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A fractional credit model with long range dependent default rate

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  • Biagini, Francesca
  • Fink, Holger
  • Klüppelberg, Claudia

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.

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  • Biagini, Francesca & Fink, Holger & Klüppelberg, Claudia, 2013. "A fractional credit model with long range dependent default rate," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1319-1347.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:4:p:1319-1347
    DOI: 10.1016/j.spa.2012.12.006
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    References listed on IDEAS

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