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

Abstract

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. The estimation highlights the interaction between market risk (diffusion variance) and credit risk (default arrival) in pricing stock options and credit default swaps. While the credit risk factor dominates credit spreads at long maturities, the stock return volatility also enters credit spreads at short maturities due to positive co-movements between the diffusion variance rate and the default arrival rate. Furthermore, while the diffusion variance rate influences the implied volatility uniformly across moneyness, the impact of the credit risk factor becomes much larger on options at lower strikes. The impact of the credit risk factor on stock options also increases with option maturity. For options maturing in six months, the contribution of the credit risk factor to option pricing is comparable in magnitude to the contribution of the diffusion variance rate.