Pricing Credit Default Swaps Under Fractal Structural Model

Abstract

This paper considers a credit default swaps (CDS) pricing under a fractal structural model, where the asset value is generated by a geometric fractional Brownian motion. In contrast to the classical structural model which is based on the geometric standard Brownian motion, the fractal one with long-dependent and self-similar behaviors matches the real asset data better. We analyze the ratio of a firm's asset value to the threshold level via the fractal structural model, and derive the first-to-default probability of the firm. Based on this, we obtain the CDS pricing formula, and also present the estimation algorithm for associated parameters and some numerical computations.