Pricing a collateralized derivative trade with a funding value adjustment - Chadd B. Hunzinger; Coenraad C. A. Labuschagne (Journal of Risk and Financial Management, 2015)
The 2008 credit crisis changed the manner in which derivative trades are conducted. One of these changes is the posting of collateral in a trade to mitigate the counterparty credit risk. Another is the realization that banks are not risk-free and, as a result, cannot borrow at the risk-free rate any longer. The latter led banks to introduced the controversial adjustment to derivative prices, known as a funding value adjustment (FVA), which is interlinked with the posting of collateral. In this paper, we extend the Cox, Ross and Rubinstein (CRR) discrete-time model to include collateral and FVA. We prove that this derived model is a discrete analogue of Piterbarg's partial differential equation (PDE), which describes the price of a collateralized derivative. The fact that the two models coincide is also verified by numerical implementation of the results that we obtain. Full article
Keywords: C51; G12; C53; G01; 330; collateral; Cox; Ross and Rubinstein model; CSA; FVA; ISDA; Piterbarg model