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

Part of: Mathematical finance Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  30 January 2018

Holger Fink
Holger Fink*
Affiliation:
Technische Universität München
*
∗ Postal address: Center for Mathematical Sciences, Technische Universität München, Parkring 13, D-85748 Garching, Germany. Email address: [email protected]
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Abstract

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Molchan-Golosov fractional Lévy processes (MG-FLPs) are introduced by way of 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 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.

Keywords

Conditional characteristic functionmacroeconomic variables processlong-range dependencefractional Brownian motionfractional Lévy processprediction

MSC classification

Primary: 60G10: Stationary processes 60G22: Fractional processes, including fractional Brownian motion 60G51: Processes with independent increments; L'evy processes 60H10: Stochastic ordinary differential equations 60H20: Stochastic integral equations 91G40: Credit risk
Secondary: 60G15: Gaussian processes 91G30: Interest rates (stochastic models) 91G60: Numerical methods (including Monte Carlo methods)
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 4 , December 2013 , pp. 983 - 1005
Copyright
© Applied Probability Trust 

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