A multinomial approach for option pricing under regime-switching jump-diffusion models

We present a multinomial approach for pricing contingent claims under a regime-switching jump-diffusion model.The algorithm transforms the regime-switching jump-diffusion process on a logarithmic scale and considers itsvalues in each regime independently. Starting from the highest volatility regime and initially ignoring the jumpcomponent in the asset price process, we have a geometric Brownian motion discretized by a trinomial modelshowing an upward, a middle, or a downward tick in each discrete period. Since a jump can cause the asset price toundergo a large change of random size, in the discrete time model we permit the asset price to change by multipleticks in a single period. This aspect is captured by building up a recombining multinomial lattice. To modelthe underlying asset dynamics in the other regimes, we keep fixed the lattice nodes established for the highestvolatility regime and simply adjust the risk-neutral probability measure in different regime states. In this way, wecan accommodate the data of an arbitrary number of regimes at the same time. The computation of derivativeprices in each regime is based on a backward induction scheme which is very fast and easy to implement.