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Variance Swaps Under Multiscale Stochastic Volatility of Volatility

Author

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  • Min-Ku Lee

    (Kunsan National University)

  • See-Woo Kim

    (Yonsei University)

  • Jeong-Hoon Kim

    (Yonsei University)

Abstract

Many hedge funds and retail investors demand volatility and variance derivatives in order to manage their exposure to volatility and volatility-of-volatility risk associated with their trading positions. The Heston model is a standard popular stochastic volatility model for pricing volatility and variance derivatives. However, it may fail to capture some important empirical features of the relevant market data due to the fact that the elasticity of volatility of volatility of the underlying price takes a special value, i.e., 1/2, whereas it has a merit of analytical tractability. We exploit a multiscale stochastic extension of volatility of volatility to obtain a better agreement with the empirical data while taking analytical advantage of the original Heston dynamics as much as possible in the context of pricing discrete variance swaps. By using an asymptotic technique with two small parameters, we derive a quasi-closed form formula for the fair strike price of variance swap and find useful pricing properties with respect to the stochastic extension parameters.

Suggested Citation

  • Min-Ku Lee & See-Woo Kim & Jeong-Hoon Kim, 2022. "Variance Swaps Under Multiscale Stochastic Volatility of Volatility," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 39-64, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-020-09834-6
    DOI: 10.1007/s11009-020-09834-6
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    2. Damir Filipovic & Damien Ackerer & Sergio Pulido, 2018. "The Jacobi Stochastic Volatility Model," Post-Print hal-01338330, HAL.
    3. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    4. 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.
    5. Yang Liu & Mariano Croce & Ivan Shaliastovich & Ric Colacito, 2016. "Volatility Risk Pass-Through," 2016 Meeting Papers 135, Society for Economic Dynamics.
    6. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    7. J.-P. Fouque & Y. F. Saporito, 2018. "Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 1003-1016, June.
    8. Xingguo Luo & Jin E. Zhang, 2012. "The Term Structure of VIX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(12), pages 1092-1123, December.
    9. Mark Broadie & Ashish Jain, 2008. "The Effect Of Jumps And Discrete Sampling On Volatility And Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 761-797.
    10. Branger, Nicole & Rodrigues, Paulo & Schlag, Christian, 2018. "Level and slope of volatility smiles in long-run risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 86(C), pages 95-122.
    11. Damien Ackerer & Damir Filipović & Sergio Pulido, 2018. "The Jacobi stochastic volatility model," Finance and Stochastics, Springer, vol. 22(3), pages 667-700, July.
    12. Wendong Zheng & Yue Kuen Kwok, 2014. "Closed Form Pricing Formulas For Discretely Sampled Generalized Variance Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 855-881, October.
    13. Huang, Darien & Schlag, Christian & Shaliastovich, Ivan & Thimme, Julian, 2018. "Volatility-of-volatility risk," SAFE Working Paper Series 210, Leibniz Institute for Financial Research SAFE.
    14. Kim, See-Woo & Kim, Jeong-Hoon, 2018. "Analytic solutions for variance swaps with double-mean-reverting volatility," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 130-144.
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