FVA and CVA for Collateralized Trades with Re-hypothecation

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• 作者：Chunhong Li and Lixin Wu
• 刊名：Wilmott
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：2016
• 期：83
• 页码：50-59
• 全文大小：3598K
• ISSN：1541-8286

文摘

Through this article we join the ongoing “FVA debate” with a strategy of bilateral replication, which enables us to price derivatives trades and identify XVAs, including the FVA. We let the issuer and buyer replicate the derivative's payoffs and the loss given the issuer's default, respectively, while taking into account the costs of funding for replication and collateral posting in the replicating portfolios. The strategy leads to a PDE for the economic value of the derivative, and the PDE also implies the unique risk-neutral pricing measure. A proper solution of the PDE gives rise to a decomposition of the derivatives economic value into the risk-free value of the derivative, the credit valuation adjustment, and the funding valuation adjustment. We show that in general the economic values to the two trading parties are different, due to the different funding needs and funding costs, and both parties may have to bear some funding costs in order to strike a deal. When the premium for buying a derivatives asset is also funded, then to the buyer the trade actually consists of two transactions: borrowing and purchasing, and the FVA for the trade can be obtained by separately evaluating the FVAs of the two transactions.