Machine Learning for Risk Calculations: A Practitioner's View (The Wiley Finance Series)

Description

State-of-the-art algorithmic deep learning and tensoring techniques for financial institutions The computational demand of risk calculations in financial institutions has ballooned and shows no sign of stopping. It is no longer viable to simply add more computing power to deal with this increased demand. The solution? Algorithmic solutions based on deep learning and Chebyshev tensors represent a practical way to reduce costs while simultaneously increasing risk calculation capabilities. Machine Learning for Risk Calculations: A Practitioner’s View provides an in-depth review of a number of algorithmic solutions and demonstrates how they can be used to overcome the massive computational burden of risk calculations in financial institutions. This book will get you started by reviewing fundamental techniques, including deep learning and Chebyshev tensors. You’ll then discover algorithmic tools that, in combination with the fundamentals, deliver actual solutions to the real problems financial institutions encounter on a regular basis. Numerical tests and examples demonstrate how these solutions can be applied to practical problems, including XVA and Counterparty Credit Risk, IMM capital, PFE, VaR, FRTB, Dynamic Initial Margin, pricing function calibration, volatility surface parametrisation, portfolio optimisation and others. Finally, you’ll uncover the benefits these techniques provide, the practicalities of implementing them, and the software which can be used. Review the fundamentals of deep learning and Chebyshev tensors Discover pioneering algorithmic techniques that can create new opportunities in complex risk calculation Learn how to apply the solutions to a wide range of real-life risk calculations. Download sample code used in the book, so you can follow along and experiment with your own calculations Realize improved risk management whilst overcoming the burden of limited computational power Quants, IT professionals, and financial risk managers will benefit from this practitioner-oriented approach to state-of-the-art risk calculation. Title Page Copyright Dedication Acknowledgements Foreword Motivation and aim of this booknotesSet BOOK OUTLINE NOTE PART One: Fundamental Approximation Methods Chapter 1: Machine Learning 1.1 INTRODUCTION TO MACHINE LEARNING 1.2 THE LINEAR MODEL 1.3 TRAINING AND PREDICTING 1.4 MODEL COMPLEXITY NOTES Chapter 2: Deep Neural Nets 2.1 A BRIEF HISTORY OF DEEP NEURAL NETS 2.2 THE BASIC DEEP NEURAL NET MODEL 2.3 UNIVERSAL APPROXIMATION THEOREMS 2.4 TRAINING OF DEEP NEURAL NETS 2.5 MORE SOPHISTICATED DNNs 2.6 SUMMARY OF CHAPTER NOTES Chapter 3: Chebyshev Tensors 3.1 APPROXIMATING FUNCTIONS WITH POLYNOMIALS 3.2 CHEBYSHEV SERIES 3.3 CHEBYSHEV TENSORS AND INTERPOLANTS 3.4 EX ANTE ERROR ESTIMATION 3.5 WHAT MAKES CHEBYSHEV POINTS UNIQUE 3.6 EVALUATION OF CHEBYSHEV INTERPOLANTS 3.7 DERIVATIVE APPROXIMATION 3.8 CHEBYSHEV SPLINES 3.9 ALGEBRAIC OPERATIONS WITH CHEBYSHEV TENSORS 3.10 CHEBYSHEV TENSORS AND MACHINE LEARNING 3.11 SUMMARY OF CHAPTER NOTES PART Two: The toolkit — plugging in approximation methods Chapter 4: Introduction: why is a toolkit needed 4.1 THE PRICING PROBLEM 4.2 RISK CALCULATION WITH PROXY PRICING 4.3 THE CURSE OF DIMENSIONALITY 4.4 THE TECHNIQUES IN THE TOOLKIT Chapter 5: Composition techniques 5.1 LEVERAGING FROM EXISTING PARAMETRISATIONS 5.2 CREATING A PARAMETRISATION 5.3 SUMMARY OF CHAPTER Chapter 6: Tensors in TT format and Tensor Extension Algorithms 6.1 TENSORS IN TT FORMAT 6.2 TENSOR EXTENSION ALGORITHMS 6.3 STEP 1 — OPTIMISING OVER TENSORS OF FIXED RANK 6.4 STEP 2 — OPTIMISING OVER TENSORS OF VARYING RANK 6.5 STEP 3 — ADAPTING THE SAMPLING SET 6.6 SUMMARY OF CHAPTER NOTES Chapter 7: Sliding Technique 7.1 SLIDE 7.2 SLIDER 7.3 EVALUATING A SLIDER 7.4 SUMMARY OF CHAPTER Chapter 8: The Jacobian projection technique 8.1 SETTING THE BACKGROUND 8.2 WHAT WE CAN RECOVER 8.3 PARTIAL DERIVATIVES VIA PROJECTIONS ONTO THE JACOBIAN NOTES PART Three: Hybrid solutions — approximation methods and the toolkit Chapter 9: Introduction 9.1 THE DIMENSIONALITY PROBLEM REVISITED 9.2 EXPLOITING THE COMPOSITION TECHNIQUE Chapter 10: The Toolkit and Deep Neural Nets 10.1 BUILDING ON P USING THE IMAGE OF G 10.2 BUILDING ON f Chapter 11: The Toolkit and Chebyshev Tensors 11.1 FULL CHEBYSHEV TENSOR 11.2 TT-FORMAT CHEBYSHEV TENSOR 11.3 CHEBYSHEV SLIDER 11.4 A FINAL NOTE Chapter 12: Hybrid Deep Neural Nets and Chebyshev Tensors Frameworks 12.1 THE FUNDAMENTAL IDEA 12.2 DNN+CT WITH STATIC TRAINING SET 12.3 DNN+CT WITH DYNAMIC TRAINING SET 12.4 NUMERICAL TESTS 12.5 ENHANCED DNN+CT ARCHITECTURES AND FURTHER RESEARCH NOTES PART Four: Applications Chapter 13: The aim 13.1 SUITABILITY OF THE APPROXIMATION METHODS 13.2 UNDERSTANDING THE VARIABLES AT PLAY NOTE Chapter 14: When to use Chebyshev Tensors and when to use Deep Neural Nets 14.1 SPEED AND CONVERGENCE 14.2 THE QUESTION OF DIMENSION 14.3 PARTIAL DERIVATIVES AND EX ANTE ERROR ESTIMATION 14.4 SUMMARY OF CHAPTER NOTES Chapter 15: Counterparty credit risk 15.1 MONTE CARLO SIMULATIONS FOR CCR 15.2 SOLUTION 15.3 TESTS 15.4 RESULTS ANALYSIS AND CONCLUSIONS 15.5 SUMMARY OF CHAPTER NOTES Chapter 16: Market Risk 16.1 VAR-LIKE CALCULATIONS 16.2 ENHANCED REVALUATION GRIDS 16.3 FUNDAMENTAL REVIEW OF THE TRADING BOOK 16.4 PROOF OF CONCEPT 16.5 STABILITY OF TECHNIQUE 16.6 RESULTS BEYOND VANILLA PORTFOLIOS — FURTHER RESEARCH 16.7 SUMMARY OF CHAPTER NOTES Chapter 17: Dynamic sensitivities 17.1 SIMULATING SENSITIVITIES 17.2 THE SOLUTION 17.3 AN IMPORTANT USE OF DYNAMIC SENSITIVITIES 17.4 NUMERICAL TESTS 17.5 DISCUSSION OF RESULTS 17.6 ALTERNATIVE METHODS 17.7 SUMMARY OF CHAPTER NOTES Chapter 18: Pricing model calibration 18.1 INTRODUCTION 18.2 SOLUTION 18.3 TEST DESCRIPTION 18.4 RESULTS WITH CHEBYSHEV TENSORS 18.5 RESULTS WITH DEEP NEURAL NETS 18.6 COMPARISON OF RESULTS VIA CT AND DNN 18.7 SUMMARY OF CHAPTER NOTES Chapter 19: Approximation of the implied volatility function 19.1 THE COMPUTATION OF IMPLIED VOLATILITY 19.2 SOLUTION 19.3 RESULTS 19.4 SUMMARY OF CHAPTER NOTES Chapter 20: Optimisation Problems 20.1 BALANCE SHEET OPTIMISATION 20.2 MINIMISATION OF MARGIN FUNDING COST 20.3 GENERALISATION — CURRENTLY “IMPOSSIBLE” CALCULATIONS 20.4 SUMMARY OF CHAPTER NOTES Chapter 21: Pricing Cloning 21.1 PRICING FUNCTION CLONING 21.2 SUMMARY OF CHAPTER NOTES Chapter 22: XVA sensitivities 22.1 FINITE DIFFERENCES AND PROXY PRICERS 22.2 PROXY PRICERS AND AAD NOTES Chapter 23: Sensitivities of exotic derivatives 23.1 BENCHMARK SENSITIVITIES COMPUTATION 23.2 SENSITIVITIES VIA CHEBYSHEV TENSORS NOTES Chapter 24: Software libraries relevant to the book 24.1 RELEVANT SOFTWARE LIBRARIES 24.2 THE MCX SUITE Appendix A: Families of orthogonal polynomials NOTE Appendix B: Exponential convergence of Chebyshev Tensors Appendix C: Chebyshev Splines on functions with no singularity points NOTE Appendix D: Computational savings details for CCR D.1 BARRIER OPTION D.2 CROSS-CURRENCY SWAP D.3 BERMUDAN SWAPTION D.4 AMERICAN OPTION NOTES Appendix E: Computational savings details for dynamic sensitivities E.1 FX SWAP E.2 EUROPEAN SPREAD OPTION NOTE Appendix F: Dynamic sensitivities on the market space F.1 THE PARAMETRISATION F.2 NUMERICAL TESTS F.3 FUTURE WORK... WHEN k > 1 NOTES Appendix G: Dynamic sensitivities and IM via Jacobian Projection technique NOTES Appendix H: MVA optimisation — further computational enhancement Bibliography Index End User License Agreement