Discounting Revisited. Valuations under Funding Costs, Counterparty Risk and Collateralization
AbstractLooking at the valuation of a swap when funding costs and counterparty risk are neglected (i.e., when there is a unique risk free discounting curve), it is natural to ask "What is the discounting curve of a swap in the presence of funding costs, counterparty risk and/or collateralization". In this note we try to give an answer to this question. The answer depends on who you are and in general it is "There is no such thing as a unique discounting curve (for swaps)." Our approach is somewhat "axiomatic", i.e., we try to make only very few basic assumptions. We shed some light on use of own credit risk in mark-to-market valuations, giving that the mark-to-market value of a portfolio increases when the owner's credibility decreases. We present two different valuations. The first is a mark-to-market valuation which determines the liquidation value of a product. It does, buy construction, exclude any funding cost. The second is a portfolio valuation which determines the replication value of a product including funding costs. We will also consider counterparty risk. If funding costs are presents, i.e., if we value a portfolio by a replication strategy then counterparty risk and funding are tied together: - In addition to the default risk with respect to our exposure we have to consider the loss of a potential funding benefit, i.e., the impact of default on funding. - Buying protection against default has to be funded itself and we account for that. The valuation naturally attributes for wrong-way-risk (i.e., the correlation between counterparty default and counterparty exposure).
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 23082.
Date of creation: 15 May 2010
Date of revision: 30 May 2010
Discounting; Valuation; Counterparty Risk; Collateral; Netting; CVA; DVA; Bond; Swap; Credit Risk; Own Credit Risk; Wrong Way Risk; Liquidity Risk;
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-11 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2011. "Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation," Papers 1112.1521, arXiv.org, revised Dec 2011.
- Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.
- Tomasz R. Bielecki & Marek Rutkowski, 2013. "Valuation and hedging of OTC contracts with funding costs, collateralization and counterparty credit risk: Part 1," Papers 1306.4733, arXiv.org, revised Jun 2013.
- Nicola Moreni & Andrea Pallavicini, 2010. "Parsimonious HJM Modelling for Multiple Yield-Curve Dynamics," Papers 1011.0828, arXiv.org.
- Marco Bianchetti & Mattia Carlicchi, 2013. "Markets Evolution After the Credit Crunch," Papers 1301.7078, arXiv.org.
- Marco, Bianchetti, 2011. "The Zeeman Effect in Finance: Libor Spectroscopy and Basis Risk Management," MPRA Paper 42247, University Library of Munich, Germany, revised 27 Oct 2012.
- Damiano Brigo & Qing Liu & Andrea Pallavicini & David Sloth, 2014. "Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes," Papers 1404.7314, arXiv.org.
- Lixin Wu, 2013. "CVA and FVA to Derivatives Trades Collateralized by Cash," Papers 1302.0465, arXiv.org.
- Damiano Brigo & Andrea Pallavicini, 2013. "CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?," Papers 1312.0128, arXiv.org, revised Dec 2013.
- Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2012. "Funding, Collateral and Hedging: uncovering the mechanics and the subtleties of funding valuation adjustments," Papers 1210.3811, arXiv.org, revised Dec 2012.
- Bianchetti, Marco & Carlicchi, Mattia, 2012. "Markets Evolution After the Credit Crunch," MPRA Paper 44023, University Library of Munich, Germany.
- Marco, Bianchetti & Mattia, Carlicchi, 2012. "Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR," MPRA Paper 42248, University Library of Munich, Germany.
- Marco Bianchetti, 2012. "The Zeeman Effect in Finance: Libor Spectroscopy and Basis Risk Management," Papers 1210.7329, arXiv.org.
- 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.
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