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A splitting strategy for the calibration of jump-diffusion models

Author

Listed:
  • Vinicius V. L. Albani

    (Federal University of Santa Catarina)

  • Jorge P. Zubelli

    (Khalifa University)

Abstract

We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time- and price-dependent volatility. Our approach uses a forward Dupire-type partial integro-differential equation for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for this map is then solved by means of a Tikhonov-type convex regularisation. The proofs of convergence and stability of the algorithm are provided together with numerical examples that illustrate the robustness of the method both for synthetic and real data.

Suggested Citation

  • Vinicius V. L. Albani & Jorge P. Zubelli, 2020. "A splitting strategy for the calibration of jump-diffusion models," Finance and Stochastics, Springer, vol. 24(3), pages 677-722, July.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:3:d:10.1007_s00780-020-00425-4
    DOI: 10.1007/s00780-020-00425-4
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    References listed on IDEAS

    as
    1. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    2. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    3. Amel Bentata & Rama Cont, 2015. "Forward equations for option prices in semimartingale models," Finance and Stochastics, Springer, vol. 19(3), pages 617-651, July.
    4. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    5. 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.
    6. S. Kindermann & P. Mayer, 2011. "On the calibration of local jump-diffusion asset price models," Finance and Stochastics, Springer, vol. 15(4), pages 685-724, December.
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    Cited by:

    1. Georgiev, Slavi G. & Vulkov, Lubin G., 2021. "Computation of the unknown volatility from integral option price observations in jump–diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 591-608.

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    More about this item

    Keywords

    Jump-diffusion simulation; Partial integro-differential equations; Finite difference schemes; Inverse problems; Tikhonov-type regularisation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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