Articlebronze2010

Mean reversion for HJMM forward rate models

42 citations0/0 files storedAdvances in Applied Probability

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Economic theories and models

Abstract

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.

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References

2007Stochastic Partial Differential Equations with Levy Noise 1997Towards a general theory of bond markets 2006Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective 2007Existence of Lévy term structure models 1987On processes of ornstein-uhlenbeck type in hilbert space

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2012Heath–Jarrow–Morton–Musiela equation with Lévy perturbation 2012On a stochastic heat equation with first order fractional noises and applications to finance

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