An analytic formula for pricing American-style convertible bonds in a regime switching model

In this paper, we consider the pricing of convertible bonds on a single underlying asset with dividend yield in a regime-switching economy. The dynamics of the risky asset are assumed to follow a Markov-modulated geometric Brownian motion. That is, the market parameters, such as the market interest rate, dividend yield and the volatility of the underlying risky asset, depend on unobservable states of the economy that are modelled by a continuous-time hidden Markov process. By means of the homotopy analysis method, an analytic formula for pricing convertible bonds with dividend yield in a two-state regime-switching model is presented.