Pricing First-to-Default under Factor Copula Model with Stochastic Recovery

A basket default swaps is a credit derivative whose underlying assets are usually bond. It has been proved that the realized recovery value of a defaultable bond can cover a large spectrum of values both across within levels of seniority and security and correlates negatively with default probability. However, recovery rate is mostly assumed as constant or exogenous, which can not capture the market evolution and may come to a wrong conclusion in pricing process. To solve above problems, this paper first introduces spot recovery into the pricing of first-to-default basket, a simplest type of basket default swaps. Considering two forms of spot recovery, the paper extends the standard Gaussian copula model to discuss the pricing of the contract respectively. Comparative numerical experiments reflect that recovery rate has an important effect on pricing and the introduction of stochastic recovery is very necessary.