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Options on realized variance by transform methods: a non-affine stochastic volatility model


  • Gabriel G. Drimus


In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model by developing efficient transform-based pricing methods. This non-affine model gives prices of options on realized variance that allow upward-sloping implied volatility of variance smiles. Heston's model [ Rev. Financial Stud ., 1993, 6 , 327--343], the benchmark affine stochastic volatility model, leads to downward-sloping volatility of variance smiles—in disagreement with variance markets in practice. Using control variates, we propose a robust method to express the Laplace transform of the variance call function in terms of the Laplace transform of the realized variance. The proposed method works in any model where the Laplace transform of realized variance is available in closed form. Additionally, we apply a new numerical Laplace inversion algorithm that gives fast and accurate prices for options on realized variance, simultaneously at a sequence of variance strikes. The method is also used to derive hedge ratios for options on variance with respect to variance swaps.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:11:p:1679-1694 DOI: 10.1080/14697688.2011.565789

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    References listed on IDEAS

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    Cited by:

    1. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082,, revised Nov 2017.
    2. Wendong Zheng & Pingping Zeng, 2015. "Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model," Papers 1504.08136,
    3. Mengzhe Zhang & Leunglung Chan, 2016. "Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-20, December.
    4. Chi Hung Yuen & Wendong Zheng & Yue Kuen Kwok, 2015. "Pricing Exotic Discrete Variance Swaps under the 3/2-Stochastic Volatility Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(5), pages 421-449, November.
    5. repec:ids:ijbder:v:3:y:2017:i:2:p:153-175 is not listed on IDEAS
    6. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "A Taylor series approach to pricing and implied vol for LSV models," Papers 1308.5019,
    7. Wendong Zheng & Yue Kuen Kwok, 2014. "Saddlepoint Approximation Methods for Pricing Derivatives on Discrete Realized Variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(1), pages 1-31, March.
    8. Wei Lin & Shenghong Li & Xingguo Luo & Shane Chern, 2015. "Consistent Pricing of VIX and Equity Derivatives with the 4/2 Stochastic Volatility Plus Jumps Model," Papers 1510.01172,, revised Nov 2015.
    9. Stéphane Goutte & Amine Ismail & Huyên Pham, 2017. "Regime-switching Stochastic Volatility Model : Estimation and Calibration to VIX options," Working Papers hal-01212018, HAL.
    10. Tim Leung & Matthew Lorig, 2015. "Optimal Static Quadratic Hedging," Papers 1506.02074,, revised Nov 2015.
    11. Xinyu WU & Hailin ZHOU, 2016. "GARCH DIFFUSION MODEL, iVIX, AND VOLATILITY RISK PREMIUM," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(1), pages 327-342.
    12. Wei Lin & Shenghong Li & Shane Chern, 2017. "Pricing VIX Derivatives With Free Stochastic Volatility Model," Papers 1703.06020,
    13. Jan Baldeaux & Katja Ignatieva & Eckhard Platen, 2016. "Detecting Money Market Bubbles," Research Paper Series 378, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382,
    15. Andrew Papanicolaou & Ronnie Sircar, 2014. "A regime-switching Heston model for VIX and S&P 500 implied volatilities," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1811-1827, October.
    16. Paolo Di Tella & Martin Haubold & Martin Keller-Ressel, 2017. "Semi-Static Variance-Optimal Hedging in Stochastic Volatility Models with Fourier Representation," Papers 1709.05527,

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