Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation

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. Under this joint specification, we derive tractable pricing solutions for stock options and credit default swaps. We estimate the joint dynamics using stock option prices and credit default swap spreads for four of the most actively traded reference companies. Our estimation shows that for all four reference companies, the default rate is much more persistent than the diffusion variance rate under both the time series measure and the risk-neutral measure. Furthermore, changes in diffusion variance are positively related to contemporaneous and subsequent changes in the default rate. Finally, the estimation reveals that the market price of default arrival risk is negative while the market price of diffusion variance risk is positive, suggesting that for individual stocks, shorting credit default swaps generates a higher average return per unit risk than shorting variance swap contracts. JEL Classification: C13; C51; G12; G13.