Moment explosions in stochastic volatility models

Authors: Leif B G Andersen Vladimir V Piterbarg

Publish Date: 2006/09/12

Volume: 11, Issue: 1, Pages: 29-50

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Abstract

In this paper we demonstrate that many stochastic volatility models have the undesirable property that moments of order higher than 1 can become infinite in finite time As arbitragefree price computation for a number of important fixed income products involves forming expectations of functions with superlinear growth such lack of moment stability is of significant practical importance For instance we demonstrate that reasonably parametrized models can produce infinite prices for Eurodollar futures and for swaps with floating legs paying either Liborinarrears or a constant maturity swap rate We systematically examine the moment explosion property across a spectrum of stochastic volatility models We show that lognormal and displaceddiffusion type models are easily prone to moment explosions whereas CEVtype models including the socalled SABR model are not Related properties such as the failure of the martingale property are also considered

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