Journal
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume 123, Issue 4, Pages 1319-1347Publisher
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DOI: 10.1016/j.spa.2012.12.006
Keywords
Credit risk; Defaultable bond; Default rate; 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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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. (C) 2013 Published by Elsevier B.V.
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