Linear Credit Risk Models

TL;DR

This paper presents a new class of linear credit risk models where survival processes and derivative prices are linear or polynomial functions of factors, enabling efficient calibration and pricing of credit instruments.

Contribution

It introduces a linear framework for credit risk modeling that allows for flexible default correlation, stochastic interest rates, and efficient polynomial approximation of option prices.

Findings

Models can produce simultaneous defaults and various default correlations.

Efficient polynomial approximation enables fast option pricing.

Calibration demonstrates the model's ability to fit CDS spread data.

Abstract

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the factors. Multi-name models can produce simultaneous defaults, generate positively as well as negatively correlated default intensities, and accommodate stochastic interest rates. A calibration study illustrates the versatility of these models by fitting CDS spread time series. A numerical analysis validates the efficiency of the option price approximation method.