Robust Calibration of a Structural-Default Model with Jumps

Abstract

CDS pricing and calibration routines in the context of a structural-default model with discontinuous firm-value process are developed. The firm-value process in the considered framework is modeled as the exponential of a jump-diffusion process with two-sided exponentially distributed jumps. Default probabilities are computed numerically by inverting the Laplace transform of first-passage times. Four Laplace-inversion algorithms, based on three different theoretical inversion formulas, are examined with respect to precision and run-time for the given problem. The resulting pricing engine is fast enough to allow for a calibration of the model to observed term structures of CDS spreads. It is demonstrated that the model explains CDS spreads of various firms with high precision. The calibration routine is developed further to a robust calibration routine that penalized deviations from a given prior. The choice of penalty is motivated by the relative entropy of two probability measures. It is shown that this routine, if applied to the calibration of the model at consecutive days, returns stable model parameters over time without giving up an excellent fit to market quotes.