Journal of Applied Probability

Conditional characteristic functions of Molchan-Golosov fractional Lévy processes with application to credit risk

Holger Fink

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 50, Number 4 (2013), 983-1005.

Dates
First available in Project Euclid: 10 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1389370095

Digital Object Identifier
doi:10.1239/jap/1389370095

Mathematical Reviews number (MathSciNet)
MR3161369

Zentralblatt MATH identifier
1294.60070

Subjects
Primary: 60G10: Stationary processes 60G22: Fractional processes, including fractional Brownian motion 60G51: Processes with independent increments; Lévy processes 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations 91G40: Credit risk
Secondary: 60G15: Gaussian processes 91G30: Interest rates (stochastic models) 91G60: Numerical methods (including Monte Carlo methods)

Keywords
Conditional characteristic function macroeconomic variables process long-range dependence fractional Brownian motion fractional Lévy process prediction

Citation

Fink, Holger. Conditional characteristic functions of Molchan-Golosov fractional Lévy processes with application to credit risk. J. Appl. Probab. 50 (2013), no. 4, 983--1005. doi:10.1239/jap/1389370095. https://projecteuclid.org/euclid.jap/1389370095


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