A fractional credit model with long range dependent default rate

Biagini, Francesca ; Fink, Holger and Klüppelberg, Claudia (2013): A fractional credit model with long range dependent default rate. In: Stochastic Processes and their Applications, Vol. 123, No. 4: pp. 1319-1347

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 03044149
• Language: English