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A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options

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  • Andersson, Kristoffer
  • Oosterlee, Cornelis W.

Abstract

In this paper, we propose a neural network-based method for approximating expected exposures and potential future exposures of Bermudan options. In a first phase, the method relies on the Deep Optimal Stopping algorithm (DOS) proposed by Becker, Cheridito, and Jentzen (2019), which learns the optimal stopping rule from Monte-Carlo samples of the underlying risk factors. Cashflow paths are then created by applying the learned stopping strategy on a new set of realizations of the risk factors. Furthermore, in a second phase the cashflow paths are projected onto the risk factors to obtain approximations of pathwise option values. The regression step is carried out by ordinary least squares as well as neural networks, and it is shown that the latter results in more accurate approximations.

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  • Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    • Handle: RePEc:eee:apmaco:v:408:y:2021:i:c:s0096300321004215
    DOI: 10.1016/j.amc.2021.126332
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    Cited by:

    1. Purba Banerjee & Vasudeva Murthy & Shashi Jain, 2024. "Method of Lines for Valuation and Sensitivities of Bermudan Options," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 245-270, January.
    2. Glau, Kathrin & Wunderlich, Linus, 2022. "The deep parametric PDE method and applications to option pricing," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    3. Jori Hoencamp & Shashi Jain & Drona Kandhai, 2023. "A Semi-Static Replication Method for Bermudan Swaptions under an Affine Multi-Factor Model," Risks, MDPI, vol. 11(10), pages 1-41, September.
    4. Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "Deep learning for CVA computations of large portfolios of financial derivatives," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    5. Purba Banerjee & Vasudeva Murthy & Shashi Jain, 2021. "Method of lines for valuation and sensitivities of Bermudan options," Papers 2112.01287, arXiv.org.
    6. Ghimire, Sujan & Deo, Ravinesh C. & Casillas-Pérez, David & Salcedo-Sanz, Sancho, 2022. "Boosting solar radiation predictions with global climate models, observational predictors and hybrid deep-machine learning algorithms," Applied Energy, Elsevier, vol. 316(C).
    7. Kentaro Hoshisashi & Yuji Yamada, 2023. "Pricing Multi-Asset Bermudan Commodity Options with Stochastic Volatility Using Neural Networks," JRFM, MDPI, vol. 16(3), pages 1-23, March.

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