BCVA AND FUNDING COSTS UNDER DIFFERENT MODELS AND DIFFERENT CREDIT CONTAGION HYPOTHESES

We derive a pricing formula for a derivative with Bilateral Counterparty Credit Risk and Funding Costs. In particular, we compute the relevant pricing adjustments to the risk-free value that need to be considered when including the risk of default of both parties in a bilateral contract, and the cost for the access to liquidity in a credit risky funding environment. When the market is asking for a risk premium to allow for funding provisions, the party has in fact the right to account for this embedded own risk of default and adjust derivative pricing accordingly. Bilateral Credit Value Adjustment is built through the concepts of Adjusted CVA and Adjusted DVA, meaning that the probability of default of one party at a certain point in time is always weigthed by the survival probability of the other party up to that moment. A fundamental assumption is that, at time of default, the credit riskless value of the derivative is considered, in case with an haircut applied in order to account for a proper recovery rate. This work reaches two main innovative results. First of all, a computation methodology for Funding Costs is provided, given that the search for a comprehensive pricing formula is still at dawn either within practioners and academics. Secondly, correlation between default risks of the two parties is included in bilateral counterparty risk pricing, and this is performed through the introduction of common jumps in the process for default intensities.