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

TL;DR

This paper extends arbitrage-free valuation models for bilateral counterparty risk to include collateral, re-hypotecation, and netting, analyzing their effects on valuation and risk adjustments with interest-rate swaps.

Contribution

It introduces a generalized framework incorporating collateral re-hypotecation and dependencies, enhancing accuracy in counterparty risk valuation models.

Findings

Re-hypotecation significantly impacts counterparty risk adjustments.

Collateral margining frequency influences valuation outcomes.

Dependencies between default times and market factors affect risk measures.

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.