal hedging when the underlying asset follows a regime-switching Markov process

Optimal hedging when the underlying asset follows a regime-switching Markov process

Stochastic Skew in Currency Options

Probability for transition of business cycle and pricing of options with correlated credit risk

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