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Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks

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  • Andrew Na
  • Justin Wan

Abstract

We propose a deep Recurrent neural network (RNN) framework for computing prices and deltas of American options in high dimensions. Our proposed framework uses two deep RNNs, where one network learns the price and the other learns the delta of the option for each timestep. Our proposed framework yields prices and deltas for the entire spacetime, not only at a given point (e.g. t = 0). The computational cost of the proposed approach is linear in time, which improves on the quadratic time seen for feedforward networks that price American options. The computational memory cost of our method is constant in memory, which is an improvement over the linear memory costs seen in feedforward networks. Our numerical simulations demonstrate these contributions, and show that the proposed deep RNN framework is computationally more efficient than traditional feedforward neural network frameworks in time and memory.

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  • Andrew Na & Justin Wan, 2023. "Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks," Papers 2301.08232, arXiv.org.
    • Handle: RePEc:arx:papers:2301.08232
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    1. repec:dau:papers:123456789/4273 is not listed on IDEAS
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Yangang Chen & Justin W. L. Wan, 2021. "Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 45-67, January.
    4. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CIRJE F-Series CIRJE-F-1069, CIRJE, Faculty of Economics, University of Tokyo.
    5. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    6. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    7. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CARF F-Series CARF-F-423, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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