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Sato processes and the valuation of structured products

Author

Listed:
  • Ernst Eberlein
  • Dilip Madan

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.

Suggested Citation

  • Ernst Eberlein & Dilip Madan, 2009. "Sato processes and the valuation of structured products," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 27-42.
  • Handle: RePEc:taf:quantf:v:9:y:2009:i:1:p:27-42
    DOI: 10.1080/14697680701861419
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    Citations

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    Cited by:

    1. Dan Pirjol & Jing Wang & Lingjiong Zhu, 2017. "Short Maturity Forward Start Asian Options in Local Volatility Models," Papers 1710.03160, arXiv.org.
    2. 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.
    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. 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.
    5. 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.
    6. Mathias Trabs, 2011. "Calibration of selfdecomposable Lévy models," SFB 649 Discussion Papers SFB649DP2011-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    8. repec:spr:annopr:v:260:y:2018:i:1:d:10.1007_s10479-016-2180-x is not listed on IDEAS

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