xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This presentation is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on replication pricing using shares and credit default swaps, we attribute the P\&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We question the effectiveness of FVA-based risk measures, and call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

Short Bio of the Speaker:

Lixin Wu earned his PhD in applied mathematics from UCLA in 1991 and he is currently a professor at Department of Mathematics at Hong Kong University of Science and Technology. Originally a specialist in numerical analysis, he switched his area of focus to financial mathematics in 1996. Since then, he has some made notable contributions to the area. He co-developed the PDE model for soft barrier options and the finite-state Markov chain model for credit contagion. He is, perhaps, best known in the financial engineering community for a series of works on market models, including an optimal calibration methodology for the standard market model, a market model with square-root volatility, a market model for credit derivatives, a market model for inflation derivatives. He has published a book, “Interest Rate Modeling: Theory and Practice” through Chapman Hall. His recent research interests include a dual-curve SABR market model for post crisis derivatives markets and the topic of xVA.