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Mean reversion for HJMM forward rate models

Part of: Stochastic analysis Stochastic processes Mathematical economics

Published online by Cambridge University Press:  01 July 2016

Anna Rusinek
Anna Rusinek*
Affiliation:
Institute of Mathematics, Polish Academy of Sciences
*
∗ Postal address: Burgemeester van Stamplein 178, 2132BH Hoofddorp, The Netherlands. Email address: [email protected]
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Abstract

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We examine the long-time behavior of forward rates in the framework of Heath-Jarrow-Morton-Musiela models with infinite-dimensional Lévy noise. We give an explicit condition under which the rates have a mean reversion property. In a special case we show that this condition is fulfilled for any Lévy process with variance smaller than a given constant, depending only on the state space and the volatility.

Keywords

Term structure of interest ratesstationary distributioninfinite-dimensional model

MSC classification

Primary: 91B70: Stochastic models
Secondary: 60G51: Processes with independent increments; L'evy processes 60H15: Stochastic partial differential equations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 2 , June 2010 , pp. 371 - 391
Copyright
Copyright © Applied Probability Trust 2010 

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