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Modelling Credit Risk in the Jump Threshold Framework

Modelling Credit Risk in the Jump Threshold Framework The jump threshold framework for credit risk modelling developed by Garreau and Kercheval enjoys the advantages of both structural- and reduced-form models. In their article, the focus is on multidimensional default dependence, under the assumptions that stock prices follow an exponential Lévy process (i.i.d. log returns) and that interest rates and stock volatility are constant. Explicit formulas for default time distributions and basket credit default swap (CDS) prices are obtained when the default threshold is deterministic, but only in terms of expectations when the default threshold is stochastic. In this article, we restrict attention to the one-dimensional, single-name case in order to obtain explicit closed-form solutions for the default time distribution when the default threshold, interest rate and volatility are all stochastic. When the interest rate and volatility processes are affine diffusions and the stochastic default threshold is properly chosen, we provide explicit formulas for the default time distribution, prices of defaultable bonds and CDS premia. The main idea is to make use of the Duffie–Pan–Singleton method of evaluating expectations of exponential integrals of affine diffusions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Modelling Credit Risk in the Jump Threshold Framework

Chiu, Chun-Yuan; Kercheval, Alec
Applied Mathematical Finance , Volume 25 (5-6): 23 – Nov 2, 2018
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Modelling Credit Risk in the Jump Threshold Framework

Abstract

The jump threshold framework for credit risk modelling developed by Garreau and Kercheval enjoys the advantages of both structural- and reduced-form models. In their article, the focus is on multidimensional default dependence, under the assumptions that stock prices follow an exponential Lévy process (i.i.d. log returns) and that interest rates and stock volatility are constant. Explicit formulas for default time distributions and basket credit default swap (CDS) prices are obtained...
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Publisher
Taylor & Francis
Copyright
© 2018 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2018.1465349
Publisher site
See Article on Publisher Site

Abstract

The jump threshold framework for credit risk modelling developed by Garreau and Kercheval enjoys the advantages of both structural- and reduced-form models. In their article, the focus is on multidimensional default dependence, under the assumptions that stock prices follow an exponential Lévy process (i.i.d. log returns) and that interest rates and stock volatility are constant. Explicit formulas for default time distributions and basket credit default swap (CDS) prices are obtained when the default threshold is deterministic, but only in terms of expectations when the default threshold is stochastic. In this article, we restrict attention to the one-dimensional, single-name case in order to obtain explicit closed-form solutions for the default time distribution when the default threshold, interest rate and volatility are all stochastic. When the interest rate and volatility processes are affine diffusions and the stochastic default threshold is properly chosen, we provide explicit formulas for the default time distribution, prices of defaultable bonds and CDS premia. The main idea is to make use of the Duffie–Pan–Singleton method of evaluating expectations of exponential integrals of affine diffusions.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Nov 2, 2018

Keywords: Credit risk; Lévy processes; affine processes

References

  • Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options
  • Valuing Corporate Securities: Some Effects of Bond Indenture Provisions
  • Transform Analysis and Asset Pricing for Affine Jump-Diffusions
  • Affine Point Processes and Portfolio Credit Risk
  • Two Singular Diffusion Problems
  • A Structural Jump Threshold Framework for Credit Risk
  • Pricing Derivatives on Financial Securities Subject to Credit Risk