Credit value adjustment for credit default swaps via the structural default model

We present a multi-dimensional jump-diffusion version of a structural default model and show how to use it in order to value the credit value adjustment for a credit default swap. We develop novel analytical and numerical methods for solving the corresponding boundary value problem with a special emphasis on the role of negative asset value jumps. Using recent market data, we show that under realistic assumptions credit value adjustment greatly reduces the value of a credit default swap sold by a risky counterparty compared with one sold by a non-risky counterparty. We identify features having the biggest impact on credit value adjustment: namely, default correlation and spread volatility.