March 2013 Conditional distributions of processes related to fractional Brownian motion
Holger Fink, Claudia Klüppelberg, Martina Zähle
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J. Appl. Probab. 50(1): 166-183 (March 2013). DOI: 10.1239/jap/1363784431


Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein–Uhlenbeck or fractional Cox–Ingersoll–Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.


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Holger Fink. Claudia Klüppelberg. Martina Zähle. "Conditional distributions of processes related to fractional Brownian motion." J. Appl. Probab. 50 (1) 166 - 183, March 2013.


Published: March 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1281.60037
MathSciNet: MR3076779
Digital Object Identifier: 10.1239/jap/1363784431

Primary: 60G15 , 60G22 , 60H10 , 60H20 , 91G30
Secondary: 60G10 , 91G60

Keywords: Affine process , conditional characteristic function , fractional affine process , fractional Brownian motion , fractional Vasicek model , interest rate , long-range dependence , macroeconomic variables process , prediction , short rate , zero-coupon bond

Rights: Copyright © 2013 Applied Probability Trust


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Vol.50 • No. 1 • March 2013
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