Conditional Characteristic Functions of Molchan-Golosov Fractional Lévy Processes with Application to Credit Risk

Molchan-Golosov fractional Lévy processes (MG-fLps) are introduced by a multivariate componentwise Molchan-Golosov 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 MG-fLps. 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