ANDREW GREEN FIMA MINSTP BA MA MAST DPHIL is a Managing Director, and Lead Rates and XVA Quant at Scotiabank with over twenty-five years of experience in quantitative finance. He has previously held leadership roles in XVA modelling at Lloyds Banking Group and Barclays Capital. He is also the author of XVA: Credit, Funding and Capital Valuation Adjustments (Wiley, 2015). Andrew has worked on interest rate, credit, and equity derivative model development and implementation during his career.

• Acknowledgments xix1 Introduction 31.1 What this book is about 31.2 The Rise of AI 51.3 The Promise of AI in Quantitative Finance 71.4 Practicalities 71.5 Reading this book 102 Feed Forward Neural Networks 132.1 Introducing Neural Networks 132.2 Regression and Classification 182.3 Activation Functions 272.4 The Universal Function Approximation Theorem 452.5 Conclusions 483 Training Neural Networks 493.1 Backpropagation and Adjoint Algorithmic Differentiation 503.2 Data Preparation and Scaling 533.3 Weight Initialization 573.4 The Choice of Loss Function 683.5 Optimization Algorithms 823.6 Common Training Problems 973.7 Batch Normalization 1043.8 Evaluation and Validation 1103.9 Sobolev Training Using Function Derivatives 1243.10 Conclusions 1314 Regularisation 1334.1 Introduction Regularisation and Generalisation 1334.2 Weight Decay 1344.3 Early Stopping 1374.4 Ensemble Methods and Dropout 1384.5 Data Augmentation 1464.6 Other Regularisation Methods 1474.7 Conclusions Regularisation Strategy 1495 Hyperparameter Optimization 1515.1 Introduction 1515.2 Manual 1555.3 Grid Search 1555.4 Random Search 1585.5 Bayesian Optimization 1595.6 Bandit-based 1655.7 Population Based Training (PBT) 1815.8 Conclusions 1846 Convolutional Neural Networks 1876.1 Introduction 1876.2 Convolutions 1886.3 Downsampling 2036.4 Data Augmentation 2066.5 Transfer Learning Using Pre-trained Networks 2116.6 Visualising Features 2136.7 Famous CNNs 2236.8 Conclusions on CNNs 2527 Sequence Models 2557.1 Introducing Sequence Models 2557.2 Recurrent Neural Networks 2577.3 Neural Natural Language Processing 2767.4 Conclusions on Sequence Models 3228 Autoencoders 3238.1 Introduction 3238.2 Autoencoders and Singular-Valued Decomposition 3258.3 Shallow and Deep Autoencoders 3328.4 Regularized and Sparse Autoencoders 3368.5 Denoising Autoencoders 3398.6 Autoencoders and Generative Models 3418.7 Conclusion 3429 Generative Models 3439.1 Introduction 3439.2 Evaluating Generative Model Performance 3459.3 Energy-based Models (EBMs) 3489.4 Variational Autoencoders (VAEs) 3839.5 Generative Adversarial Networks (GANs) 3969.6 Latent Diffusion Models (LDMs) 4919.7 Conclusions on Generative Models 49310 Deep Reinforcement Learning 49510.1 Introduction 49510.2 Key Concepts in Reinforcement Learning 49610.3 Markov Decision Processes (MDPs) and the Bellman Equations 50610.4 Dynamic Programming and Policy Search 50910.5 Monte Carlo Methods for RL 51610.6 TD Learning 53510.7 Deep Q Networks (DQNs) 54610.8 Policy Gradient 56110.9 Actor-Critic Methods 56710.10 Conclusions 56811 Derivative Valuation using Neural Networks 57111.1 Introduction 57111.2 Derivative Valuation using Neural Networks trained as Non-parametric Models 57211.3 Derivative Valuation Function Approximation 58412 High Dimensional PDE and BSDE Solvers 60312.1 Introduction 60312.2 Deep Galerkin Method (DGM) 60412.3 Deep BSDE Solvers 61912.4 Projection and Martingale Solvers 64112.5 Deep Path Dependent PDEs (DPPDE) 64212.6 Physics Informed Neural Networks (PINNs) 64412.7 Deep Backward Dynamic Programming (DBDP) 64612.8 Deep Splitting (DS) 64712.9 Conclusions 64913 Deep Monte Carlo and Optimal Stopping 65113.1 Introduction 65113.2 Deep Monte Carlo 65313.3 Deep Optimal Stopping and Applications 68513.4 Conclusion Deep Monte Carlo 70314 Static Replication using Neural Networks 70514.1 (Semi) Static Replication 70514.2 Neural Static Replication 70814.3 Conclusions on Neural Static Replication 71615 Volatility Surfaces 71715.1 Introduction 71715.2 Volatility Surface Models 71815.3 Deep Learning Volatility Surfaces 72215.4 Deep Local Volatility 73615.5 Conclusions 75016 Model Calibration 75116.1 Introduction 75116.2 Model Calibration 75216.3 Conclusion on Deep Calibration 76717 XVA 76917.1 Introduction 76917.2 Credit Curve Mapping 77117.3 Exposure Calculation using Neural Networks 78417.4 Conclusions on Deep XVA 79118 Generating Realistic Market Data 79318.1 Introduction and Classical Methods 79318.2 Motivation and Applications of Synthetic Financial Market Data 79618.3 Time Series Generation 79818.4 Generating Higher Dimensional Market Data Structures 86418.5 Completing Market Data - imputing missing values 88618.6 Conclusions Synthetic Market Data 88819 Deep Hedging 89319.1 Introduction 89319.2 Approaches to Deep Hedging 89419.3 Deep Hedging Examples 93519.4 Conclusion 94220 The Future Quant 95720.1 Conclusion on Deep Learning 95720.2 The Future of Quantitative Analytics 95920.3 The Future Quant 96020.4 A Final Word 960

ANDREW GREEN FIMA MINSTP BA MA MAST DPHIL is a Managing Director, and Lead Rates and XVA Quant at Scotiabank with over twenty-five years of experience in quantitative finance. He has previously held leadership roles in XVA modelling at Lloyds Banking Group and Barclays Capital. He is also the author of XVA: Credit, Funding and Capital Valuation Adjustments (Wiley, 2015). Andrew has worked on interest rate, credit, and equity derivative model development and implementation during his career.

• Acknowledgments xix1 Introduction 31.1 What this book is about 31.2 The Rise of AI 51.3 The Promise of AI in Quantitative Finance 71.4 Practicalities 71.5 Reading this book 102 Feed Forward Neural Networks 132.1 Introducing Neural Networks 132.2 Regression and Classification 182.3 Activation Functions 272.4 The Universal Function Approximation Theorem 452.5 Conclusions 483 Training Neural Networks 493.1 Backpropagation and Adjoint Algorithmic Differentiation 503.2 Data Preparation and Scaling 533.3 Weight Initialization 573.4 The Choice of Loss Function 683.5 Optimization Algorithms 823.6 Common Training Problems 973.7 Batch Normalization 1043.8 Evaluation and Validation 1103.9 Sobolev Training Using Function Derivatives 1243.10 Conclusions 1314 Regularisation 1334.1 Introduction Regularisation and Generalisation 1334.2 Weight Decay 1344.3 Early Stopping 1374.4 Ensemble Methods and Dropout 1384.5 Data Augmentation 1464.6 Other Regularisation Methods 1474.7 Conclusions Regularisation Strategy 1495 Hyperparameter Optimization 1515.1 Introduction 1515.2 Manual 1555.3 Grid Search 1555.4 Random Search 1585.5 Bayesian Optimization 1595.6 Bandit-based 1655.7 Population Based Training (PBT) 1815.8 Conclusions 1846 Convolutional Neural Networks 1876.1 Introduction 1876.2 Convolutions 1886.3 Downsampling 2036.4 Data Augmentation 2066.5 Transfer Learning Using Pre-trained Networks 2116.6 Visualising Features 2136.7 Famous CNNs 2236.8 Conclusions on CNNs 2527 Sequence Models 2557.1 Introducing Sequence Models 2557.2 Recurrent Neural Networks 2577.3 Neural Natural Language Processing 2767.4 Conclusions on Sequence Models 3228 Autoencoders 3238.1 Introduction 3238.2 Autoencoders and Singular-Valued Decomposition 3258.3 Shallow and Deep Autoencoders 3328.4 Regularized and Sparse Autoencoders 3368.5 Denoising Autoencoders 3398.6 Autoencoders and Generative Models 3418.7 Conclusion 3429 Generative Models 3439.1 Introduction 3439.2 Evaluating Generative Model Performance 3459.3 Energy-based Models (EBMs) 3489.4 Variational Autoencoders (VAEs) 3839.5 Generative Adversarial Networks (GANs) 3969.6 Latent Diffusion Models (LDMs) 4919.7 Conclusions on Generative Models 49310 Deep Reinforcement Learning 49510.1 Introduction 49510.2 Key Concepts in Reinforcement Learning 49610.3 Markov Decision Processes (MDPs) and the Bellman Equations 50610.4 Dynamic Programming and Policy Search 50910.5 Monte Carlo Methods for RL 51610.6 TD Learning 53510.7 Deep Q Networks (DQNs) 54610.8 Policy Gradient 56110.9 Actor-Critic Methods 56710.10 Conclusions 56811 Derivative Valuation using Neural Networks 57111.1 Introduction 57111.2 Derivative Valuation using Neural Networks trained as Non-parametric Models 57211.3 Derivative Valuation Function Approximation 58412 High Dimensional PDE and BSDE Solvers 60312.1 Introduction 60312.2 Deep Galerkin Method (DGM) 60412.3 Deep BSDE Solvers 61912.4 Projection and Martingale Solvers 64112.5 Deep Path Dependent PDEs (DPPDE) 64212.6 Physics Informed Neural Networks (PINNs) 64412.7 Deep Backward Dynamic Programming (DBDP) 64612.8 Deep Splitting (DS) 64712.9 Conclusions 64913 Deep Monte Carlo and Optimal Stopping 65113.1 Introduction 65113.2 Deep Monte Carlo 65313.3 Deep Optimal Stopping and Applications 68513.4 Conclusion Deep Monte Carlo 70314 Static Replication using Neural Networks 70514.1 (Semi) Static Replication 70514.2 Neural Static Replication 70814.3 Conclusions on Neural Static Replication 71615 Volatility Surfaces 71715.1 Introduction 71715.2 Volatility Surface Models 71815.3 Deep Learning Volatility Surfaces 72215.4 Deep Local Volatility 73615.5 Conclusions 75016 Model Calibration 75116.1 Introduction 75116.2 Model Calibration 75216.3 Conclusion on Deep Calibration 76717 XVA 76917.1 Introduction 76917.2 Credit Curve Mapping 77117.3 Exposure Calculation using Neural Networks 78417.4 Conclusions on Deep XVA 79118 Generating Realistic Market Data 79318.1 Introduction and Classical Methods 79318.2 Motivation and Applications of Synthetic Financial Market Data 79618.3 Time Series Generation 79818.4 Generating Higher Dimensional Market Data Structures 86418.5 Completing Market Data - imputing missing values 88618.6 Conclusions Synthetic Market Data 88819 Deep Hedging 89319.1 Introduction 89319.2 Approaches to Deep Hedging 89419.3 Deep Hedging Examples 93519.4 Conclusion 94220 The Future Quant 95720.1 Conclusion on Deep Learning 95720.2 The Future of Quantitative Analytics 95920.3 The Future Quant 96020.4 A Final Word 960

ANDREW GREEN FIMA MINSTP BA MA MAST DPHIL is a Managing Director, and Lead Rates and XVA Quant at Scotiabank with over twenty-five years of experience in quantitative finance. He has previously held leadership roles in XVA modelling at Lloyds Banking Group and Barclays Capital. He is also the author of XVA: Credit, Funding and Capital Valuation Adjustments (Wiley, 2015). Andrew has worked on interest rate, credit, and equity derivative model development and implementation during his career.

• Acknowledgments xix1 Introduction 31.1 What this book is about 31.2 The Rise of AI 51.3 The Promise of AI in Quantitative Finance 71.4 Practicalities 71.5 Reading this book 102 Feed Forward Neural Networks 132.1 Introducing Neural Networks 132.2 Regression and Classification 182.3 Activation Functions 272.4 The Universal Function Approximation Theorem 452.5 Conclusions 483 Training Neural Networks 493.1 Backpropagation and Adjoint Algorithmic Differentiation 503.2 Data Preparation and Scaling 533.3 Weight Initialization 573.4 The Choice of Loss Function 683.5 Optimization Algorithms 823.6 Common Training Problems 973.7 Batch Normalization 1043.8 Evaluation and Validation 1103.9 Sobolev Training Using Function Derivatives 1243.10 Conclusions 1314 Regularisation 1334.1 Introduction Regularisation and Generalisation 1334.2 Weight Decay 1344.3 Early Stopping 1374.4 Ensemble Methods and Dropout 1384.5 Data Augmentation 1464.6 Other Regularisation Methods 1474.7 Conclusions Regularisation Strategy 1495 Hyperparameter Optimization 1515.1 Introduction 1515.2 Manual 1555.3 Grid Search 1555.4 Random Search 1585.5 Bayesian Optimization 1595.6 Bandit-based 1655.7 Population Based Training (PBT) 1815.8 Conclusions 1846 Convolutional Neural Networks 1876.1 Introduction 1876.2 Convolutions 1886.3 Downsampling 2036.4 Data Augmentation 2066.5 Transfer Learning Using Pre-trained Networks 2116.6 Visualising Features 2136.7 Famous CNNs 2236.8 Conclusions on CNNs 2527 Sequence Models 2557.1 Introducing Sequence Models 2557.2 Recurrent Neural Networks 2577.3 Neural Natural Language Processing 2767.4 Conclusions on Sequence Models 3228 Autoencoders 3238.1 Introduction 3238.2 Autoencoders and Singular-Valued Decomposition 3258.3 Shallow and Deep Autoencoders 3328.4 Regularized and Sparse Autoencoders 3368.5 Denoising Autoencoders 3398.6 Autoencoders and Generative Models 3418.7 Conclusion 3429 Generative Models 3439.1 Introduction 3439.2 Evaluating Generative Model Performance 3459.3 Energy-based Models (EBMs) 3489.4 Variational Autoencoders (VAEs) 3839.5 Generative Adversarial Networks (GANs) 3969.6 Latent Diffusion Models (LDMs) 4919.7 Conclusions on Generative Models 49310 Deep Reinforcement Learning 49510.1 Introduction 49510.2 Key Concepts in Reinforcement Learning 49610.3 Markov Decision Processes (MDPs) and the Bellman Equations 50610.4 Dynamic Programming and Policy Search 50910.5 Monte Carlo Methods for RL 51610.6 TD Learning 53510.7 Deep Q Networks (DQNs) 54610.8 Policy Gradient 56110.9 Actor-Critic Methods 56710.10 Conclusions 56811 Derivative Valuation using Neural Networks 57111.1 Introduction 57111.2 Derivative Valuation using Neural Networks trained as Non-parametric Models 57211.3 Derivative Valuation Function Approximation 58412 High Dimensional PDE and BSDE Solvers 60312.1 Introduction 60312.2 Deep Galerkin Method (DGM) 60412.3 Deep BSDE Solvers 61912.4 Projection and Martingale Solvers 64112.5 Deep Path Dependent PDEs (DPPDE) 64212.6 Physics Informed Neural Networks (PINNs) 64412.7 Deep Backward Dynamic Programming (DBDP) 64612.8 Deep Splitting (DS) 64712.9 Conclusions 64913 Deep Monte Carlo and Optimal Stopping 65113.1 Introduction 65113.2 Deep Monte Carlo 65313.3 Deep Optimal Stopping and Applications 68513.4 Conclusion Deep Monte Carlo 70314 Static Replication using Neural Networks 70514.1 (Semi) Static Replication 70514.2 Neural Static Replication 70814.3 Conclusions on Neural Static Replication 71615 Volatility Surfaces 71715.1 Introduction 71715.2 Volatility Surface Models 71815.3 Deep Learning Volatility Surfaces 72215.4 Deep Local Volatility 73615.5 Conclusions 75016 Model Calibration 75116.1 Introduction 75116.2 Model Calibration 75216.3 Conclusion on Deep Calibration 76717 XVA 76917.1 Introduction 76917.2 Credit Curve Mapping 77117.3 Exposure Calculation using Neural Networks 78417.4 Conclusions on Deep XVA 79118 Generating Realistic Market Data 79318.1 Introduction and Classical Methods 79318.2 Motivation and Applications of Synthetic Financial Market Data 79618.3 Time Series Generation 79818.4 Generating Higher Dimensional Market Data Structures 86418.5 Completing Market Data - imputing missing values 88618.6 Conclusions Synthetic Market Data 88819 Deep Hedging 89319.1 Introduction 89319.2 Approaches to Deep Hedging 89419.3 Deep Hedging Examples 93519.4 Conclusion 94220 The Future Quant 95720.1 Conclusion on Deep Learning 95720.2 The Future of Quantitative Analytics 95920.3 The Future Quant 96020.4 A Final Word 960