Deeply Learning Derivatives

This paper uses deep learning to value derivatives. The approach is broadly applicable, and we use a call option on a basket of stocks as an example. We show that the deep learning model is accurate and very fast, capable of producing valuations a million times faster than traditional models. We develop a methodology to randomly generate appropriate training data and explore the impact of several parameters including layer width and depth, training data quality and quantity on model speed and accuracy.

[1]  Giovanni Cesari,et al.  Modelling, Pricing, and Hedging Counterparty Credit Exposure , 2009 .

[2]  Pierre Henry-Labordere,et al.  Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM , 2017 .

[3]  Zhongmin Luo,et al.  CDS Rate Construction Methods by Machine Learning Techniques , 2017 .

[4]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[6]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[7]  Ignacio Ruiz,et al.  Chebyshev Methods for Ultra-Efficient Risk Calculations , 2018 .

[8]  Andrew David Green,et al.  XVA: Credit, Funding and Capital Valuation Adjustments: Green/XVA , 2015 .

[9]  Paolo Tenti,et al.  Forecasting Foreign Exchange Rates Using Recurrent Neural Networks , 1996, Appl. Artif. Intell..

[10]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[11]  Yee Whye Teh,et al.  A Fast Learning Algorithm for Deep Belief Nets , 2006, Neural Computation.

[12]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[13]  Maximilian Mair,et al.  Chebyshev interpolation for parametric option pricing , 2015, Finance Stochastics.

[14]  Robert Culkin,et al.  Machine Learning in Finance : The Case of Deep Learning for Option Pricing , 2017 .

[15]  Ruslan Salakhutdinov,et al.  On Characterizing the Capacity of Neural Networks using Algebraic Topology , 2018, ArXiv.

[16]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[17]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[18]  Charu C. Aggarwal,et al.  Neural Networks and Deep Learning , 2018, Springer International Publishing.

[19]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[20]  Dorota Kurowicka,et al.  Generating random correlation matrices based on vines and extended onion method , 2009, J. Multivar. Anal..

[21]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[22]  E Weinan,et al.  Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations , 2017, Communications in Mathematics and Statistics.