Publication
Differential Machine Learning
Differential Machine Learning -- working paper
What is it about?
Differential machine learning is a novel family of function approximation algorithms, with remarkable performance in cases where high quality first order differentials wrt input parameters are available. In the context of pricing and risk management of financial derivatives, differential ML works with pathwise differentials computed with automatic differentiation (AAD) to learn pricing functions with unreasonable effectiveness.
Why is it important?
Applications in finance include risk reports of complex trading books in multiple scenarios, backtesting and regulatory / capital computations like XVA, CCR, FRTB or SIMM-MVA. Differential ML effectively learns high quality pricing approximations with sufficient speed, accuracy and guarantee to produce accurate risk reports and metrics without the massive computation load.
Perspectives
This is the result of over 6 months of intensive research at Danske Bank. We started with extensions of the classic Longstaff-Schwartz method to modern deep learning, with the objective of finding general methods with guaranteed convergence towards high quality approximations learned on small datasets. The turning point occurred when we thought of leveraging AAD generated pathwise differentials to teach neural networks, not only punctual examples, but the shape of the pricing functions. From that point, the machinery started working efficiently and reliably, seamlessly generalizing to increasingly complex problems, including application to counterparty credit risk (CCR) on large complex trading books.
Antoine
Savine
Danske Bank A/S
