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

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.