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This paper generalizes the framework for arbitrage-free valuation ofbilateral counterparty risk to the case where collateral is included, withpossible re-hypotecation. We analyze how the payout of claims is modified whencollateral 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 andthe counterparty and the underlying portfolio risk factors. We usearbitrage-free stochastic dynamical models, including also the effect ofinterest rate and credit spread volatilities. The impact of re-hypotecation, ofcollateral margining frequency and of dependencies on the bilateralcounterparty risk adjustment is illustrated with a numerical example.

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