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Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model

Author

Listed:
  • NICOLAS LANGRENÉ

    (Real Options and Financial Risk, CSIRO, Bayview Avenue, Clayton, Victoria 3168, Australia)

  • GEOFFREY LEE

    (Real Options and Financial Risk, CSIRO, Bayview Avenue, Clayton, Victoria 3168, Australia)

  • ZILI ZHU

    (Real Options and Financial Risk, CSIRO, Bayview Avenue, Clayton, Victoria 3168, Australia)

Abstract

We examine the inverse gamma (IGa) stochastic volatility model with time-dependent parameters. This nonaffine model compares favorably in terms of volatility distribution and volatility paths to classical affine models such as the Heston model, while being as parsimonious (only four stochastic parameters). In practice, this means more robust calibration and better hedging, explaining its popularity among practitioners. Closed-form volatility-of-volatility expansions are obtained for the price of vanilla options, which allow for very fast pricing and calibration to market data. Specifically, the price of a European put option with IGa volatility is approximated by a Black–Scholes price plus a weighted combination of Black–Scholes Greeks, with weights depending only on the four time-dependent parameters of the model. The accuracy of the expansion is illustrated on several calibration tests on foreign exchange market data. This paper shows that the IGa model is as simple, more realistic, easier to implement and faster to calibrate than classical transform-based affine models. We therefore hope that the present work will foster further research on nonaffine models favored by practitioners such as the IGa model.

Suggested Citation

  • Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
  • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:05:n:s021902491650031x
    DOI: 10.1142/S021902491650031X
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    Cited by:

    1. Yiannis A. Papadopoulos & Alan L. Lewis, 2018. "A First Option Calibration of the GARCH Diffusion Model by a PDE Method," Papers 1801.06141, arXiv.org.
    2. Peter Carr & Sander Willems, 2019. "A lognormal type stochastic volatility model with quadratic drift," Papers 1908.07417, arXiv.org.
    3. Kaustav Das & Nicolas Langren'e, 2020. "Explicit approximations of option prices via Malliavin calculus in a general stochastic volatility framework," Papers 2006.01542, arXiv.org, revised Jan 2024.
    4. Qinwen Zhu & Grégoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing," Mathematics, MDPI, vol. 9(5), pages 1-21, March.
    5. Dongdong Hu & Hasanjan Sayit & Frederi Viens, 2023. "Pricing basket options with the first three moments of the basket: log-normal models and beyond," Papers 2302.08041, arXiv.org, revised Feb 2023.
    6. Armstrong, Margaret & Langrené, Nicolas & Petter, Renato & Chen, Wen & Petter, Carlos, 2019. "Accounting for tailings dam failures in the valuation of mining projects," Resources Policy, Elsevier, vol. 63(C), pages 1-1.
    7. Kaustav Das & Nicolas Langren'e, 2018. "Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility," Papers 1812.07803, arXiv.org, revised Oct 2021.
    8. Qinwen Zhu & Gregoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian approximation of the rough Bergomi model for Monte Carlo option pricing," Post-Print hal-02910724, HAL.
    9. Yuri F. Saporito & Xu Yang & Jorge P. Zubelli, 2017. "The Calibration of Stochastic-Local Volatility Models - An Inverse Problem Perspective," Papers 1711.03023, arXiv.org.

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