Conditional characteristic functions of molchan-golosov fractionallévy processes with application to credit risk

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Abstract

Molchan-Golosov fractional Lévy processes (MG-FLPs) are introduced by way of a mul-tivariate 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 predictions concerning multivariate fractional Brownian motion, fractional subordinators, and general fractional stochastic differential equations. Examples are the fractional Lévy Ornstein-Uhlenbeck and Cox-Ingersoll-Ross models. As an application we present a fractional credit model with a long range dependent hazard rate and calculate bond prices. © Applied Probability Trust 2013.

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Fink, H. (2013). Conditional characteristic functions of molchan-golosov fractionallévy processes with application to credit risk. Journal of Applied Probability, 50(4), 983–1005. https://doi.org/10.1239/jap/1389370095

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