Efficient calibration of the shifted square-root diffusion model to credit default swap spreads using asymptotic approximations

TL;DR

This paper introduces a closed-form asymptotic approximation for calibrating the shifted square-root diffusion model to credit default swap spreads, improving efficiency without assuming uncorrelated interest rates and default intensities.

Contribution

We develop a novel asymptotic approximation method for the SSRD model that simplifies calibration to market CDS spreads without the uncorrelated assumption.

Findings

The approximation accurately fits market CDS data.

Calibration process is significantly faster than existing methods.

The method remains robust across different market conditions.

Abstract

We derive a closed-form approximation for the credit default swap (CDS) spread in the two-dimensional shifted square-root diffusion (SSRD) model using asymptotic coefficient expansion technique to approximate solutions of nonlinear partial differential equations. Specifically, we identify the Cauchy problems associated with two terms in the CDS spread formula that lack analytical solutions and derive asymptotic approximations for these terms. Our approximation does not require the assumption of uncorrelated interest rate and default intensity processes as typically required for calibration in the SSRD model. Through several calibration studies using market data on CDS spread, we demonstrate the accuracy and efficiency of our proposed formula.