This paper consists of two parts. In the first part, through the calculation of “binomial correlation measure”, we suggest that from the perspective of default correlation it would be better to use structural approach rather than reduced form approach for pricing derivatives with two counterparties and its CVA calculation unless default intensities follow jump-diffusion process in latter one. In the second part, we derive the pricing model for CDS with counterparty risk and its CVA calculation by Black-Cox first passage time model in structural approach. Different from most of the previous paper our recovery is based on the CDS with counterparty risk, so the pricing model is a boundary-value problem of fully-nonlinear PDE. To solve it, we introduce an approximation problem by penalty model in reduced form approach by assuming an incentive function. Also finite element method and iteration approach are used. The numerical results show the convergence of approximation problem, iteration problem and finite element method, a comparison between CVA with different recovery rules and also the impact of wrong-way risk and right-way risk on CVA.

In this article, we consider a regulated market and explore the default events. By using a so-called reflected Ornstein-Uhlenbeck process with two-sided barriers to formulate the price dynamics, we derive the expression on the conditional default probability. In the cases of single observation and multiple observations, the conditional default probabilities are explicitly expressed in terms of the inverse Laplace transforms. Finally, we present a numerical simulation associated with the conditional default probability.