Parallel Approach to Monte Carlo Simulation for Option Price Sensitivities Using the Adjoint and Interval Analysis

  • Grzegorz Kozikowski
  • Bartłomiej Jacek KubicaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8385)


This paper concerns a new approach to evaluation of Option Price sensitivities using the Monte Carlo simulation, based on the parallel GPU architecture and Automatic Differentiation methods. In order to study rounding errors, the interval arithmetic is used. Considerations are based on two implementations of the algorithm – the sequential and parallel ones. For efficient differentiation, the Adjoint method is employed. Computational experiments include analysis of performance, uncertainty error and rounding error and consider Black-Scholes and Heston models.


Option pricing The greeks Automatic Differentiation The Adjoint Calibration Interval analysis CUDA 


  1. 1.
  2. 2.
    Nvidia, CUDA SDK Documentation.
  3. 3.
  4. 4.
    Nvidia, CUDA CURAND Library.
  5. 5.
    Beck, P.-D., Nehmeier, M.: Parallel interval newton method on CUDA. In: Manninen, P., Öster, P. (eds.) PARA 2012. LNCS, vol. 7782, pp. 454–464. Springer, Heidelberg (2013) Google Scholar
  6. 6.
    Bücker, M.: Automatic Differentiation: Applications, Theory and Implementation. Springer, Berlin (1981)Google Scholar
  7. 7.
    Hull, J.C.: Options, Futures and other Derivatives, 8th edn. Prentice Hall, Upper Saddle River (2011)Google Scholar
  8. 8.
    Kozikowski, G.: Implementation of automatic differentiation library using the OpenCL technology. BEng thesis, Faculty of Electronics and Information Technology, WUT (2011)Google Scholar
  9. 9.
    Kozikowski, G.: Evaluation of option price sensitives based on the Automatic Differentiation methods using CUDA. Master’s Thesis, Faculty of Electronics and Information Technology, WUT (2013)Google Scholar
  10. 10.
    Kozikowski, G., Kubica, B.J.: Interval arithmetic and automatic differentiation on GPU using OpenCL. In: Manninen, P., Öster, P. (eds.) PARA 2012. LNCS, vol. 7782, pp. 489–503. Springer, Heidelberg (2013) Google Scholar
  11. 11.
    Kubica, B.J.: A class of problems that can be solved using interval algorithms. Computing 94(2–4), 271–280 (2012). (SCAN 2010 proceedings)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
  13. 13.
    Tadjouddine, E.M., Cao, Y.: An option pricing model calibration using algorithmic differentiation. In: Gelenbe, E., Lent, R., Sakellari, G. (eds.) Computer and Information Sciences II, pp. 577–581. Springer, London (2012) Google Scholar
  14. 14.
    Werbos, P.: Backpropagation through time: what it does and how to do it. Proc. IEEE 78, 1550–1560 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Grzegorz Kozikowski
    • 1
  • Bartłomiej Jacek Kubica
    • 2
    Email author
  1. 1.School of Computer ScienceUniversity of ManchesterManchesterUK
  2. 2.Institute of Control and Computation EngineeringWarsaw University of TechnologyWarsawPoland

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