ARBITRAGE-FREE VALUATION OF BILATERAL COUNTERPARTY RISK FOR INTEREST-RATE PRODUCTS: IMPACT OF VOLATILITIES AND CORRELATIONS

Damiano Brigo (), Andrea Pallavicini () and Vasileios Papatheodorou ()
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Andrea Pallavicini: Financial Engineering, Mediobanca, Piazzetta Cuccia 1, Milano, 20121, Italy
Vasileios Papatheodorou: Barclays Capital, London, EC3P 3AH, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 06, pages 773-802

Abstract: The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustment (CVA) 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, 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 close-out netting rules in our examples, although other agreements, such as periodic margining or collateral posting, 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 (search for similar items in EconPapers)
Date: 2011
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