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Vanilla Option Pricing on Stochastic Volatility market models

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  • Dell'Era, Mario

Abstract

We want to discuss the option pricing on stochastic volatility market models, in which we are going to consider a generic function β (νt ) for the drift of volatility process. It is our intention choose any equivalent martingale measure, so that the drift of volatility process, respect at the new measure, is zero. This technique is possible when the Girsanov theorem is satisfied, since the stochastic volatility models are uncomplete markets, thus one has to choice an arbitrary risk price of volatility. In all this cases we are able to compute the price of Vanilla options in a closed form. To name a few, we can think to the popular Heston’s model, in which the solution is known in literature, unless of an inverse Fourier transform.

Suggested Citation

  • Dell'Era, Mario, 2010. "Vanilla Option Pricing on Stochastic Volatility market models," MPRA Paper 25645, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:25645
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    3. Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
    4. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
    5. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
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    More about this item

    Keywords

    Vanilla Option pricing on Stochastic volatility market models;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C0 - Mathematical and Quantitative Methods - - General

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