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Rough stochastic elasticity of variance and option pricing

Author

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  • Cao, Jiling
  • Kim, Jeong-Hoon
  • Kim, See-Woo
  • Zhang, Wenjun

Abstract

This study is concerned with the elasticity of variance for risky assets. We show that the elasticity of variance for S&P500 exhibits short-range correlations. By using asymptotic and martingale methods, we obtain a semi-analytical expression for the option price in the two-scale regime where the constant elasticity of variance is perturbed by a smooth and bounded function of a rapid fractional Ornstein–Uhlenbeck process with Hurst exponent within (0,12). The associated implied volatility is presented and discussed. As a result, the scope of Markov stochastic elasticity of variance model is extended to a non-Markov case.

Suggested Citation

  • Cao, Jiling & Kim, Jeong-Hoon & Kim, See-Woo & Zhang, Wenjun, 2020. "Rough stochastic elasticity of variance and option pricing," Finance Research Letters, Elsevier, vol. 37(C).
    • Handle: RePEc:eee:finlet:v:37:y:2020:i:c:s1544612319308050
    DOI: 10.1016/j.frl.2019.101381
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    References listed on IDEAS

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    1. Josselin Garnier & Knut Sølna, 2018. "Option pricing under fast-varying and rough stochastic volatility," Annals of Finance, Springer, vol. 14(4), pages 489-516, November.
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    5. Giulia Livieri & Saad Mouti & Andrea Pallavicini & Mathieu Rosenbaum, 2018. "Rough volatility: Evidence from option prices," IISE Transactions, Taylor & Francis Journals, vol. 50(9), pages 767-776, September.
    6. Josselin Garnier & Knut Solna, 2016. "Option pricing under fast-varying long-memory stochastic volatility," Papers 1604.00105, arXiv.org, revised Apr 2018.
    7. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Josselin Garnier & Knut Sølna, 2019. "Option pricing under fast‐varying long‐memory stochastic volatility," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 39-83, January.
    10. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," Papers 1507.03004, arXiv.org, revised May 2017.
    11. Kim, Jeong-Hoon & Yoon, Ji-Hun & Lee, Jungwoo & Choi, Sun-Yong, 2015. "On the stochastic elasticity of variance diffusions," Economic Modelling, Elsevier, vol. 51(C), pages 263-268.
    12. Josselin Garnier & Knut Solna, 2017. "Option Pricing under Fast-varying and Rough Stochastic Volatility," Papers 1707.00610, arXiv.org, revised Apr 2018.
    13. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
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    Cited by:

    1. Cao, Jiling & Kim, Jeong-Hoon & Liu, Wenqiang & Zhang, Wenjun, 2023. "Rescaling the double-mean-reverting 4/2 stochastic volatility model for derivative pricing," Finance Research Letters, Elsevier, vol. 58(PB).
    2. Seo, Jun-Ho & Kim, Jeong-Hoon, 2022. "Multiscale stochastic elasticity of variance for options and equity linked annuity; A Mellin transform approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 303-320.
    3. Xia, Kun & Yang, Xuewei & Zhu, Peng, 2023. "Delta hedging and volatility-price elasticity: A two-step approach," Journal of Banking & Finance, Elsevier, vol. 153(C).

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    More about this item

    Keywords

    Short range correlation; Stochastic elasticity of variance; Fractional Ornstein–Uhlenbeck process; Hurst exponent; Mean reversion;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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