A fractional credit model with long range dependent default rate

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• 作者：Francesca Biagini^a ; ^{biagini@math.lmu.de} ; Holger Fink^b ; ^{fink@ma.tum.de} ; ; Claudia Klü ; ppelberg^b ; ^{cklu@ma.tum.de}
• 关键词：primary ; 60G12 ; 60G51 ; 60H10 ; 60H20 ; 91B70 ; secondary ; 60G10 ; 60G99 ; 91B28
• 刊名：Stochastic Processes and their Applications
• 出版年：2013
• 出版时间：April, 2013
• 年：2013
• 卷：123
• 期：4
• 页码：1319-1347
• 全文大小：314 K

文摘

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.