A Regime-Switching Model for European Options

We study the pricing of European-style options, with the rate of return and the volatility of the underlying asset depending on the market mode or regime that switches among a finite number of states. This regime-switching model is formulated as a geometric Brownian motion modulated by a finite-state Markov chain. With a Girsanov-like change of measure, we derive the option price using risk-neutral valuation. We also develop a numerical approach to compute the pricing formula, using a successive approximation scheme with a geometric rate of convergence. Using numerical examples of simple, two- or three-state Markov chain models, we are able to demonstrate the presence of the volatility smile and volatility term structure.

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