Pricing a Collateralized Derivative Trade with a Funding Value Adjustment

Chadd B. Hunzinger and Coenraad C.A. Labuschagne
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Chadd B. Hunzinger: Rand Merchant Bank, 1 Merchant Place, Cnr Fredman Drive & Rivonia Road, Sandton 2196, South Africa
Coenraad C.A. Labuschagne: Department of Finance and Investment Management, University of Johannesburg, PO Box 524, Aucklandpark 2006, South Africa

JRFM, 2015, vol. 8, issue 1, 1-26

Abstract: 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.

Keywords: collateral; Cox, Ross and Rubinstein model; CSA; FVA; ISDA; Piterbarg model (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2015
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