Abstracts

We develop an arbitrage-free framework for consistent valuation of OTC derivative trades with collateralization, counterparty credit risk, and funding costs. Based on the risk-neutral pricing principle, we derive a general pricing equation where CVA, DVA, and FVA are introduced by simply modifying the payout cash-flows of the deal. Funding risk breaks the bilateral nature of the deal price and makes the pricing problem a highly non-linear and recursive one. This means that FVA is not generally an additive adjustment as commonly assumed by market participants. Our framework addresses common market practices of ISDA governed deals without restrictive assumptions on collateral margin payments and close-out netting rules. In particular, we allow for asymmetric collateral and funding rates. The pricing equation can be cast as a set of iterative equations that can be solved by least-squares Monte Carlo and we propose such a simulation algorithm. Our numerical results confirm that funding risk does have a non-trivial impact on the deal price.