An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model

TL;DR

This paper introduces a semi-analytical formula for pricing default swaptions within the SSRJD model, enabling efficient calibration and consistent hedging of credit derivatives, while capturing realistic volatility smiles.

Contribution

The paper derives an exact semi-analytical pricing formula for default swaptions in the SSRJD model, enhancing computational efficiency and calibration accuracy.

Findings

The model fits observed volatility smiles well.

Calibration to CDS and a few swaptions is effective.

Pricing is faster and more accurate than previous methods.

Abstract

We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consistently. We show with numerical experiments that the model implies plausible volatility smiles.