Option Pricing Using a Regime Switching Stochastic Discount Factor

The paper discusses the pricing of derivatives using a stochastic discount factor modeled as a regime switching geometric Brownian motion. The regime switching is driven by a continuous time hidden Markov chain representing changes in the economy. The stochastic discount factor enables to define a risk neutral measure. We model the stock price as discounted future dividends driven by the same continuous time Markov chain. The stochastic discount factor is used to price European style options under the historical probability measure. The introduction of occupation times of the Markov chain and the corresponding conditional characteristic function allows the evaluation of the expected value of European type claims. The option price is given as a semi-analytical form using the Fourier transform.