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

TL;DR

This paper introduces a tractable structural model for credit default swap calibration that accurately captures default probabilities and can be used for efficient counterparty risk valuation in equity swaps.

Contribution

It develops a new structural model with analytical default probabilities and demonstrates its calibration to market CDS quotes, enabling practical credit and counterparty risk pricing.

Findings

Model provides analytical default probabilities based on dynamics parameters.

Calibration aligns the model with market CDS quotes effectively.

Application to equity swap counterparty risk pricing shows practical advantages.

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.