March 19, 2005
We propose a dynamically consistent framework that allows joint valuation and estimation of stock options and credit default swaps written on the same reference company. We model default as controlled by a Poisson process with a stochastic default arrival rate. When default occurs, the stock price drops to zero. Prior to default, the stock price follows a continuous process with stochastic volatility. The instantaneous default rate and instantaneous diffusion variance rate follow a bivariate continuous Markov process, with its dynamics specified to capture the empirical evidence on stock option prices and credit default swap spreads.