Pricing Equity Default Swaps under an approximation to the CGMY L\'{e}% vy Model

TL;DR

This paper develops a method to price equity default swaps by approximating the CGMY Lévy process with a phase type distribution, enabling exact first passage time calculations and comparison with credit default swap prices.

Contribution

It introduces a closed-form Wiener-Hopf factorization for a phase type approximation to the CGMY process, facilitating precise first passage time computations for pricing equity default swaps.

Findings

Exact first passage time computation via Laplace inversion.

Pricing of equity default swaps with recovery rate using the model.

Comparison of EDS prices with credit default swap prices.

Abstract

The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY L\'{e}vy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral process for which we infer the first passage times of stock prices to 30% of the price level at contract initiation. These distributions are then used in pricing 50% recovery rate equity default swap (EDS) contracts and the resulting prices are compared with the prices of credit default swaps (CDS). An illustrative analysis is presented for these contracts on Ford and GM.