A class of stochastic volatility models and the q-optimal martingale measure

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Abstract

This paper proposes an approach under which the q-optimal martingale measure, for the case where continuous processes describe the evolution of the asset price and its stochastic volatility, exists for all finite time horizons. More precisely, it is assumed that while the ‘mean–variance trade-off process’ is uniformly bounded, the volatility and asset are imperfectly correlated. As a result, under some regularity conditions for the parameters of the corresponding Cauchy problem, one obtains that the qth moment of the corresponding Radon–Nikodym derivative does not explode in finite time.
Original languageEnglish
Pages (from-to)1111-1117
JournalQuantitative Finance
Volume12
Issue number7
Early online date4 Aug 2011
DOIs
Publication statusPublished - 1 Jul 2012

Keywords / Materials (for Non-textual outputs)

  • Applied mathematical finance
  • Options pricing
  • Stochastic volatility
  • Martingales
  • Continuous time models
  • Correlation
  • Derivative pricing models

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