In this thesis we discuss option pricing and hedging under regime switching models. To the standard model we add jumps of various types. In particular, we consider a jump that is synchronous with a change in the regime state. Thus, for example, we can define a process such that the stock price moves to a high volatility state and simultaneously has a large downward jump in returns. This type of model is consistent with market experience. We derive the compensator for our synchronous jumps and price options on such a price process using Fourier transforms. We also test the model on S&P futures options and show that it performs significantly better than a jump diffusion model. Furthermore, we look at the problem of hedging options under finitely many regime states and with finitely many possible jump sizes. We find risk-free hedge portfolios using the risk-free asset, the underlying asset, and finitely many options. Our risk-free trading strategy is consistent with any equivalent martingale measure, and so does not in itself specify which measure should be used to price options.

In this thesis we discuss option pricing and hedging under regime switching models. To the standard model we add jumps of various types. In particular, we consider a jump that is synchronous with a change in the regime state. Thus, for example, we can define a process such that the stock price moves to a high volatility state and simultaneously has a large downward jump in returns. This type of model is consistent with market experience. We derive the compensator for our synchronous jumps and price options on such a price process using Fourier transforms. We also test the model on S&P futures options and show that it performs significantly better than a jump diffusion model. Furthermore, we look at the problem of hedging options under finitely many regime states and with finitely many possible jump sizes. We find risk-free hedge portfolios using the risk-free asset, the underlying asset, and finitely many options. Our risk-free trading strategy is consistent with any equivalent martingale measure, and so does not in itself specify which measure should be used to price options.