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DISCRETE CREDIT BARRIER MODELS CLAUDIO ALBANESE AND OLIVER X. CHEN
 

Summary: DISCRETE CREDIT BARRIER MODELS
CLAUDIO ALBANESE AND OLIVER X. CHEN
Abstract. The model introduced in this article is designed to provide a consistent represen-
tation for both the real-world and pricing measures for the credit process. We find that good
agreement with historical and market data can be achieved across all credit ratings simulta-
neously. The model is characterized by an underlying stochastic process that takes on values
on a discrete lattice and represents credit quality. Rating transitions are associated to barrier
crossings and default events are associated with an absorbing state. The stochastic process
has state dependent volatility and jumps which are estimated by using empirical migration
and default rates. A risk-neutralizing drift is estimated to consistently match the average
spread curves corresponding to all the various ratings.
1. Introduction
The credit model developed in this paper is specified with respect to aggregate data. That
is, the credit quality of individual obligors is modelled within the wider context of all firms that
issue debt. There are various advantages to working in the aggregate approach: the model is
cohesive and intuitive, insight into the individual processes can be gained when examined in the
wider context, and a larger class of derivative contracts can be priced.
In the statistical measure the model is calibrated to fit historical average rating transition and
default probabilities. The underlying stochastic process in the model represents credit quality
and rating transitions are associated to barrier crossings. While the volatility structure is shared

  

Source: Albanese, Claudio - Department of Mathematics, King's College London

 

Collections: Mathematics