Bilateral Counterparty Risk Valuation for Interest-Rate Products: Impact of Volatilities and Correlations

23 Pages Posted: 17 Nov 2009 Last revised: 4 Feb 2010

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Vasileios Papatheodorou

Barclays Capital

Date Written: November 17, 2009

Abstract

The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, as developed more in detail in Brigo and Capponi (2008), including the default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net present value of the contract at the relevant default times. We allow for correlation between the default times of the investor and counterparty, and for correlation of each with the underlying risk factor, namely interest rates. We also analyze the often neglected impact of credit spread volatility. We include Netting in our examples, although other agreements such as Margining and Collateral are left for future work.

Keywords: Counterparty Risk, Arbitrage-Free Credit Valuation Adjustment, Interest Rate Swaps, Interest Rate Derivatives, Credit Valuation Adjustment, Bilateral Risk, Credit Spread Volatility, Default Correlation, Stochastic Intensity, Short Rate Models, Copula Functions, Wrong Way Risk

JEL Classification: C15, C63, C65, G12, G13

Suggested Citation

Brigo, Damiano and Pallavicini, Andrea and Papatheodorou, Vasileios, Bilateral Counterparty Risk Valuation for Interest-Rate Products: Impact of Volatilities and Correlations (November 17, 2009). Available at SSRN: https://ssrn.com/abstract=1507845 or http://dx.doi.org/10.2139/ssrn.1507845

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Andrea Pallavicini (Contact Author)

Banca IMI ( email )

Largo Mattioli 3
Milan, MI 20121
Italy
+39 02 7261 (Phone)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

Vasileios Papatheodorou

Barclays Capital ( email )

London
United Kingdom

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