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.
Highlights
The 2008 credit crisis emphasized the importance of managing counterparty credit risk correctly.One of the ways to mitigate counterparty credit risk is by posting collateral within a derivative trade.Collateral is a borrower’s pledge of specific assets to a lender, to secure repayment of a liability.For exchange traded derivatives, i.e., stock options, counterparty credit risk is reduced, because the two counterparties in the trade are required to post margins to the exchange
funding value adjustment (FVA) is the difference between the price of the derivative and the collateral posted in the trade, multiplied by the difference between growing this amount at the funding rate and the collateral rate
We show that the difference in price of a credit support annex (CSA) trade and a non-CSA trade is a funding value adjustment
Summary
The 2008 credit crisis emphasized the importance of managing counterparty credit risk correctly. One of the ways to mitigate counterparty credit risk is by posting collateral within a derivative trade. The 2008 credit crisis drove home the realization that banks are not risk-free, and banks became unable to borrow at preferential rates This resulted in banks charging a funding value adjustment (FVA). FVA is the difference between the price of the derivative and the collateral posted in the trade, multiplied by the difference between growing this amount at the funding rate and the collateral rate This amount is discounted back to the initial time. A numerical implementation is provided in Section 6, followed by a concluding section
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