Abstract
We propose a model for the credit markets in which the random default times of bonds are assumed to be given as functions of one or more independent “market factors”. Market participants are assumed to have partial information about each of the market factors, represented by the values of a set of market factor information processes. The market filtration is taken to be generated jointly by the various information processes and by the default indicator processes of the various bonds. The value of a discount bond is obtained by taking the discounted expectation of the value of the default indicator function at the maturity of the bond, conditional on the information provided by the market filtration. Explicit expressions are derived for the bond price processes and the associated default hazard rates. The latter are not given a priori as part of the model but rather are deduced and shown to be functions of the values of the information processes. Thus the “perceived” hazard rates, based on the available information, determine bond prices, and as perceptions change so do the prices. In conclusion, explicit expressions are derived for options on discount bonds, the values of which also fluctuate in line with the vicissitudes of market sentiment.
MSC (2010): 91G40, 93E11, 60G40, 94Axx
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Acknowledgements
The authors are grateful to seminar participants at the Workshop on Incomplete Information on Mathematical Finance, Chemnitz (June 2009), the Kyoto Workshop on Mathematical Finance and Related Topics in Economics and Engineering (August 2009), Quant Congress Europe, London (November 2009), King’s College London (December 2009), Hitotsubashi University, Tokyo (February 2010) and Hiroshima University (February 2010) for helpful comments and suggestions. Part of this work was carried out while LPH was visiting the Aspen Center for Physics (September 2009), and Kyoto University (August and October 2009). DCB and LPH thank HSBC, Lloyds TSB, Shell International, and Yahoo Japan for research support.
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Brody, D.C., Hughston, L.P., Macrina, A. (2011). Credit Risk, Market Sentiment and Randomly-Timed Default. In: Crisan, D. (eds) Stochastic Analysis 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15358-7_13
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DOI: https://doi.org/10.1007/978-3-642-15358-7_13
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