Credit Risk, Market Sentiment and Randomly-Timed Default

Dorje C. Brody, Lane P. Hughston and Andrea Macrina

Chapter 6 in Financial Informatics:An Information-Based Approach to Asset Pricing, 2022, pp 113-126 from World Scientific Publishing Co. Pte. Ltd.

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. Themarket 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.

Keywords: Financial Mathematics; Mathematical Finance; Financial Markets; Informatics; Asset Pricing; Asset Price Dynamics; Stochastic Modelling; Information Process; Information Flow; Signal Processing; Filtration; Brownian Motion; Brownian Bridge; Change of Measure; Stochastic Volatility; Credit Risk; Default; Equities; Bonds; Collateralized Debt Obligation; Discount Bond; Lévy Process; Lévy Random Bridge; Lévy Information; Gamma Bridge; Markov Bridge; Pricing Kernel; Option Pricing; Informed Traders; Insurance; Reinsurance; Insurance Claims; Bond Portfolio; Heat Kernel; Markov Process; Variance Gamma Process; Ornstein-Uhlenbeck Process; Commodities; Fake News (search for similar items in EconPapers)
JEL-codes: C02 C6 G12 (search for similar items in EconPapers)
Date: 2022
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