Option pricing under regime switching

Abstract This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357–84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.

[1]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[2]  M. Rubinstein.,et al.  Recovering Probability Distributions from Option Prices , 1996 .

[3]  J. Duan,et al.  Série Scientifique Scientific Series Empirical Martingale Simulation for Asset Prices Empirical Martingale Simulation for Asset Prices , 2022 .

[4]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[5]  Nicolas P. B. Bollen.  Valuing Options in Regime-Switching Models , 1998 .

[6]  Campbell R. Harvey,et al.  Dividends and S&P 100 index option valuation , 1992 .

[7]  Jin-Chuan Duan,et al.  Augmented GARCH (p,q) process and its diffusion limit , 1997 .

[8]  J. Duan.  THE GARCH OPTION PRICING MODEL , 1995 .

[9]  Stephen Gray.  Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process , 1996 .

[10]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[11]  Jeff Fleming,et al.  Implied volatility functions: empirical tests , 1996, IEEE/IAFE 1996 Conference on Computational Intelligence for Financial Engineering (CIFEr).

[12]  Jin-Chuan Duan,et al.  American option pricing under GARCH by a Markov chain approximation , 2001 .

[13]  Peter H. Ritchken,et al.  Pricing Options under Generalized GARCH and Stochastic Volatility Processes , 1999 .

[14]  Jin-Chuan Duan.  A Unified Theory of Option Pricing under Stochastic Volatility from GARCH to Diffusion , 1994 .

[15]  A. Lo,et al.  Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices , 1998 .

[16]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[17]  Thomas H. McCurdy,et al.  Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth , 1994 .

[18]  Geert Bekaert,et al.  On Biases in the Measurement of Foreign Exchange Risk Premiums , 1991 .