Statistical Inference for Time-changed Brownian Motion Credit Risk Models

TL;DR

This paper introduces a new statistical inference approach for time-changed Brownian motion credit risk models, demonstrating their superior performance over traditional models on real CDS data.

Contribution

It develops an efficient inference method for TCBM credit models using the 'first passage of the second kind' and compares two TCBM variants to the Black-Cox model.

Findings

TCBM models outperform Black-Cox in fitting CDS data

Two TCBM variants show significant improvement with minimal added complexity

Efficient inference method enables practical application of TCBM models

Abstract

We consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM) with the time-change taken to be an independent increasing process. Following the approach of Black and Cox, one defines the time of default to be the first passage time for the log-leverage ratio to cross the level zero. Rather than adopt the classical notion of first passage, with its associated numerical challenges, we accept an alternative notion applicable for TCBMs called "first passage of the second kind". We demonstrate how statistical inference can be efficiently implemented in this new class of models. This allows us to compare the performance of two versions of TCBMs, the variance gamma (VG) model and the exponential jump model (EXP), to the Black-Cox model. When applied to a 4.5 year long data set of weekly credit default swap (CDS) quotes for Ford Motor Co, the conclusion is that the two TCBM models, with essentially one extra parameter, can significantly outperform the classic Black-Cox model.