www.morganmarkets.comGlobal Quantitative & Derivatives Strategy07 August 2019Big Data and AI StrategiesA Practitioner's Introduction to Neural NetworksGlobal Quantitative and Derivatives StrategyPeng Cheng, CFA AC(1-212)

[email protected] J Murphy, PhD(1-212)

[email protected] Kolanovic, PhD(1-212)

[email protected] Morgan Securities LLCSee page 22 for analyst certification and important disclosures.J.P. Morgan does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this report. Investors should consider this report as only a single factor in making their investment decision.? The report aimsto demystify neural networksfor our readers in a practitioner-friendly way.? The neural network architectureis explainedby comparing it to the familiar linear regression model.? Using simulated data, we demonstratehow to construct a neural network from scratch in R.? We then move on to using real world dataand examinethe correspondence between neural networks and existing, well-known financial models for volatility forecasting:o Feedforward neural networkvs. ARCHo Recurrent neural networkvs. GARCH(1, 1)o Long short term memory networkvs. GARCH(p, q)? Finally LSTM isused to forecast volatility of S&P 500 and EURUSD, and its performance is comparedagainst GARCH(1, 1).2Global Quantitative & Derivatives Strategy07 August 2019Peng Cheng, CFA(1-212)

[email protected] this report we aim to demystify neural network for our readers by putting it in a more familiar financial context.Whenthere is already an abundance of literature on neural networksavailable, why the need for another report?Compared to other fieldsin which neural networks havebeen widely applied, the problems we face in finance are relatively unique, and therefore require separate treatments. We summarizebelowwhat are,in our view,the unique challenges investors facewhen learning about neural networks.Classification vs. regressionNeural networksare most often discussed in the context of classification, wherey variables are either Boolean orcategorical. The vast majority of the interesting problems in finance are concerned withcontinuous variablesand are therefore regression problems.Financial models are not expressed as flow chartsNeural networksare almost always illustrated by graphsseen in Figure 1and Figure 2, which are unfamiliar to investorssince financial models are rarelyexpressed as such.Figure 1: Sample illustration of a neural networkSource: Wikipedia/Glosser.caFigure 2: Sample illustration of a cellin an LSTM neural networkSource: Wikipedia/Guillaume Chevalier3Global Quantitative & Derivatives Strategy07 August 2019Peng Cheng, CFA(1-212)

[email protected] terminologyIn addition, terms such as activation function, bias, forwardand backpropagationare not commonly found in our glossary, even though very similar concepts already exist in finance.Lack of working examplesWhile our colleagues demonstrated the many challengesthat neural networks posewhen applied to forecasting equity return,finance-related examples, especially the ones that demonstrate predictive power, are few and far between.The goal of this report is to introduce neural networks in a practitioner-friendly way, taking into account the points raised above. We first explain the neural network architecture by comparing it to the familiar linear regression model. We then demonstrate how to construct a neural network from scratch in R using simulated data. Finally we move on to real world data and examine the correspondence between neural networks and existing, well-known financial models for volatility forecasting.Revisiting the Neural Network ArchitectureLinear model as a special case of neural networkHow would we interpret the graphical representation of a neural network?Westart out by showing thata linear regression model can be represented similarly. Forinstance, themodel

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