A fractional credit model with long range dependent default rate |
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Authors: | Francesca Biagini Holger Fink Claudia Klüppelberg |
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Institution: | 1. Department of Mathematics, Ludwig-Maximilians Universität, 80333 Munich, Germany;2. Center for Mathematical Sciences, Technische Universität München, 85748 Garching, Germany |
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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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Keywords: | primary 60G12 60G51 60H10 60H20 91B70 secondary 60G10 60G99 91B28 |
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