Lookback option pricing for regime-switching jump diffusion models

In this paper, we will introduce a numerical method to price the European lookback oating strike put options where the underlying asset price is modeled by a generalized regime-switching jump di_usion process. In the Markov regime-switching model, the option value is a solution of a coupled system of nonlinear integro-di_erential partial di_erential equations. Due to the complexity of regime-switching model, the jump process involved, and the nonlinearity, closed-form solutions are virtually impossible to obtain. We use Markov chain approximation techniques to construct a discrete-time Markov chain to approximate the option value. Convergence of the approximation algorithms is proved. Examples are presented to demonstrate the applicability of the numerical methods.