Option pricing under regime-switching jump–diffusion models

We present an explicit formula and a multinomial approach for pricing contingent claims under a regime-switching jump–diffusion model. The explicit formula, obtained as an expectation of Merton-type formulae for jump–diffusion processes, allows to compute the price of European options in the case of a two-regime economy with lognormal jumps, while the multinomial approach allows to accommodate an arbitrary number of regimes and a generic jump size distribution, and is suitable for pricing American-style options. The latter algorithm discretizes log-returns in each regime independently, starting from the highest volatility regime where a recombining multinomial lattice is established. In the remaining regimes, lattice nodes are the same but branching probabilities are adjusted. Derivative prices are computed by a backward induction scheme.