A General Ratings-based Credit Spread Model
Document ID: 2007-78 (previously 2007/011)
Published on: 1st September 2007
Author: Steven Morrison
The Barrie & Hibbert credit model uses a rating-based approach based around a 1-year transition matrix describing the probability of transition between different credit ratings. In the current implementation of this model, the real-world transition matrix is assumed to be constant through time, while the risk-neutral matrix is derived by adjusting this real-world matrix using a stochastic "market price of credit risk" variable. Thus all stochastic variation in credit spreads is assumed to be a result of changes in investors' required credit risk-premium rather than changes in real-world expected default losses (which are assumed constant) .
This note describes a modification to the B&H credit model in which both the risk-neutral transition matrix and the real-world transition matrix are allowed to vary stochastically. Furthermore, the model introduces additional parameters describing the transformation from the real-world to the risk-neutral transition matrix. There are thus more degrees of freedom which can be used to fit to a larger number of credit spreads simultaneously. This more general model structure includes the current B&H credit model as a special case.
