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Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs

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  • Fernández, J.L.
  • Ferreiro, A.M.
  • García-Rodríguez, J.A.
  • Leitao, A.
  • López-Salas, J.G.
  • Vázquez, C.

Abstract

For the calibration of the parameters in static and dynamic SABR stochastic volatility models, we propose the application of the GPU technology to the Simulated Annealing global optimization algorithm and to the Monte Carlo simulation. This calibration has been performed for EURO STOXX 50 index and EUR/USD exchange rate with an asymptotic formula for volatility or Monte Carlo simulation. Moreover, in the dynamic model we propose an original more general expression for the functional parameters, specially well suited for the EUR/USD exchange rate case. Numerical results illustrate the expected behavior of both SABR models and the accuracy of the calibration. In terms of computational time, when the asymptotic formula for volatility is used the speedup with respect to CPU computation is around 200 with one GPU. Furthermore, GPU technology allows the use of Monte Carlo simulation for calibration purposes, the computational time with CPU being prohibitive.

Suggested Citation

  • Fernández, J.L. & Ferreiro, A.M. & García-Rodríguez, J.A. & Leitao, A. & López-Salas, J.G. & Vázquez, C., 2013. "Static and dynamic SABR stochastic volatility models: Calibration and option pricing using GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 55-75.
    • Handle: RePEc:eee:matcom:v:94:y:2013:i:c:p:55-75
    DOI: 10.1016/j.matcom.2013.05.007
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    References listed on IDEAS

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    1. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
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    Cited by:

    1. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.
    2. Eudald Romo & Luis Ortiz-Gracia, 2021. "SWIFT calibration of the Heston model," Papers 2103.01570, arXiv.org.
    3. A. M. Ferreiro & J. A. Garc'ia & J. G. L'opez-Salas & C. V'azquez, 2024. "SABR/LIBOR market models: pricing and calibration for some interest rate derivatives," Papers 2408.01470, arXiv.org.
    4. Eudald Romo & Luis Ortiz-Gracia, 2021. "SWIFT Calibration of the Heston Model," Mathematics, MDPI, vol. 9(5), pages 1-20, March.
    5. Tianyao Chen & Xue Cheng & Jingping Yang, 2019. "Common Decomposition of Correlated Brownian Motions and its Financial Applications," Papers 1907.03295, arXiv.org, revised Nov 2020.

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