Probability for transition of business cycle and pricing of options with correlated credit risk

Abstract

In this paper we propose the transition probability of business cycle for the pricing of options with credit risk. In order to describe business cycles of markets, the regime switching model is considered. We provide the probability density functions of the occupation time of the high volatility regime via Laplace transforms. Using these functions we derive the analytic valuation formulae for options with correlated credit risk and business cycle. We also illustrate the important properties of options with numerical graphs.