IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v177y2020icp467-486.html
   My bibliography  Save this article

A new calibration of the Heston Stochastic Local Volatility Model and its parallel implementation on GPUs

Author

Listed:
  • Ferreiro-Ferreiro, Ana María
  • García-Rodríguez, José A.
  • Souto, Luis
  • Vázquez, Carlos

Abstract

In this article we propose a new more general calibration of the Heston Stochastic-Local Volatility (HSLV) model. More precisely, the main contribution is to perform the direct calibration of the whole set of parameters at the same time instead of the usual two steps procedure. Moreover, the proposed approach allows to use exotic options to calibrate the HSLV model, thus making it more flexible and general. However, as there are no analytical formulas available to price exotic options to calibrate the model, the cost function (the HSLV pricer) involved in the calibration process must be computed using Monte Carlo methods, thus leading to a highly demanding computational problem. Therefore, we also propose efficient parallel GPU implementations of Monte Carlo techniques for the pricers. Furthermore, for solving the resulting global optimization problem, we develop customized parallel multi-CPU implementations of two of the most common stochastic metaheuristic global optimization algorithms: Differential Evolution and Simulated Annealing. A comparison between both algorithms has been made. This second level of parallelization has been carried out by the implementation of the cost function as a single GPU kernel and keeping the OpenMP parallelization for the optimization algorithm, thus leading to a hybrid multi-GPU implementation of the calibrator. All these implementations have been tested with real market data for European and barrier options in the context of foreign exchange markets.

Suggested Citation

  • Ferreiro-Ferreiro, Ana María & García-Rodríguez, José A. & Souto, Luis & Vázquez, Carlos, 2020. "A new calibration of the Heston Stochastic Local Volatility Model and its parallel implementation on GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 467-486.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:467-486
    DOI: 10.1016/j.matcom.2020.04.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420301129
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.04.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alexander Lipton & Andrey Gal & Andris Lasis, 2014. "Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1899-1922, November.
    2. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    3. A. Ferreiro & J. García & J. López-Salas & C. Vázquez, 2013. "An efficient implementation of parallel simulated annealing algorithm in GPUs," Journal of Global Optimization, Springer, vol. 57(3), pages 863-890, November.
    4. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    5. Anthonie W. Van Der Stoep & Lech A. Grzelak & Cornelis W. Oosterlee, 2014. "The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-30.
    6. 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.
    7. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    8. Ferreiro-Ferreiro, Ana M. & García-Rodríguez, José A. & Souto, Luis & Vázquez, Carlos, 2019. "Basin Hopping with synched multi L-BFGS local searches. Parallel implementation in multi-CPU and GPUs," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 282-298.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kim, Donghyun & Choi, Sun-Yong & Yoon, Ji-Hun, 2021. "Pricing of vulnerable options under hybrid stochastic and local volatility," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Ana M. Ferreiro & Enrico Ferri & José A. García & Carlos Vázquez, 2021. "Global Optimization for Automatic Model Points Selection in Life Insurance Portfolios," Mathematics, MDPI, vol. 9(5), pages 1-19, February.
    3. Ghosh, Abhijit & Mishra, Chittaranjan, 2021. "Highly efficient parallel algorithms for solving the Bates PIDE for pricing options on a GPU," Applied Mathematics and Computation, Elsevier, vol. 409(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrei Cozma & Christoph Reisinger, 2017. "Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models," Papers 1706.07375, arXiv.org, revised Oct 2018.
    2. João Pedro Vidal Nunes & Tiago Ramalho Viegas Alcaria, 2016. "Valuation of forward start options under affine jump-diffusion models," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 727-747, May.
    3. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    4. Andrei Cozma & Christoph Reisinger, 2015. "Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process," Papers 1601.00919, arXiv.org.
    5. Calvet, Laurent E. & Fearnley, Marcus & Fisher, Adlai J. & Leippold, Markus, 2015. "What is beneath the surface? Option pricing with multifrequency latent states," Journal of Econometrics, Elsevier, vol. 187(2), pages 498-511.
    6. Carl Chiarella & Susanne Griebsch & Boda Kang, 2013. "Investigating Time-Efficient Methods to Price Compound Options in the Heston Model," Research Paper Series 328, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Andrei Cozma & Matthieu Mariapragassam & Christoph Reisinger, 2015. "Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets," Papers 1501.06084, arXiv.org, revised Oct 2016.
    8. Jingtang Ma & Wenyuan Li & Harry Zheng, 2017. "Dual control Monte Carlo method for tight bounds of value function under Heston stochastic volatility model," Papers 1710.10487, arXiv.org.
    9. Sergey Nasekin & Wolfgang Karl Hardle, 2020. "Model-driven statistical arbitrage on LETF option markets," Papers 2009.09713, arXiv.org.
    10. Maarten Wyns & Jacques Du Toit, 2016. "A Finite Volume - Alternating Direction Implicit Approach for the Calibration of Stochastic Local Volatility Models," Papers 1611.02961, arXiv.org.
    11. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    12. Marcos Escobar-Anel & Weili Fan, 2023. "The SEV-SV Model—Applications in Portfolio Optimization," Risks, MDPI, vol. 11(2), pages 1-34, January.
    13. Damir Filipovi'c & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Papers 1711.08043, arXiv.org, revised Jul 2019.
    14. Song-Ping Zhu & Xin-Jiang He, 2018. "A hybrid computational approach for option pricing," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-16, September.
    15. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    16. Sigurd Emil Rømer & Rolf Poulsen, 2020. "How Does the Volatility of Volatility Depend on Volatility?," Risks, MDPI, vol. 8(2), pages 1-18, June.
    17. Andrey Itkin, 2023. "The ATM implied skew in the ADO-Heston model," Papers 2309.15044, arXiv.org.
    18. Eudald Romo & Luis Ortiz-Gracia, 2021. "SWIFT calibration of the Heston model," Papers 2103.01570, arXiv.org.
    19. Carl Chiarella & Boda Kang & Gunter H. Meyer, 2010. "The Evaluation Of Barrier Option Prices Under Stochastic Volatility," Research Paper Series 266, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Rong Du & Duy-Minh Dang, 2023. "Fourier Neural Network Approximation of Transition Densities in Finance," Papers 2309.03966, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:467-486. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.