Pricing Counterparty Risk Including Collateralization, Netting Rules, Re-Hypothecation and Wrong-Way Risk

by Damiano Brigo of Imperial College London,
Agostino Capponi of Purdue University,
Andrea Pallavicini of Imperial College London, and
Vasileios Papatheodorou of Barclays Capital

March 2013

Abstract: This article is concerned with the arbitrage-free valuation of bilateral counterparty risk through stochastic dynamical models when collateral is included, with possible rehypothecation. The payout of claims is modified to account for collateral margining in agreement with International Swap and Derivatives Association (ISDA) documentation. The analysis is specialized to interest-rate and credit derivatives. In particular, credit default swaps are considered to show that a perfect collateralization cannot be achieved under default correlation. Interest rate and credit spread volatilities are fully accounted for, as is the impact of re-hypothecation, collateral margining frequency, and dependencies.

JEL Classification: G13.

AMS Classification: 60J75, 91B70.

Keywords: Counterparty risk, credit valuation adjustment, collateral, margining procedure, credit-spread volatility, default correlation, wrong-way risk, gap risk.

Published in: International Journal of Theoretical and Applied Finance, Vol. 16, No. 2, (March 2013).

Previously titled: Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment including Re-Hypotecation and Netting

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