Approximation to Default Swaptions in Reduced-Form Framework: Calibration and Comparison of Intensity Dynamics

Abstract

We develop an approximation to pricing default swaptions in general intensity models which yields a fast and accurate analytic/semi-analytic solution to the valuation problem. We consider several dynamics for intensity and derive 'extended transforms' for inverse Gaussian- and tempered stable Ornstein-Uhlenbeck processes. Having convenient pricing formulae, we are able to provide the first account of calibration of intensity models to credit options. Further, we extend the model by adding a shift, thus resulting in a tractable model that keeps the intensity positive, matches closely implied volatilities of default swaptions, and fits exactly the CDS spreads.