Volterra equation for pricing and hedging in a regime switching market

It is known that the risk minimizing price of European options in Markovmodulated market satisfies a system of coupled PDE, known as generalized B-S-M PDE. In this paper, another system of equations, which can be categorized as a Volterra integral equations of second kind, are considered. It is shown that this system of integral equations has smooth solution and the solution solves the generalized B-S-M PDE. Apart from showing existence and uniqueness of the PDE, this IE representation helps to develop a new computational method. It enables to compute the European option price and corresponding optimal hedging strategy by using quadrature method.