On changes of measure in stochastic volatility models

Wong, Bernard; Heyde, C. C.

doi:https://doi.org/10.1155/JAMSA/2006/18130

International Journal of Stochastic Analysis

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Volume 2006 | Article ID 018130 | https://doi.org/10.1155/JAMSA/2006/18130

On changes of measure in stochastic volatility models

Bernard Wong²and C. C. Heyde^1,3

Received12 Jul 2006

Accepted05 Oct 2006

Published06 Dec 2006

Abstract

Pricing in mathematical finance often involves taking expected values under different equivalent measures. Fundamentally, one needs to first ensure the existence of ELMM, which in turn requires that the stochastic exponential of the market price of risk process be a true martingale. In general, however, this condition can be hard to validate, especially in stochastic volatility models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.

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Copyright

Copyright © 2006 Bernard Wong and C. C. Heyde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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