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Sato processes and the valuation of structured products

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  • Ernst Eberlein
  • Dilip Madan
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    Abstract

    We report on the adequacy of using Sato processes to value equity structured products. In models used to price options on realized variance, the latter must be a random variable with a positive variance. An analysis of this variance of realized variance for Sato processes shows that these processes may be suited to option contracts on realized volatility. Nonlinear pricing principles based on hedging to acceptability are outlined for the purpose of pricing structured transactions. It is shown that, typically, different products should be priced using different models. Pricing comparisons of Sato process prices with other standard models like Heston stochastic volatility, with and without jumps, VGSA, local volatility and local CGMY are also provided. Sato processes tend to overprice cliquets relative to other models. They also maintain the value of long dated out-of-the-money realized variance options.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680701861419
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 9 (2009)
    Issue (Month): 1 ()
    Pages: 27-42

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    Handle: RePEc:taf:quantf:v:9:y:2009:i:1:p:27-42

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    Web page: http://www.tandfonline.com/RQUF20

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    Related research

    Keywords: Equity options; Levy process; Mathematical finance; Stochastic volatility; Stochastic processes;

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    Cited by:
    1. Gabriel Drimus, 2010. "A forward started jump-diffusion model and pricing of cliquet style exotics," Review of Derivatives Research, Springer, vol. 13(2), pages 125-140, July.
    2. Fabozzi, Frank J. & Leccadito, Arturo & Tunaru, Radu S., 2014. "Extracting market information from equity options with exponential Lévy processes," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 125-141.
    3. Gabriel Drimus & Walter Farkas, 2013. "Local volatility of volatility for the VIX market," Review of Derivatives Research, Springer, vol. 16(3), pages 267-293, October.
    4. Mathias Trabs, 2011. "Calibration of selfdecomposable Lévy models," SFB 649 Discussion Papers SFB649DP2011-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Gabriel G. Drimus, 2012. "Options on realized variance by transform methods: a non-affine stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 12(11), pages 1679-1694, November.

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