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

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