Bayesian Inference for a Structural Credit Risk Model with Stochastic Volatility and Stochastic Interest Rates

Abstract

We develop a novel structural credit risk model that extends the original Merton model by allowing for stochastic interest rates and stochastic volatility. The model is estimated using Bayesian methods implemented via a Markov chain Monte Carlo algorithm, in light of the demonstrable advantages of likelihood approaches and the importance of taking into account parameter uncertainty documented in the literature. We solve the nontrivial computational problem of contingent claim valuation in our set-up by using a Taylor series approximation to the expectation of the claim payoffs under the risk-neutral measure. Finally, we illustrate our model and compare it against the Merton model with real data on a nonfinancial firm (Ford Motor Company) and three financial firms (Citigroup, Goldman Sachs, and Lehman Brothers) during the recent financial crisis. ( JEL: G24, C01)