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. Deep Learning and Tensoring 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.

IGNACIO RUIZ, PhD, is the head of Counterparty Credit Risk Measurement and Analytics at Scotiabank. Prior to that he has been head quant for Counterparty Credit Risk Exposure Analytics at Credit Suisse, head of Equity Risk Analytics at BNP Paribas and he founded MoCaX Intelligence, from where he offered his services as an independent consultant. He holds a PhD in Physics from the University of Cambridge.

MARIANO ZERON, PhD, is Head of Research and Development at MoCaX Intelligence. Prior to that he was a quant researcher at Areski Capital. He has extensive experience with Chebyshev Tensors and Deep Neural Nets applied to risk calculations. He holds a PhD in Mathematics from the University of Cambridge.

I Fundamental Approximation Methods 31

1 Machine Learning 33

2 Deep Neural Nets 77

3 Chebyshev Tensors 109

II The toolkit | plugging in approximation methods155

4 Introduction: why is a toolkit needed 157

5 Composition techniques 165

6 Tensors in TT format and Tensor Extension Algorithms 177

7 Sliding technique 197

8 The Jacobian projection technique 203

III Hybrid solutions | approximation methods and the toolkit 215

9 Introduction 217

10 The Toolkit and Deep Neural Nets 221

11 The Toolkit and Chebyshev Tensors 225

12 Hybrid Deep Neural Nets and Chebyshev Tensors Frameworks 229

13 The Aim 247

14 When to use Chebyshev Tensors and when Deep Neural Nets253

15 Counterparty Credit Risk 271

16 Market Risk 323

17 Dynamic sensitivities 363

18 Pricing model calibration 385

19 Approximation of the implied volatility function 407

20 Optimisation Problems 435

21 Pricing Cloning 451

22 XVA sensitivities 461

23 Sensitivities of exotic derivatives 467

24 Software libraries relevant to the book 475

Appendix A Families of orthogonal polynomials 501

Appendices

Appendix B Exponential convergence of Chebyshev Tensors 503

Appendix C Chebyshev Splines on functions with no singularity

points 507

Appendix D Computational savings details for CCR 511

Appendix E computational savings details for dynamic sensitivi-ties 519

Appendix F Dynamic sensitivities on the market space 523

Appendix G Dynamic sensitivities and IM via Jacobian Projec-tion technique 53