The Dynamic BCCVA Of The Bilateral Counterparty Risk In The Density Model

In this paper, we talk about the credit risk model, in which both investors and counterparties might default.We assume that there exists two collateral accounts, and assume that default times of investors and counterparties satisfy the density hypothesis. Moreover, there exists contagion between their default times, and the contagion will be re?ected in the density process.We mainly discuss Bilateral Collateralized Credit Valuation Adjustment(i.e. BCCVA). We separate BCCVA price into three parts, and describe each part with ?nancial implications, then we use the backward stochastic differential equations(i.e. BSDEs)to describe the dynamic of each part explicitly.As an example, we discuss the ’double’ Cox model, in which the BSDEs becomes more simple.