IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1301.3118.html
   My bibliography  Save this paper

A parallel implementation of a derivative pricing model incorporating SABR calibration and probability lookup tables

Author

Listed:
  • Qasim Nasar-Ullah

Abstract

We describe a high performance parallel implementation of a derivative pricing model, within which we introduce a new parallel method for the calibration of the industry standard SABR (stochastic-\alpha \beta \rho) stochastic volatility model using three strike inputs. SABR calibration involves a non-linear three dimensional minimisation and parallelisation is achieved by incorporating several assumptions unique to the SABR class of models. Our calibration method is based on principles of surface intersection, guarantees convergence to a unique solution and operates by iteratively refining a two dimensional grid with local mesh refinement. As part of our pricing model we additionally present a fast parallel iterative algorithm for the creation of dynamically sized cumulative probability lookup tables that are able to cap maximum estimated linear interpolation error. We optimise performance for probability distributions that exhibit clustering of linear interpolation error. We also make an empirical assessment of error propagation through our pricing model as a result of changes in accuracy parameters within the pricing model's multiple algorithmic steps. Algorithms are implemented on a GPU (graphics processing unit) using Nvidia's Fermi architecture. The pricing model targets the evaluation of spread options using copula methods, however the presented algorithms can be applied to a wider class of financial instruments.

Suggested Citation

  • Qasim Nasar-Ullah, 2013. "A parallel implementation of a derivative pricing model incorporating SABR calibration and probability lookup tables," Papers 1301.3118, arXiv.org.
  • Handle: RePEc:arx:papers:1301.3118
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1301.3118
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    as
    1. Graeme West, 2005. "Calibration of the SABR Model in Illiquid Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 371-385.
    2. Schwartz, Eduardo S., 1977. "The valuation of warrants: Implementing a new approach," Journal of Financial Economics, Elsevier, vol. 4(1), pages 79-93, January.
    3. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1301.3118. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.