A Multidimensional Regime-Switching Model For European Options

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.