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Credit Risk, Market Sentiment and Randomly-Timed Default

In: Financial Informatics An Information-Based Approach to Asset Pricing

Author

Listed:
  • Dorje C. Brody
  • Lane P. Hughston
  • Andrea Macrina

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.

Suggested Citation

  • Dorje C. Brody & Lane P. Hughston & Andrea Macrina, 2022. "Credit Risk, Market Sentiment and Randomly-Timed Default," World Scientific Book Chapters, in: Dorje Brody & Lane Hughston & Andrea Macrina (ed.), Financial Informatics An Information-Based Approach to Asset Pricing, chapter 6, pages 113-126, World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789811246494_0006
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    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;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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