Prediction of fractional convoluted Lévy processes with application to credit risk

نویسنده

  • Holger Fink
چکیده

Fractional convoluted Lévy processes (fcLps) are introduced by a multivariate componentwise Molchan-Gosolov transformation based on an n-dimensional driving Lévy process. Using results of fractional calculus and infinitely divisible distributions we are able to calculate the conditional characteristic function of integrals driven by fcLps. This leads to important prediction results including the case of multivariate fractional Brownian motion, fractional subordinators or general fractional stochastic differential equations. Examples are the fractional Lévy Ornstein-Uhlenbeck or Cox-Ingersoll-Ross model. As an application we present a fractional credit model with a long range dependent hazard rate and calculate bond prices. AMS 2000 Subject Classifications: primary: 60G10, 60G22, 60G51, 60H10, 60H20, 91G40 secondary: 60G15, 91G30, 91G60

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تاریخ انتشار 2010