| We study the pricing of European options, with the rate of return and the volatility of the underlying asset depending on the market mode or regime that switches. This regime-witching 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, along with a system of partial differantial equations that govern the option price, with smoothed boundary conditions. We al-so develop a numerical approach to compute the pricing formula, using a successive approximation scheme with a geometric rate of convergence. |
