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Calibration of stochastic volatility models: A Tikhonov regularization approach

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  • Dai, Min
  • Tang, Ling
  • Yue, Xingye

Abstract

We aim to calibrate stochastic volatility models from option prices. We develop a Tikhonov regularization approach with an efficient numerical algorithm to recover the risk neutral drift term of the volatility (or variance) process. In contrast to most existing literature, we do not assume that the drift term has any special structure. As such, our algorithm applies to calibration of general stochastic volatility models. An extensive numerical analysis is presented to demonstrate the efficiency of our approach. Interestingly, our empirical study reveals that the risk neutral variance processes recovered from market prices of options on S&P 500 index and EUR/USD exchange rate are indeed linearly mean-reverting.

Suggested Citation

  • Dai, Min & Tang, Ling & Yue, Xingye, 2016. "Calibration of stochastic volatility models: A Tikhonov regularization approach," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 66-81.
    • Handle: RePEc:eee:dyncon:v:64:y:2016:i:c:p:66-81
    DOI: 10.1016/j.jedc.2016.01.002
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    Cited by:

    1. He, Xin-Jiang & Zhu, Song-Ping, 2017. "How should a local regime-switching model be calibrated?," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 149-163.
    2. Giovanni Amici & Paolo Brandimarte & Francesco Messeri & Patrizia Semeraro, 2023. "Multivariate L\'evy Models: Calibration and Pricing," Papers 2303.13346, arXiv.org, revised Jul 2023.
    3. Julio Guerrero & Giuseppe Orlando, 2022. "Stochastic Local Volatility models and the Wei-Norman factorization method," Papers 2201.11241, arXiv.org.
    4. Chen Zhang & Giovanni Amici & Marco Morandotti, 2024. "Calibrating the Heston Model with Deep Differential Networks," Papers 2407.15536, arXiv.org.
    5. Ruan, Xinfeng & Zhang, Jin E., 2018. "Equilibrium variance risk premium in a cost-free production economy," Journal of Economic Dynamics and Control, Elsevier, vol. 96(C), pages 42-60.

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    More about this item

    Keywords

    Calibration; Stochastic volatility model; Tikhonov regularization; Inverse problem;
    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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