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

2011/01/20 by Brigo, Damiano, Capponi, Agostino, Pallavicini, Andrea +1
#60J75 #91B70 #Computational Finance (q-fin.CP) #FOS: Economics and business #Pricing of Securities (q-fin.PR) #Risk Management (q-fin.RM)

paper · doi:10.48550/arxiv.1101.3926

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.

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