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Second order multiscale stochastic volatility asymptotics: stochastic terminal layer analysis and calibration

Author

Listed:
  • Jean-Pierre Fouque

    (University of California)

  • Matthew Lorig

    (University of Washington)

  • Ronnie Sircar

    (Princeton University)

Abstract

Multiscale stochastic volatility models have been developed as an efficient way to capture the principal effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book by Fouque et al. (Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives, 2011) analyzes models in which the volatility of the underlying is driven by two diffusions – one fast mean-reverting and one slowly varying – and provides a first order approximation for European option prices and for the implied volatility surface, which is calibrated to market data. Here, we present the full second order asymptotics, which are considerably more complicated due to a terminal layer near the option expiration time. We find that to second order, the implied volatility approximation depends quadratically on log-moneyness, capturing the convexity of the implied volatility curve seen in data. We introduce a new probabilistic approach to the terminal layer analysis needed for the derivation of the second order singular perturbation term, and calibrate to S&P 500 options data.

Suggested Citation

  • Jean-Pierre Fouque & Matthew Lorig & Ronnie Sircar, 2016. "Second order multiscale stochastic volatility asymptotics: stochastic terminal layer analysis and calibration," Finance and Stochastics, Springer, vol. 20(3), pages 543-588, July.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:3:d:10.1007_s00780-016-0298-y
    DOI: 10.1007/s00780-016-0298-y
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    References listed on IDEAS

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    1. repec:cup:cbooks:9780521843584 is not listed on IDEAS
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    Citations

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    Cited by:

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    2. Eduardo Abi Jaber & Shaun & Li & Xuyang Lin, 2024. "Fourier-Laplace transforms in polynomial Ornstein-Uhlenbeck volatility models," Papers 2405.02170, arXiv.org.
    3. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    4. Sun-Yong Choi & Sotheara Veng & Jeong-Hoon Kim & Ji-Hun Yoon, 2022. "A Mellin Transform Approach to the Pricing of Options with Default Risk," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1113-1134, March.
    5. Yuri F. Saporito, 2018. "First-Order Asymptotics Of Path-Dependent Derivatives In Multiscale Stochastic Volatility Environment," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-22, May.

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    More about this item

    Keywords

    Stochastic volatility; Implied volatility; Calibration; Multiscale asymptotics;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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