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High-Performance Hardware Acceleration of Asset Simulations

  • Christian de Schryver
  • Henning Marxen
  • Stefan Weithoffer
  • Norbert Wehn
Chapter

Abstract

State-of-the-art financial computations based on realistic market models like the Heston model require a high computational effort, since no closed-form solutions are available in general. Due to the fact that the underlying asset behavior predictions are mainly based on number crunching operations, FPGAs are promising target devices for this task. In this chapter, we give an overview about current problems and solutions in the finance and insurance domain and show how state-of-the-art market models and solution methods have increased the necessary computational power over time. For the reason of universality and robustness, we focus on Monte Carlo methods that require a huge amount of normally distributed random numbers. We summarize the state-of-the-art and present efficient hardware architectures to obtain these numbers, together with comprehensive quality investigations. Build on these high-quality random number generators, we present an efficient FPGA architecture for option pricing in the Heston model, tailored to FPGAs. For the problem pricing European barrier options in the Heston model we show that a Xilinx Virtex-5 device can save up to 97% of energy, providing the same simulation throughput as a Nvidia Tesla 2050 GPU.

Keywords

Option Price Random Number Generator Data Path Memory Bank Barrier Option 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    T. Becker, Q. Jin, W. Luk, S. Weston, Dynamic constant reconfiguration for explicit finite difference option pricing, in 2011 International Conference on Reconfigurable Computing and FPGAs (ReConFig) (IEEE Computer Society, Los Alamitos, USA, 2011), pp. 176–181. ISBN-13: 978-0-7695-4551-6. doi:10.1109/ReConFig.2011.29Google Scholar
  2. 2.
    A. Bernemann, R. Schreyer, K. Spanderen, Pricing structured equity products on GPUs, in 2010 IEEE Workshop on High Performance Computational Finance (WHPCF) (IEEE, Red Hook, USA, 2010), pp. 1–7. ISBN: 978-1-4244-9061-5. doi:10.1109/WHPCF.2010.5671821Google Scholar
  3. 3.
    A. Bernemann, R. Schreyer, K. Spanderen, Accelerating exotic option pricing and model calibration using GPUs (2011), http://ssrn.com/abstract=1753596. Accessed 28th January 2013
  4. 4.
    F. Black, M. Scholes, The pricing of options and corporate liabilities. J. Polit. Econ. 81(3), 637–654 (1973)CrossRefGoogle Scholar
  5. 5.
    G. Chatziparaskevas, A. Brokalakis, I. Papaefstathiou, An FPGA-based parallel processor for Black-Scholes option pricing using finite differences schemes, in Proceedings of Design, Automation and Test in Europe, 2012 (DATE ’12), EDAA (2012), ISBN: 978-3-9810801-6Google Scholar
  6. 6.
    R.C.C. Cheung, D.U. Lee, W. Luk, J.D. Villasenor, Hardware generation of arbitrary random number distributions from uniform distributions via the inversion method. IEEE Trans. Very Large Scale Integrat. (VLSI) Syst. 15(8), 952–962 (2007). doi:10.1109/TVLSI.2007.900748, http://dx.doi.org/10.1109/TVLSI.2007.900748 Google Scholar
  7. 7.
    I.L. Dalal, D. Stefan, A hardware framework for the fast generation of multiple long-period random number streams, in Proceedings of the 16th International ACM/SIGDA Symposium on Field Programmable Gate Arrays, FPGA ’08 (ACM, New York, 2008), pp. 245–254. doi:10.1145/1344671.1344707, http://doi.acm.org/10.1145/1344671.1344707
  8. 8.
    S. Gilani, The real reason for the global financial crisis...the story no one’s talking about (2008), http://moneymorning.com/2008/09/18/credit-default-swaps/. Accessed 28th January 2013
  9. 9.
    S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6(2), 327 (1993). doi:10.1093/rfs/6.2.327Google Scholar
  10. 10.
    Q. Jin, W. Luk, D.B. Thomas, Unifying finite difference option-pricing for hardware acceleration, in International Conference on Field Programmable Logic and Applications (FPL), 2011 (IEEE Computer Society, Los Alamitos, USA, 2011), pp. 6–9. ISBN: 978-0-7695-4529-5. doi:10.1109/FPL.2011.12Google Scholar
  11. 11.
    R. Korn, E. Korn, G. Kroisandt, Monte Carlo Methods and Models in Finance and Insurance (CRC Press, Boca Raton, 2010)CrossRefMATHGoogle Scholar
  12. 12.
    P. L’Ecuyer, R. Simard, TestU01: a C library for empirical testing of random number generators. ACM Trans. Math. Softw. 33(4), 22 (2007). doi:http://doi.acm.org/10.1145/1268776.1268777
  13. 13.
    D.U. Lee, W. Luk, J. Villasenor, P.Y. Cheung, Hierarchical segmentation schemes for function evaluation, in 2003 IEEE International Conference on Field-Programmable Technology (FPT), 2003. Proceedings (The University of Tokyo, Tokyo, Japan, 2003), pp. 92–99. ISBN: 0-7803-8320-6. doi:10.1109/FPT.2003.1275736Google Scholar
  14. 14.
    D.U. Lee, R. Cheung, W. Luk, J. Villasenor, Hierarchical segmentation for hardware function evaluation. IEEE Trans. Very Large Scale Integrat. (VLSI) Syst. 17(1), 103–116 (2009). doi:10.1109/TVLSI.2008.2003165Google Scholar
  15. 15.
    T.G. Lewis, W.H. Payne, Generalized feedback shift register pseudorandom number algorithm. J. ACM 20(3), 456–468 (1973). doi:10.1145/321765.321777, http://doi.acm.org/10.1145/321765.321777 Google Scholar
  16. 16.
    H. Marxen, A. Kostiuk, R. Korn, C. de Schryver, S. Wurm, I. Shcherbakov, N. Wehn, Algorithmic complexity in the Heston model: an implementation view, in 2011 IEEE Workshop on High Performance Computational Finance (WHPCF) (ACM, New York, USA, 2011), ISBN: 978-1-4244-9061-5Google Scholar
  17. 17.
    M. Matsumoto, T. Nishimura, Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simulat. 8(1), 3–30 (1998). doi:http://doi.acm.org/10.1145/272991.272995
  18. 18.
    O. Mencer, E. Vynckier, J. Spooner, S. Girdlestone, O. Charlesworth, Finding the right level of abstraction for minimizing operational expenditure, in 2011 IEEE Workshop on High Performance Computational Finance (WHPCF) (ACM, New York, USA, 2011), ISBN: 978-1-4244-9061-5Google Scholar
  19. 19.
    R.C. Merton, Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4(1), 141–183 (1973)CrossRefMathSciNetGoogle Scholar
  20. 20.
    G.W. Morris, M. Aubury, Design space exploration of the European option benchmark using hyperstreams, in International Conference on Field Programmable Logic and Applications, 2007. FPL 2007, IEEE (2007), pp. 5–10. ISBN: 1-4244-1060-6 doi:10.1109/FPL.2007.4380617Google Scholar
  21. 21.
    NVIDIA Corporation: Computational finance website (2012), http://www.nvidia.com/object/computational_finance.html. Accessed 28th January 2013
  22. 22.
    F. Panneton, P. L’Ecuyer, M. Matsumoto, Improved long-period generators based on linear recurrences modulo 2. ACM Trans. Math. Softw. 32(1), 1–16 (2006). doi:10.1145/1132973.1132974, http://doi.acm.org/10.1145/1132973.1132974 Google Scholar
  23. 23.
    QuantLib - A free/open-source library for quantitative finance (2012), http://quantlib.org. Accessed 28th January 2013
  24. 24.
    C. de Schryver, D. Schmidt, N. Wehn, E. Korn, H. Marxen, R. Korn, A new hardware efficient inversion based random number generator for non-uniform distributions, in 2010 International Conference on Reconfigurable Computing and FPGAs (ReConFig) (IEEE Computer Society, Los Alamitos, USA, 2010), pp. 190–195. ISBN: 978-0-7695-4314-7. doi:10.1109/ReConFig.2010.20CrossRefGoogle Scholar
  25. 25.
    C. de Schryver, I. Shcherbakov, F. Kienle, N. Wehn, H. Marxen, A. Kostiuk, R. Korn, An energy efficient FPGA accelerator for Monte Carlo option pricing with the Heston model, in 2011 International Conference on Reconfigurable Computing and FPGAs (ReConFig) (IEEE Computer Society, Los Alamitos, USA, 2011), pp. 468–474. ISBN-13: 978-0-7695-4551-6. doi:10.1109/ReConFig.2011.11Google Scholar
  26. 26.
    C. de Schryver, M. Jung, N. Wehn, H. Marxen, A. Kostiuk, R. Korn, Energy efficient acceleration and evaluation of financial computations towards real-time pricing, in Knowledge-Based and Intelligent Information and Engineering Systems, ed. by A. König, A. Dengel, K. Hinkelmann, K. Kise, R.J. Howlett, L.C. Jain. Lecture Notes in Computer Science, vol. 6884 (Springer, Berlin, 2011), pp. 177–186. Proceedings of 15th International Conference on Knowledge-Based and Intelligent Information & Engineering Systems (KES)Google Scholar
  27. 27.
    C. de Schryver, H. Marxen, D. Schmidt, Hardware accelerators for financial mathematics - methodology, results and benchmarking, in Proceedings of 1st Young Researcher Symposium (YRS) 2011, pp. 55–60 (Center for Mathematical and Computational Modelling (CM)2, (CM)2, Nachwuchsring, 2011). http://CEUR-WS.org/Vol-750/yrs08.pdf. ISSN: 1613-0073, urn:nbn:de:0074-750-0
  28. 28.
    C. de Schryver, D. Schmidt, N. Wehn, E. Korn, H. Marxen, A. Kostiuk, R. Korn, A hardware efficient random number generator for nonuniform distributions with arbitrary precision. Int. J. Reconfigurable Comput. (IJRC) 2012 (2012). doi:10.1155/2012/675130. Article ID 675130, 11 pagesGoogle Scholar
  29. 29.
    J. Stratoudakis, Hardware acceleration of Monte Carlo simulation for option pricing (2012), http://wallstreetfpga.com. Accessed 28th January 2013
  30. 30.
    J. Stratoudakis, Hardware acceleration of Monte Carlo simulation for option pricing (2012), https://decibel.ni.com/content/docs/DOC-9984. Accessed 28th January 2013
  31. 31.
    D.B. Thomas, J.A. Bower, W. Luk, Automatic generation and optimisation of reconfigurable financial Monte-Carlo simulations, in IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2007. ASAP, IEEE (2007), pp. 168–173. ISBN: 1-4244-1027-4. doi:10.1109/ASAP.2007.4429975Google Scholar
  32. 32.
    D.B. Thomas, W. Luk, P.H. Leong, J.D. Villasenor, Gaussian random number generators. ACM Comput. Surv. 39(4), 11 (2007). doi:http://doi.acm.org/10.1145/1287620.1287622 Google Scholar
  33. 33.
    X. Tian, K. Benkrid, American option pricing on reconfigurable hardware using least-squares Monte Carlo method, in International Conference on Field-Programmable Technology, 2009. FPT 2009, IEEE (2009), pp. 263–270. ISBN: 978-1-4244-4377-2. doi:10.1109/FPT.2009.5377662Google Scholar
  34. 34.
    X. Tian, K. Benkrid, X. Gu, High performance Monte-Carlo based option pricing on FPGAs. Eng. Lett. 16(3), 434–442 (2008)Google Scholar
  35. 35.
    P. Warren, City business races the Games for power. The Guardian (2008), http://www.guardian.co.uk/technology/2008/may/29/energy.olympics2012. Accessed 28th January 2013
  36. 36.
    S. Weston, J.T. Marin, J. Spooner, O. Pell, O. Mencer, Accelerating the computation of portfolios of tranched credit derivatives, in 2010 IEEE Workshop on High Performance Computational Finance (WHPCF) (IEEE, Red Hook, USA, 2010), pp. 1–8. ISBN: 978-1-4244-9061-5. doi:10.1109/WHPCF.2010.5671822Google Scholar
  37. 37.
    S. Weston, J. Spooner, J.T. Marin, O. Pell, O. Mencer, FPGAs speed the computation of complex credit derivatives. Xcell J. 74, 18–25 (2011)Google Scholar
  38. 38.
    C. Wynnyk, M. Magdon-Ismail, Pricing the American option using reconfigurable hardware, in International Conference on Computational Science and Engineering, 2009. CSE ’09, vol. 2 (IEEE Computer Society, Los Alamitos, USA, 2009), pp. 532–536. ISBN-13: 978-0-7695-3823-5. doi:10.1109/CSE.2009.496Google Scholar
  39. 39.
    Xilinx: XPower estimator (XPE) (2011), http://www.xilinx.com/products/technology/power/index.htm. Accessed 28th January 2013
  40. 40.
    B. Zhang, C.W. Oosterlee, Acceleration of option pricing technique on graphics processing units. Tech. Rep. 10-03, Delft University of Technology (2010)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Christian de Schryver
    • 1
  • Henning Marxen
    • 2
  • Stefan Weithoffer
    • 1
  • Norbert Wehn
    • 1
  1. 1.Microelectronic Systems Design Research GroupUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Stochastic Control and Financial Mathematics GroupUniversity of KaiserslauternKaiserslauternGermany

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