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An inhomogeneous semi-Markov model for the term structure of credit risk spreads

Part of: Markov processes Special processes

Published online by Cambridge University Press:  01 July 2016

Aglaia Vasileiou  and
P.-C. G. Vassiliou
Aglaia Vasileiou*
Affiliation:
UBS Investment Bank, London
P.-C. G. Vassiliou*
Affiliation:
Aristotle University of Thessaloniki
*
∗ Postal address: UBS Investment Bank, 100 Liverpool Street, London EC2M 2RH, UK. Email address: aglaia.vasileiou@ubs.com
∗∗ Postal address: Statistics and Operations Research Section, Mathematics Department, Aristotle University of Thessaloniki, Thessaloniki, 54006, Greece. Email address: vasiliou@math.auth.gr
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Abstract

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We model the evolution of the credit migration of a corporate bond as an inhomogeneous semi-Markov chain. The valuation of a defaultable bond is done with the use of the forward probability of no default up to maturity time. It is proved that, under the forward probability measure, the semi-Markov property is maintained. We find the functional relationships between the forward transition probability sequences and the real-world probability sequences. The stochastic monotonicity properties of the inhomogeneous semi-Markov model, which play a prominent role in these issues, are studied in detail. Finally, we study the term structure of credit spread, provide an algorithm for the estimation of the forward probabilities of transitions under the risk premium assumptions, and present an estimation method for the real-world probability sequences.

Keywords

Credit ratinginhomogeneous semi-Markov chainstochastic monotonicity

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 60K15: Markov renewal processes, semi-Markov processes 60J27: Continuous-time Markov processes on discrete state spaces
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 1 , March 2006 , pp. 171 - 198
Copyright
Copyright © Applied Probability Trust 2006 

Footnotes

This study has been performed in a private capacity and the opinions expressed in it should not be attributed to UBS Investment Bank.

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