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

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  • Sotirios Sabanis

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 q th moment of the corresponding Radon--Nikodym derivative does not explode in finite time.

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  • Sotirios Sabanis, 2012. "A class of stochastic volatility models and the q -optimal martingale measure," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1111-1117, February.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:7:p:1111-1117
    DOI: 10.1080/14697688.2011.568950
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    References listed on IDEAS

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    1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    2. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    3. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52, January.
    4. Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, vol. 1(3), pages 181-227.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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