Differential Machine Learning

51 Pages Posted: 4 Jun 2020 Last revised: 30 Sep 2020

See all articles by Brian Norsk Huge

Brian Norsk Huge

Saxo Bank

Antoine Savine

Danske Bank; University of Copenhagen - Copenhagen University

Date Written: January 3, 2020


Differential machine learning combines automatic adjoint differentiation (AAD) with modern machine learning (ML) in the context of risk management of financial Derivatives. We introduce novel algorithms for training fast, accurate pricing and risk approximations, online, in real-time, with convergence guarantees. Our machinery is applicable to arbitrary Derivatives instruments or trading books, under arbitrary stochastic models of the underlying market variables. It effectively resolves computational bottlenecks of Derivatives risk reports and capital calculations.

Differential ML is a general extension of supervised learning, where ML models are trained on examples of not only inputs and labels but also differentials of labels wrt inputs. It is also applicable in many situations outside finance, where high-quality first-order derivatives wrt training inputs are available. Applications in Physics, for example, may leverage differentials known from first principles to learn function approximations more effectively.

In finance, AAD computes pathwise differentials with remarkable efficacy so differential ML algorithms provide extremely effective pricing and risk approximations. We can produce fast analytics in models too complex for closed-form solutions, extract the risk factors of complex transactions and trading books, and effectively compute risk management metrics like reports across a large number of scenarios, backtesting and simulation of hedge strategies, or regulations like XVA, CCR, FRTB or SIMM-MVA.

TensorFlow implementation is available on https://github.com/differential-machine-learning

Keywords: automatic differentiation, machine learning, deep learning, neural networks, quantitative finance, risk management, derivatives, trading systems, financial regulation, options, pricing, monte carlo, least square method, regression, PCA

Suggested Citation

Huge, Brian Norsk and Savine, Antoine, Differential Machine Learning (January 3, 2020). Available at SSRN: https://ssrn.com/abstract=3591734 or http://dx.doi.org/10.2139/ssrn.3591734

Brian Norsk Huge

Saxo Bank ( email )


Antoine Savine (Contact Author)

Danske Bank ( email )

DK-1092 Copenhagen K

HOME PAGE: http://antoinesavine.com

University of Copenhagen - Copenhagen University ( email )

studiestraede 6
copenhagen, 1455

HOME PAGE: http://www.math.ku.dk/english/staff/?pure=en/persons/590245

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