  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.
