Option Pricing in a Jump-Diffusion Model with Regime-Switching

Nowadays, the regime switching model has become a popular model in mathematical finance and actuarial science. Thus, pricing the regime switching risk is an important issue. In Naik (1993), a jump diffusion model with two regimes is studied. In this paper, we extend the model of Naik (1993) to a multi-regime case. We present a trinominal tree method to price options in the extended model. Our results show that the trinominal tree method in this paper is an effective method; it is very fast and easy to implement. Compared with the existing methodologies, the proposed method has an obvious advantage when one needs to price exotic options and the number of regime states is large. Various numerical examples are presented to illustrate the ideas and methodologies.

Keywords: Jump-diffusion model, Trinominal tree method, Regime switching, Option pricing, Price of regime switching risk.