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The Calibration of Stochastic-Local Volatility Models - An Inverse Problem Perspective

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  • Yuri F. Saporito
  • Xu Yang
  • Jorge P. Zubelli

Abstract

We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers recently. More precisely, given a local volatility surface and a choice of stochastic volatility parameters, we calibrate the corresponding leverage function. Our approach makes use of regularization techniques from the inverse-problem theory, respecting the integrity of the data and thus avoiding data interpolation. The result is a stable and robust algorithm which is resilient to instabilities in the regions of low probability density of the spot price and of the instantaneous variance. We substantiate our claims with numerical experiments using simulated as well as real data.

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  • 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.
    • Handle: RePEc:arx:papers:1711.03023
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    References listed on IDEAS

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    1. Vinicius Albani & Adriano De Cezaro & Jorge P. Zubelli, 2017. "Convex Regularization Of Local Volatility Estimation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-37, February.
    2. 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.
    3. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching to nonaffine stochastic volatility: a closed-form expansion for the Inverse Gamma model," Post-Print hal-02909113, HAL.
    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. Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
    6. Nicolas Langren'e & Geoffrey Lee & Zili Zhu, 2015. "Switching to non-affine stochastic volatility: A closed-form expansion for the Inverse Gamma model," Papers 1507.02847, arXiv.org, revised Mar 2016.
    7. Benjamin Jourdain & Alexandre Zhou, 2016. "Existence of a calibrated regime switching local volatility model and new fake Brownian motions," Papers 1607.00077, arXiv.org, revised Jan 2017.
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    Cited by:

    1. Dmitri Goloubentsev & Evgeny Lakshtanov, 2019. "Remarks on stochastic automatic adjoint differentiation and financial models calibration," Papers 1901.04200, arXiv.org, revised Dec 2019.
    2. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A generative adversarial network approach to calibration of local stochastic volatility models," Papers 2005.02505, arXiv.org, revised Sep 2020.
    3. Orcan Ogetbil & Narayan Ganesan & Bernhard Hientzsch, 2020. "Calibrating Local Volatility Models with Stochastic Drift and Diffusion," Papers 2009.14764, arXiv.org, revised May 2023.
    4. Matteo Gambara & Josef Teichmann, 2020. "Consistent Recalibration Models and Deep Calibration," Papers 2006.09455, arXiv.org, revised Jul 2021.

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