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


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


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,
  • Handle: RePEc:arx:papers:1711.03023

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    References listed on IDEAS

    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
    3. 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,, revised Mar 2016.
    4. Benjamin Jourdain & Alexandre Zhou, 2016. "Existence of a calibrated regime switching local volatility model and new fake Brownian motions," Papers 1607.00077,, revised Jan 2017.
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    Cited by:

    1. Dmitri Goloubentcev & Evgeny Lakshtanov, 2019. "Remarks on stochastic automatic adjoint differentiation and financial models calibration," Papers 1901.04200,

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