Credit Pricing under Lévy Setting

The CreditGradesTM is a structural model extensively applied for estimating credit spreads. The model is built on the hypothesis that an event of default occurs when the asset value of a firm hits a barrier, which corresponds to the recovery value of the firm's debt. The asset value is described by a Geometric Brownian motion and the barrier is made stochastic to allow instantaneous defaults. It is verified that this model leads to higher short-term spreads than those produced without the barrier volatility. Moreover empirical evidence suggests that the underlying (log)normal distribution does not accurately describe the true behavior of the asset. We propose a new model, in line with the CreditGradesTM model, but under which we assume that the asset price process is described by an exponential of a (non-Brownian) Lévy process. In this way we take into account asymmetry and fat-tail behavior and, by including jumps in the process, we can produce instantaneous default with a deterministic barrier. Under the new model we show how to price a Credit Default Swap and work out the details in the case of a Variance Gamma Lévy process. The valuation is based on the solution of a Partial-Differential Integral Equation and the pricing of digital barrier option under the model considered.

CARIBONI Jessica;  WIM Schoutens; 

2005-12-13

JRC31315