Pricing dynamic fund protections with regime switching

This paper deals with the valuation of dynamic fund protections in a Markov regime-switching environment. The volatility switches over time subject to a continuous-time Markov chain. Using a regime-switching diffusion process to describe the primary mutual fund value, explicit solutions of the Laplace transforms of the value of the dynamic fund protection are obtained through martingale technique. Moreover, we analyze the value of dynamic fund protections under a generalized regime-switching jump diffusion model. Due to the complexity of Markov regime-switching, the jump process involved, and the nonlinearity, closed-form formulas for dynamic fund protection prices are virtually impossible to obtain. We design a numerical algorithm according to the Markov chain approximation techniques and obtain numerical results of the value of dynamic fund protection.