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Exploiting Mixed-Precision Arithmetics in a Multilevel Monte Carlo Approach on FPGAs

  • Steffen OmlandEmail author
  • Mario Hefter
  • Klaus Ritter
  • Christian Brugger
  • Christian De Schryver
  • Norbert Wehn
  • Anton Kostiuk

Abstract

Nowadays, high-speed computations are mandatory for financial and insurance institutes to survive in competition and to fulfill the regulatory reporting requirements that have just toughened over the last years. A majority of these computations are carried out on huge computing clusters, which are an ever increasing cost burden for the financial industry. There, state-of-the-art CPU and GPU architectures execute arithmetic operations with predefined precisions only, that may not meet the actual requirements for a specific application. Reconfigurable architectures like Field Programmable Gate Arrays (FPGAs) have a huge potential to accelerate financial simulations while consuming only very low energy by exploiting dedicated precisions in optimal ways. In this work we present a novel methodology to speed up Multilevel Monte Carlo (MLMC) simulations on reconfigurable architectures. The idea is to aggressively lower the precisions for different parts of the algorithm without loosing any accuracy at the end. For this, we have developed a novel heuristic for selecting an appropriate precision at each stage of the simulation that can be executed with low costs at runtime. Further, we introduce a cost model for reconfigurable architectures and minimize the cost of our algorithm without changing the overall error. We consider the showcase of pricing Asian options in the Heston model. For this setup we improve one of the most advanced simulation methods by a factor of 3–9× on the same platform.

Keywords

Mean Square Error Monte Carlo Discretization Scheme Asian Option Heston Model 
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.

Notes

Acknowledgements

We gratefully acknowledge the partial financial support from the Center of Mathematical and Computational Modelling (CM)2of the University of Kaiserslautern. Furthermore we thank Maxeler Technologies Ltd. for providing their technology.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Steffen Omland
    • 1
    Email author
  • Mario Hefter
    • 1
  • Klaus Ritter
    • 1
  • Christian Brugger
    • 2
  • Christian De Schryver
    • 2
  • Norbert Wehn
    • 2
  • Anton Kostiuk
    • 3
  1. 1.Computational Stochastics Research GroupUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Microelectronic Systems Design Research GroupUniversity of KaiserslauternKaiserslauternGermany
  3. 3.Stochastic Control and Financial Mathematics GroupUniversity of KaiserslauternKaiserslauternGermany

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