Asset Pricing in a Semi-Markov Modulated Market with Time-dependent Volatility

Abstract: This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime switching models have been well-documented. This project extends that notion to a class of semi-Markov processes known as age-dependent processes. We also allow for time-dependence in volatility within regimes. We show that the problem of option pricing in such a market is equivalent to solving a certain integral equation.