CVA AND FVA TO DERIVATIVES TRADES COLLATERALIZED BY CASH

Lixin Wu ()
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Lixin Wu: Department of Mathematics, University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 05, 1-22

Abstract: In this paper, we consider replication pricing of derivatives that are partially collateralized by cash. We let issuer replicate the derivatives payout using shares and cash, and let buyer replicate the loss given the counterparty default using credit default swaps. The costs of funding for replication and collateral posting are taken into account in the pricing process. A partial differential equation (PDE) for the derivatives price is established, and its solution is provided in a Feynman–Kac formula, which decomposes the derivatives value into the risk-free value of the derivative plus credit valuation adjustment (CVA) and funding valuation adjustment (FVA). For most derivatives, we show that CVAs can be evaluated analytically or semi-analytically, while FVAs as well as the derivatives values can be solved recursively through numerical procedures due to their interdependence. In numerical demonstrations, continuous and discrete margin revisions are considered, respectively, for an equity call option and a vanilla interest-rate swap.

Keywords: Counterparty default risk; credit valuation adjustment; funding valuation adjustment; partial differential equation (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219024915500351

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