Explicit solutions to European options in a regime-switching economy

We provide closed-form solutions for European option values when the dynamics of both the short rate and volatility of the underlying price process are modulated by a continuous-time Markov chain with a finite number of ''economic states''. Extensions involving dividends, currencies and cost of carry are further explored.

[1]  Robert J. Elliott,et al.  PORTFOLIO OPTIMIZATION, HIDDEN MARKOV MODELS AND TECHNICAL ANALYSIS OF P&F CHARTS , 2002 .

[2]  Raul Susmel,et al.  Regime-Switching Stochastic Volatility and Short-Term Interest Rates , 2001 .

[3]  Robert J. Elliott,et al.  American options with regime switching , 2002 .

[4]  Andrew Ang,et al.  Regime Switches in Interest Rates , 1998 .

[5]  Thomas H. Goodwin Business-Cycle Analysis with a Markov-Switching Model , 1993 .

[6]  James D. Hamilton,et al.  Autoregressive conditional heteroskedasticity and changes in regime , 1994 .

[7]  Andrew J. Filardo Business-Cycle Phases and Their Transitional Dynamics , 1994 .

[8]  Simon van Norden,et al.  Regime Switching in Stock Market Returns , 1997 .

[9]  Xin Guo,et al.  Closed-Form Solutions for Perpetual American Put Options with Regime Switching , 2004, SIAM J. Appl. Math..

[10]  John B. Moore,et al.  Hidden Markov Models: Estimation and Control , 1994 .

[11]  K. Singleton,et al.  Term Structure Dynamics in Theory and Reality , 2002 .

[12]  James D. Hamilton Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates , 1988 .

[13]  Yong Zeng,et al.  A ffine Regime-Switching Models for Interest Rate Term Structure , 2004 .

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

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

[16]  James D. Hamilton,et al.  Long Swings in the Dollar: Are They in the Data and Do Markets Know It? The American Economic Review , 1990 .

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

[18]  Xin Guo,et al.  Information and option pricings , 2001 .

[19]  J. Hull Options, Futures, and Other Derivatives , 1989 .

[20]  Robert J. Elliott,et al.  An interest rate model with a Markovian mean reverting level , 2002 .

[21]  Wolfgang J. Runggaldier,et al.  Mean-variance hedging of options on stocks with Markov volatilities , 1995 .

[22]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.