Risk-Minimizing Hedging of Counterparty Risk

TL;DR

This paper develops a dynamic hedging strategy for counterparty risk in credit derivatives using a novel credit model with interacting default intensities, providing explicit solutions for risk minimization.

Contribution

It introduces a new credit model with interacting intensities and derives a closed-form risk-minimizing hedging strategy using nonlinear recursive systems.

Findings

Closed-form risk-minimizing strategies for credit derivatives

Application to credit swaps, risky bonds, and first-to-default claims

Empirically driven model with interacting default intensities

Abstract

We study dynamic hedging of counterparty risk for a portfolio of credit derivatives. Our empirically driven credit model consists of interacting default intensities which ramp up and then decay after the occurrence of credit events. Using the Galtchouk-Kunita-Watanabe decomposition of the counterparty risk price payment stream, we recover a closed-form representation for the risk minimizing strategy in terms of classical solutions to nonlinear recursive systems of Cauchy problems. We discuss applications of our framework to the most prominent class of credit derivatives, including credit swap and risky bond portfolios, as well as first-to-default claims.