We provide a model of hedge fund securing financing from a prime broker where deterioration in collateral value exacerbates counterparty risk and liquidity risk for the prime broker due to strategic actions of hedge funds. Costs of liquidity insurance and enforcing contracts determine hedge fund leverage. The model provides several new insights. First, it uncovers a new channel for funding liquidity that can explain why illiquid funds fare worse in times of stress and why better governed funds fared better during the financial crisis. Second, the model provides a new testable hypothesis that systematic or idiosyncratic shocks to fundamentals of bank holding companies may spillover to connected hedge funds through internal capital markets. It also offers an identification strategy to distinguish between possible competing hypotheses. Third, strong governance at hedge funds may reduce incentives to invest in profitable opportunities. Fourth, banking reforms such as Supplementary Leverage Ratio, Liquidity Coverage Ratio and Standing Repo Facility intended to improve resilience of banks may also make hedge funds less vulnerable to shocks in the banking sector. Fifth, the model offers a possible reconciliation for the mixed evidence on the impact of leverage on hedge fund survival documented in the literature.

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.