Differential Machine Learning

Risk management with AAD and ML: an unreasonably effective combination

Working paper: on ssrn
GitHub: github.com/differential-machine-learning
TensorFlow notebook: on Google Colab

Differential machine learning (ML) is an extension of supervised learning, where ML models are trained on examples of not only inputs and labels but also differentials of labels to inputs, applicable in all situations where high quality first order derivatives wrt training inputs are available.

In the context of financial Derivatives and risk management, pathwise differentials are efficiently computed with automatic adjoint differentiation (AAD). Differential machine learning gives us unreasonably effective pricing and risk approximation. We can produce fast pricing 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.

The article focuses on differential deep learning (DL), arguably the strongest application. Standard DL trains neural networks (NN) on punctual examples, whereas differential DL teaches them the shape of the target function, hence the performance. We included numerical examples, both idealized and real world.

In the online appendices, we apply differential learning to other ML models, like classic regression or principal component analysis (PCA), with equally remarkable results.

We posted a TensorFlow implementation on Google Colab, including examples from the paper and a discussion of practical implementation.

Open In Colab
basket option price approximation from simulated data
with standard and differential deep learning

RiskMinds 2019

Flying Monday to Amsterdam with my colleagues from Superfly Analytics of Danske Bank, including Brian Huge and Ove Scavenius, to attend the RiskMinds 2019 risk management conference and the award ceremony, where our group is nominated for ‘Excellence in risk management and modeling’.

EDIT: Superfly Analytics now won the award:

Excellence in Risk Management and Modelling, winner: Superfly Analytics at Danske Bank

We will be presenting our vision of modern risk management systems and the ‘One Analytics’ platform: full front to back consistency with scripting of cash-flows , model hierarchies and AAD. Further, we will present ‘Deep Analytics’: leveraging risk management systems with AI to learn revaluation and risk analytics on the fly. For those unable to attend, we posted our slides online here:

www.deep-analytics.org

click on the picture to see the presentation