
 Credit Default Swaps with Counterparty Risk: A Calibrated Markov Model by Michael Walker of the University of Toronto March 28, 2005 Abstract: This article describes a continuoustime Markov approach to the risk neutral pricing of a credit default swap with counterparty risk. The key parameters in the approach are the transition rates, which naturally incorporate the ideas of contagion. Correlation (which is timedependent) is a derived quantity, which results from contagion. An expansion in powers of a small parameter (a riskneutral default probability) allows analytic formulae to be obtained for all relevant quantities. Thus, the problem of the calibration of the model to the market prices of the bonds of the reference entity and the counterparty, as well as to the credit default swap spreads of the reference entity (which are independent of the bond spreads in the case of counterparty risk), is solved. This is done with the help of analytic results for the spread of a credit default swap with counterparty risk, as well as for other derivative prices. A comparison with results produced by the marketstandard Gaussian copula approach indicates that the marketstandard approach could be significantly improved by allowing the copula correlation coefficient to be timedependent. Keywords: credit default swap, counterparty risk, Markov model, contagion, Gaussian copula. Published in: Journal of Credit Risk, Vol. 2, No. 1, (Spring 2006), pp. 3149. Books Referenced in this paper: (what is this?) 