The Wiener–Hopf factorization is obtained in closed form for a phase-type approximation to the CGMY Lévy 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 contracts and the resulting prices are compared with the prices of credit default swaps. An illustrative analysis is presented for these contracts on Ford and GM.