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On full calibration of hybrid local volatility and regime‐switching models

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  • Xin‐Jiang He
  • Song‐Ping Zhu

Abstract

Calibrating local regime‐switching models is a challenging problem, especially when the volatility functions are assumed to depend on both of the underlying price and time. In this paper, the inverse problem of determining local volatility functions is firstly established and then solved through the Tikhonov regularization to obtain the optimal solution, which is achieved iteratively through a newly designed numerical algorithm. While our numerical tests with artificial data show that our algorithm can provide quite accurate and stable results, its performance with the involvement of real market data have been further demonstrated using options written on the S&P 500 index.

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  • Xin‐Jiang He & Song‐Ping Zhu, 2018. "On full calibration of hybrid local volatility and regime‐switching models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(5), pages 586-606, May.
    • Handle: RePEc:wly:jfutmk:v:38:y:2018:i:5:p:586-606
    DOI: 10.1002/fut.21901
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    Cited by:

    1. Lin, Sha & He, Xin-Jiang, 2020. "Pricing variance and volatility swaps with stochastic volatility, stochastic interest rate and regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Xin-Jiang He & Song-Ping Zhu, 2019. "Variance And Volatility Swaps Under A Two-Factor Stochastic Volatility Model With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-19, June.

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