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Complications with stochastic volatility models

Part of: Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Carlos A. Sin
Carlos A. Sin*
Affiliation:
UBS
*
∗ Postal address: UBS-Limited, 100 Liverpool Street, London EC2M 2RH, UK.
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Abstract

We show a class of stock price models with stochastic volatility for which the most natural candidates for martingale measures are only strictly local martingale measures, contrary to what is usually assumed in the finance literature. We also show the existence of equivalent martingale measures, and provide one explicit example.

Keywords

Strictly local martingaleschange of probability measureoption pricing

MSC classification

Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 1 , March 1998 , pp. 256 - 268
Copyright
Copyright © Applied Probability Trust 1998 

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