Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment Including Re-Hypotecation and Netting

39 Pages Posted: 20 Jan 2011

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Agostino Capponi

Columbia University

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Vasileios Papatheodorou

Barclays Capital

Date Written: January 20, 2011

Abstract

This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize our analysis to interest-rate swaps as underlying portfolio, and allow for mutual dependences between the default times of the investor and the counterparty and the underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models, including also the effect of interest rate and credit spread volatilities. The impact of re-hypotecation, of collateral margining frequency and of dependencies on the bilateral counterparty risk adjustment is illustrated with a numerical example.

Keywords: Counterparty Risk, Bilateral CVA, Collateral Management, Collateral Re-Hypothecation, Close-Out Amount, Margining Procedure, Netting Rules, Hybrid Products, Correlation, Risk Neutral Valuation, Default Risk, Interest Rate Models, Default Intensity Models

JEL Classification: G13

Suggested Citation

Brigo, Damiano and Capponi, Agostino and Pallavicini, Andrea and Papatheodorou, Vasileios, Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment Including Re-Hypotecation and Netting (January 20, 2011). Available at SSRN: https://ssrn.com/abstract=1744101 or http://dx.doi.org/10.2139/ssrn.1744101

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

Agostino Capponi

Columbia University ( email )

S. W. Mudd Building
New York, NY 10027
United States

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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