Pricing Equity Default Swaps under the jump to default extended CEV Model

Equity default swaps (EDS) are hybrid credit-equity products that provide a bridge from credit default swaps (CDS) to equity derivatives with barriers. This paper develops an analytical solution to the EDS pricing problem under the Jump-to-Default Extended Constant Elasticity Variance Model (JDCEV) of Carr and Linetsky. Mathematically, we obtain an analytical solution to the first passage time problem for the JDCEV diffusion process with killing (jump to default). In particular, we obtain analytical results for the present values of the protection payoff at the triggering event, periodic premium payments up to the triggering event, and the interest accrued from the previous periodic premium payment up to the triggering event, and determine arbitrage-free equity default swap rates and compare them with corresponding CDS rates.