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Differential ML with a Difference

Author

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  • Paul Glasserman
  • Siddharth Hemant Karmarkar

Abstract

Differential ML (Huge and Savine 2020) is a technique for training neural networks to provide fast approximations to complex simulation-based models for derivatives pricing and risk management. It uses price sensitivities calculated through pathwise adjoint differentiation to reduce pricing and hedging errors. However, for options with discontinuous payoffs, such as digital or barrier options, the pathwise sensitivities are biased, and incorporating them into the loss function can magnify errors. We consider alternative methods for estimating sensitivities and find that they can substantially reduce test errors in prices and in their sensitivities. Using differential labels calculated through the likelihood ratio method expands the scope of Differential ML to discontinuous payoffs. A hybrid method incorporates gamma estimates as well as delta estimates, providing further regularization.

Suggested Citation

  • Paul Glasserman & Siddharth Hemant Karmarkar, 2025. "Differential ML with a Difference," Papers 2512.05301, arXiv.org.
    • Handle: RePEc:arx:papers:2512.05301
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    References listed on IDEAS

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    3. Matthew F. Dixon & Igor Halperin & Paul Bilokon, 2020. "Frontiers of Machine Learning and Finance," Springer Books, in: Machine Learning in Finance, chapter 0, pages 519-541, Springer.
    4. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
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