A fractional credit model with long range dependent default rate

Francesca Biagini, Holger Fink, Claudia Klüppelberg

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we start with a bivariate fractional Vasicek model for short and default rate, which allows for fairly explicit calculations. We calculate the prices of corresponding defaultable zero-coupon bonds by invoking Wick calculus. Applying a Girsanov theorem we derive today's prices of European calls and compare our results to the classical Brownian model.

Original languageEnglish
Pages (from-to)1319-1347
Number of pages29
JournalStochastic Processes and their Applications
Volume123
Issue number4
DOIs
StatePublished - 2013

Keywords

  • Credit risk
  • Default rate
  • Defaultable bond
  • Derivatives pricing
  • Fractional Brownian motion
  • Fractional Vasicek model
  • Hazard rate
  • Interest rate
  • Long range dependence
  • Macroeconomic variables process
  • Option pricing
  • Prediction
  • Short rate
  • Wick product

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