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Deep learning Profit & Loss

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Listed:
  • Pietro Rossi
  • Flavio Cocco
  • Giacomo Bormetti

Abstract

Building the future profit and loss (P&L) distribution of a portfolio holding, among other assets, highly non-linear and path-dependent derivatives is a challenging task. We provide a simple machinery where more and more assets could be accounted for in a simple and semi-automatic fashion. We resort to a variation of the Least Square Monte Carlo algorithm where interpolation of the continuation value of the portfolio is done with a feed forward neural network. This approach has several appealing features not all of them will be fully discussed in the paper. Neural networks are extremely flexible regressors. We do not need to worry about the fact that for multi assets payoff, the exercise surface could be non connected. Neither we have to search for smart regressors. The idea is to use, regardless of the complexity of the payoff, only the underlying processes. Neural networks with many outputs can interpolate every single assets in the portfolio generated by a single Monte Carlo simulation. This is an essential feature to account for the P&L distribution of the whole portfolio when the dependence structure between the different assets is very strong like the case where one has contingent claims written on the same underlying.

Suggested Citation

  • Pietro Rossi & Flavio Cocco & Giacomo Bormetti, 2020. "Deep learning Profit & Loss," Papers 2006.09955, arXiv.org, revised Aug 2020.
    • Handle: RePEc:arx:papers:2006.09955
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    3. Ryan Ferguson & Andrew Green, 2018. "Deeply Learning Derivatives," Papers 1809.02233, arXiv.org, revised Oct 2018.
    4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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