Semi-Analytical Pricing for General Default Intensity Models

2026-06-19

AI Summary

This study addresses the computational complexity and insufficient accuracy in pricing credit derivatives under general intensity-based models by proposing a semi-analytical approximation framework rooted in path integral methods. The approach jointly models default intensity using the Black–Karasinski model and foreign exchange devaluation dynamics, achieving high accuracy and computational efficiency even in high-volatility and long-maturity regimes. Compared to conventional numerical techniques, the framework substantially enhances pricing performance for products such as Quanto CDS and is readily applicable to practical contexts like XVA calculations. The method thus offers both theoretical novelty and strong engineering utility.

Abstract

Using the path-integral formalism, we develop an accurate and easy-to-compute semi-analytical approximation for a general class of {default intensity} models. We illustrate the accuracy of the method by presenting results for the Black-Karasinski model for which the proposed approximation provides remarkably accurate results, even in regimes of high volatility and multi-year time horizons. The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of applications in econometrics and derivatives pricing, including the computation of XVA for credit products. As a practical example, we consider the pricing of a quanto Credit Default Swap (CDS) under stochastic intensity of default and an FX devaluation model.

Problem

• default intensity
• derivatives pricing
• semi-analytical approximation
• XVA
• Credit Default Swap

Innovation

• semi-analytical approximation
• default intensity models
• path-integral formalism
• XVA pricing
• quanto CDS