Credit Default Swap Calibration and Equity Swap Valuation Under Counterparty Risk with a Tractable Structural Model

Abstract

In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We essentially show how to use structural models with a calibration capability that is typical of the much more tractable credit-spread based intensity models.

We apply the structural model to a concrete calibration case and observe what happens to the calibrated dynamics when the CDS-implied credit quality deteriorates as the firm approaches default. Finally we provide a typical example of a case where the calibrated structural model can be used for credit pricing in a much more convenient way than a calibrated reduced form model: The pricing of counterparty risk in an equity swap.

Keywords: Credit Derivatives, Structural Models, Black Cox Model, Credit Default Swaps, Calibration, Analytical Tractability, Monte Carlo Simulation, Equity Swaps, Counterparty Risk, Barrier Options

JEL Classification: G13