Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation
In this paper we describe how to include funding and margining costs into a risk-neutral pricing framework for counterparty credit risk. We consider realistic settings and we include in our models the common market practices suggested by the ISDA documentation without assuming restrictive constraints on margining procedures and close-out netting rules. In particular, we allow for asymmetric collateral and funding rates, and exogenous liquidity policies and hedging strategies. Re-hypothecation liquidity risk and close-out amount evaluation issues are also covered. We define a comprehensive pricing framework which allows us to derive earlier results on funding or counterparty risk. Some relevant examples illustrate the non trivial settings needed to derive known facts about discounting curves by starting from a general framework and without resorting to ad hoc hypotheses. Our main result is a bilateral collateralized counterparty valuation adjusted pricing equation, which allows to price a deal while taking into account credit and debt valuation adjustments along with margining and funding costs in a coherent way. We find that the equation has a recursive form, making the introduction of an additive funding valuation adjustment difficult. Yet, we can cast the pricing equation into a set of iterative relationships which can be solved by means of standard least-square Monte Carlo techniques.
References listed on IDEAS
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- Damiano Brigo & Massimo Morini, 2010. "Dangers of Bilateral Counterparty Risk: the fundamental impact of closeout conventions," Papers 1011.3355, arXiv.org.
- Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2009. "Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlations," Papers 0911.3331, arXiv.org, revised Feb 2010.
- Damiano Brigo, 2011. "Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lending," Papers 1111.1331, arXiv.org, revised Jun 2012.
- Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Arbitrage-Free Valuation Of Bilateral Counterparty Risk For Interest-Rate Products: Impact Of Volatilities And Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 773-802.
- Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
- Fries, Christian P., 2010. "Discounting Revisited. Valuations under Funding Costs, Counterparty Risk and Collateralization," MPRA Paper 23082, University Library of Munich, Germany, revised 30 May 2010.
- Damiano Brigo & Cristin Buescu & Massimo Morini, 2011. "Impact of the first to default time on Bilateral CVA," Papers 1106.3496, arXiv.org.