High performance computing in finance problems, methods, and solutions

High-Performance Computing in Finance Problems, Methods, and Solutions High-Performance Computing in Finance Problems, Methods, and Solutions Edited by M A H Dempster Juho Kanniainen John Keane Erik Vynckier MATLAB R is a trademark of The MathWorks, Inc and is used with permission The MathWorks does not warrant the accuracy of the text or exercises in this book This book’s use or discussion of MATLAB R software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB R software CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 c 2018 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed on acid-free paper International Standard Book Number-13: 978-1-4822-9966-3 (Hardback) This book contains information obtained from authentic and highly regarded 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www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data Names: Dempster, M A H (Michael Alan Howarth), 1938- editor | Kanniainen, Juho editor | Keane, John editor | Vynckier, Erik editor Title: High-performance computing in finance : problems, methods, and solutions / [edited by] M.A.H Dempster [and three others] Description: Boca Raton, FL : CRC Press, 2018 Identifiers: LCCN 2017052035| ISBN 9781482299663 (hardback) | ISBN 9781315372006 (ebook) Subjects: LCSH: Finance Mathematical models | Finance Data processing Classification: LCC HG106 H544 2018 | DDC 332.01/5118 dc23 LC record available at https://lccn.loc.gov/2017052035 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Editors xi Contributors xiii Introduction xvii I Computationally Expensive Problems in the Financial Industry Computationally Expensive Problems in Investment Banking Jonathan Rosen, Christian Kahl, Russell Goyder, and Mark Gibbs Using Market Sentiment to Enhance Second-Order Stochastic Dominance Trading Models Gautam Mitra, Christina Erlwein-Sayer, Cristiano Arbex Valle, and Xiang Yu The Alpha Engine: Designing an Automated Trading Algorithm Anton Golub, James B Glattfelder, and Richard B Olsen Portfolio Liquidation and Ambiguity Aversion ´ Alvaro Cartea, Ryan Donnelly, and Sebastian Jaimungal Challenges in Scenario Generation: Modeling Market and Non-Market Risks in Insurance Douglas McLean II Numerical Methods in Financial High-Performance Computing (HPC) Finite Difference Methods for Medium- and High-Dimensional Derivative Pricing PDEs Christoph Reisinger and Rasmus Wissmann 25 49 77 115 173 175 vii viii Contents Multilevel Monte Carlo Methods for Applications in Finance Michael B Giles and Lukasz Szpruch 197 Fourier and Wavelet Option Pricing Methods Stefanus C Maree, Luis Ortiz-Gracia, and Cornelis W Oosterlee 249 A Practical Robust Long-Term Yield Curve Model M A H Dempster, Elena A Medova, Igor Osmolovskiy, and Philipp Ustinov 273 10 Algorithmic Dierentiation Uwe Naumann, Jonathan Hă user, Jens Deussen, and Jacques du Toit 315 11 Case Studies of Real-Time Risk Management via Adjoint Algorithmic Differentiation (AAD) Luca Capriotti and Jacky Lee 339 12 Tackling Reinsurance Contract Optimization by Means of Evolutionary Algorithms and HPC Omar Andres Carmona Cortes and Andrew Rau-Chaplin 371 13 Evaluating Blockchain Implementation of Clearing and Settlement at the IATA Clearing House Sergey Ivliev, Yulia Mizgireva, and Juan Ivan Martin 391 III HPC Systems: Hardware, Software, and Data with Financial Applications 411 14 Supercomputers Peter Schober 413 15 Multiscale Dataflow Computing in Finance Oskar Mencer, Brian Boucher, Gary Robinson, Jon Gregory, and Georgi Gaydadjiev 441 16 Manycore Parallel Computation John Ashley and Mark Joshi 471 17 Practitioner’s Guide on the Use of Cloud Computing in Finance Binghuan Lin, Rainer Wehkamp, and Juho Kanniainen 509 Contents 18 Blockchains and Distributed Ledgers in Retrospective and Perspective Alexander Lipton ix 537 19 Optimal Feature Selection Using a Quantum Annealer Andrew Milne, Mark Rounds, and Peter Goddard 561 Index 589 600 Implementation approaches of AD, 19–20 Implicit functions, 325 convex optimization, 326 linear systems, 325 nonlinear systems, 325–326 theorem, 360–362 Improved MLMC method, 202 Indifference prices, 66 Individual banks, money creation by, 553–554 Inferring states method, 290 Infiniband, 449 Infinitesimal perturbation analysis, see Pathwise sensitivity approach Information flow, 31 Information service, 70 Information theory, novel insights from, 62–64 Infrastructure as a Service (IaaS), 143 Inhomogeneous heat equation, 186 In-memory data aggregation, 17 Input/output operations (I/O operations), 442, 517 Input parameters, 216 In-sample goodness-of-fit, 300–303 Instantaneous short rate, 280 Instruction Level Parallelism (ILP), 479–480 Instruction parallel, 479–480 Intel(R) Xeon (R) CPU E5–2643, 491 Intel CPU, 476 “Interaction Between Law and Society” PhD thesis, 70 Interest rate products, 340 pathwise derivative method, 344–349 real-time risk management, 344 Interest rates, 468 swap pricing, 462–463 Internal model, 120 Internal model method (IMM), 12, 13 International Air Transport Association (IATA), 392 International Data Corporation (IDC), 511 International Swaps & Derivatives Association (ISDA), 467 master agreement, Intrinsic time, 54, 56 Index coastline representation of price curve, 58 events, 57 Inventory, 80 penalization, 90–91 Investment, banking industry, 116 strategies, 53 Investment banking, computationally expensive problems in AD, 17–22 financial investments, hardware, 15–17 hedging, 14–15 RCR, 11–14 technology, 15–22 trading, 14–15 valuation requirements, 5–10 I/O operations, see Input/output operations ISDA, see International Swaps & Derivatives Association Iterated extended Kalman filter (IEKF), 290 IT legacy, 521 J Jacobians, 20, 21 Jarrow–Landau–Turnbull model, 138 Job scheduler, 516 Joslin–Singleton–Zhu model (JSZ model), 281, 282 Jump-adapted discretization, 222 Jump-adapted Milstein discretization, 223 MLMC for constant jump rate, 223–224 MLMC for path-dependent rates, 224–226 Jump-adapted thinning, 225 Jump-diffusions, 222, 223, 241 L´evy processes, 226–227 Merton’s jump diffusion model, 139 MLMC for, 222 SDE, 222 Jump-to-default process, JUQUEEN supercomputer, 419, 427, 429 Index K K20c NVIDIA graphics card, 485 Kalman filter (KF), 275, 309 measurement equation, 286 transition equation, 286 Kelly Criterion, 29 Kelly Strategy (KS), 38 Kernels, 493 KF, see Kalman filter Knight Capital, 52 k-Nearest Neighbors classification schemes (k-NN classification schemes), 565 Know your customer (KYC), 538 Kolmogorov forward equation, 177 Kooderive, 502, 503 Krippner approach, 291 KS, see Kelly Strategy KVA, see Capital value adjustment KYC, see Know your customer L λ hyper-parameter, 155, 156 Land titles, 543 Lapse, 148 Large DFE memory (LMem), 445, 549 LASSO regression, 532 Layers, 372 L-CSC, 417, 437 Least-squares on GPU, 498–499 Lee and Carter model, 147 Legal frameworks, 11 Levenberg–Marquardt technique, 133, 140 L´evy area, 204, 229 L´evy processes, 226–227, 255, 266 LIBOR, see London Interbank Offered Rate LIBOR market model (LMM), 116, 136, 217, 320, 344, 464, 484, 485, 486 data collection phase, 499–500 design overview, 492–493 in discrete time, 488–489 least-squares and multiple regressions on GPU, 498–499 memory use, threads, and blocks, 493–495 601 multiple regression, 489–491 packages and hardware, 491 path generation, 495–497 pricing phase, 500–501 product specification and design, 497–498 simulation, 345–349 speed comparisons and numerical results, 501–504 with stochastic volatility, 125 Life cycle investment decisions optimization using MATLAB, 431 approach, 433 discrete time dynamic programming, 433 implementation, 434 parallelization, 433–434, 437 problem, 432–433 results, 434–436 Likelihood maximization, 291 Likelihood ratio method (LRM), 216 Limiting factor, 423 Limit order placement, 79 Linear systems, 325 LINPACK performance list, 416 Lipschitz condition, 105 Lipschitz functions, 235 Liquidation, 77 Liquid financial markets, 51 Liquidity-providing investment algorithms, 51–52 Liquidity profile improving, 399 Little’s law, 479 LMM, see LIBOR market model LoadLeveler, 414 Local volatility process, 315–316 Log-asset price processes, 250 Logical threading logical thread on GPU, 481 models, 480–481 Logistic regression, 565 QUBO feature selection with, 579–580 recursive feature elimination with, 580–582 Log-likelihood, 287 function calculation, 309–310 objective function, 298 602 Lognormal asset-price process, 127 Lognormal equity asset model, 139 Log-normal models, London Interbank Offered Rate (LIBOR), 463; see also LIBOR market model (LMM) data, 299 Long-Term Capital Management, 284n7 Long-term models, 53 Longevity risk, 147 “Long only” SSD portfolios, 29 “Long–short” strategy, 29 Long–short discrete optimization model, 34–35 Longstaff–Schwartz algorithm for put options, 331 Lookback options, 209–211 Low truncation dimension, 176 LP model solution, 39–40 LRM, see Likelihood ratio method Lyapunov exponent, 141n22 M Machine learning packages, 570 Macroscopic complexity, 60 Magnetic effects, 571 Manycore parallel computation computer architecture, 472–473 LIBOR market model, 486–504 NVIDIA’s recent GPUs, 484 parallelism and execution, 480–484 parallelism and performance, 477–480 parallelism imperative, 473–475 practitioner, 472 systems architecture, 475–477 Market data, 30 Market dynamics, 121 Market-consistent embedded value (MCEV), 122 Market orders (MO), 79 ambiguity aversion effects on MO execution, 95–97 feedback controls, 93–95 inclusion of, 93 optimal depth and MO execution boundary, 95 Market-price-of-risk, 121, 128, 285 Index Market risk, capital calculation, 12 Markit, 137 Markowitz model, 29 Markowitz-style objective, 534 Massively Parallel Processing (MPP), 414 Master–worker pattern, 434 Mathematical formulation of model, 397 discrete-time optimal control model, 397–399 final mathematical formulation of model, 402–403 values of control variables, 400–401 variants of objective function, 399 MATLAB, 418, 420 approach, 433 discrete time dynamic programming, 433 implementation, 434 life cycle investment decisions optimization using, 431 parallelization, 433–434, 437 problem, 432–433 results, 434–436 version R2012b, 434 MaxCompiler, 447 compiling dataflow application with, 450 Maxeler computing systems, 443 dataflow oriented computing paradigm, 443 MPC-C systems couple x86 server-grade CPUs, 445 MPC-N series systems, 447 SLiC, 451 Maxeler dataflow systems, 445, 461 DFEs in cloud, 447–449 MPC-C series architecture, 446 MPC-N series architecture, 447 MPC-X series architecture, 446 MaxelerOS, 447, 456 Maxeler RiskAnalytics DFE-accelerated components, 467 platform, 461–462 Maxeler Technologies, 443 “Maximum drawdown” dynamic risk measures, 29, 38 Index Maximum likelihood, 22 Maximum likelihood estimation (MLE), 275, 290 Maximum Performance Computing, 448 MaxJ, 450–451, 452, 453, 454, 455 MaxRing, 445, 449 MCEV, see Market-consistent embedded value MCR, see Minimum capital requirement MCT, see Monetary circuit theory Mean-variance optimization framework, 530 Measured service, 511 Measurement covariance matrix, 296 error process, 286 Medium-and high-dimensional derivative pricing PDEs asset-dependent correlation, 193 decomposition methods, 182–184 different base cases with nonconstant parameters, 188 finite difference schemes, 179–181 theoretical results, 185–187 time-dependent exponential correlation, 190, 191 time-dependent simple correlation, 189–190 time-dependent volatilities, exponential correlation, 191–192 time-dependent volatilities, simple correlation, 190–191, 192 Memory management on GPU, 482 Memory use, 493–495 Merkle trees, 544 Mersenne twister, 144 Merton’s jump diffusion model, 139 Mesh-based methods, 176 Message Passing Interface (MPI), 415–416, 418, 419, 479 approach, 428 combination technique, 428–429 decomposition, 428 implementation, 429 parallelization, 429 pricing basket options using, 427 problem, 427–428 results, 429–431 603 Metrics, 382–383 Micro-architectural innovations, 442 Microsoft Azure, 524 Microsoft’s Azure, 142 Microsoft’s Service Fabric, 143 Microsoft Windows Azure Cloud, 529 Middleware, 516 solutions, 521 Midprice, 79 Midprice drift, 90 equivalence to inventory penalization, 90–91 Milstein discretization, 231–233 Milstein scheme, 209–211; see also Multidimensional Milstein scheme Miners, see Notaries minimize() function, 571–573 Minimum capital requirement (MCR), 118 Mining, 546 Minor embedding, 572 Minute-based pricing model, 524 Mixed precision arithmetic, 239–240 MLE, see Maximum likelihood estimation MLMC methods, see Multilevel Monte Carlo methods MO, see Market orders Model calibration toolkits, 125 Model risk, 116 Modern FVA models, 10 Modern macroeconomic thinking, 551 Monetary circuit, 551–552 Monetary circuit theory (MCT), 552 Money creation by banking system, 554 general aspects, 552–553 by individual banks, 553–554 by two banks, 554, 555 Money management dynamic strategy using, 38–39 volatility pumping via, 29 Monotonicity, 119 Monte Carlo (MC) bond pricing, 291 greeks, 216–217 methods, 4, 517, 518, 529 option pricing, 514 604 Monte Carlo (MC) (Continued ) simulations, 6, 9, 16, 118, 122, 199–200, 332, 340, 422, 423, 430, 443, 484–485, 514 trials, 125, 142 Monte Carlo scenario generation, 275 simulation, 274 Moody’s Analytics, 125, 519 RiskIntegrity Suite ESG, 124, 126 Moody’s KMV model, 138 Moore’s law, 415, 473 MOPBIL, 379, 380, 383–385 Mortality risk, 147 MPC-C series architecture, 446 MPC-N series architecture, 447 MPC-X series architecture, 446 MPI, see Message Passing Interface MPP, see Massively Parallel Processing MRA, see Multi resolution analysis Multidimensional Black–Scholes model, 485 Multidimensional Milstein scheme, 227 antithetic multilevel Monte Carlo estimator, 227–228 Clark–Cameron example, 228–231 Milstein discretization, 231–233 piecewise linear interpolation analysis, 233–235 simulations for antithetic Monte Carlo, 235–236 Multifactor yield curve models and drawbacks, 276 availability, 277–280 classification of three-factor affine short rate models, 280–281 difficulties with Gaussian affine models, 282–283 requirements for model development, 276–277 Multilevel checkpointing schemes, 324 Multilevel implementation, 225 Multilevel method, 237 mixed precision arithmetic, 239–240 nested simulation, 238 stochastic partial differential equations, 237 truncated series expansions, 238–239 Multilevel Monte Carlo Greeks, 216, 218 Index conditional Monte Carlo for pathwise sensitivity, 218–219 European call, 218 Monte Carlo Greeks, 216–217 optimal number of samples, 220 split pathwise sensitivities, 219–220 vibrato Monte Carlo, 220–222 Multilevel Monte Carlo methods (MLMC methods), 198, 199, 202; see also Fourier and wavelet option pricing methods algorithm, 205–206 Brownian bridge interpolation, analysis of, 242–244 Euler and Milstein discretizations, 203–205 improved multilevel Monte Carlo, 202 for jump-diffusion processes, 222–227 Monte Carlo, 199–200 multidimensional Milstein scheme, 227–236 multilevel method, other uses of, 237 multilevel Monte Carlo algorithm, 205–206 multilevel Quasi-Monte Carlo, 240 pricing with, 206–215 SDE, 202–203 theorem, 200–201 Multilevel Quasi-Monte Carlo, 240 Multilevel treatment, 238 Multiple regression, 489–491 Multiple regressions on GPU, 498–499 Multiple strike pricing, 270–271 Multi resolution analysis (MRA), 255 Multiscale dataflow computing in finance conventional control-flow oriented processor, 444 correlation, 459–461 dataflow paradigm, 443–445 dataflow programming principles, 449–457 development process and design optimization, 457–459 financial application examples, 461–469 Maxeler dataflow systems, 445–449 605 Index Multiscale dataflow programming, 449 ecosystem, 448–449 Multithreaded implementations, 442 Mutual information, 569 scores, 576 N NAG, see Numerical Algorithms Group Ltd National Institute of Standards and Technology (NIST), 510 NCM, see Nearest correlation matrix N-dimensional heat equation, 183 Nearest correlation matrix (NCM), 332–334 Negative interest rates, 555–557 Negative nominal interest rates, challenge of, 116 Nelson and Siegel rate parameter, 132 Nelson–Siegel functional extrapolation, 132 Nested simulation, 238 Nested stochastic problem, 122 Network IO, 476 Neural networks, 565 News analytics data, 30 meta data, 30 sentiment score, 32 Newton method, 332 Newton–Raphson iterations, 35 New York Stock Exchange (NYSE), 535 NIKKEI 227, 40 NIKKEI 252 components, 38, 40 NImpact, 33 NIST, see National Institute of Standards and Technology NLP problem, see Non-linear optimization problem Nominal interest-rate models, 133–138 Nominal short rate, 287 Nonconstant parameters, base cases with, 188 Nonembarrassingly parallel computing problem, 513, 514 Non-Gaussian simulation processes, Nonlinear black correction for EFM model, 283 black correction for negative rates, 287–288 EFM model calibration, 285–287 stylized properties of Black models, 288, 289 three-factor basic EFM model, 284–285 Nonlinear black correction for EFM model, 283 EFM model calibration, 285–287 three-factor basic EFM model, 284–285 Nonlinear equations, 35 Non-linear optimization problem (NLP problem), 36 Nonlinear problem, Nonlinear systems, 325–326 Normal copula, 145, 146 Non-market risks, 143 Non-negativity, 139 Notaries, 539, 546 Numerical Algorithms Group Ltd (NAG), 297 library, 292 Numerix’ Oneview ESG, 124 NumPy array, 571 NVidia’s GPU computation, 143 NYSE, see New York Stock Exchange O OANDA trading platform, 71 Objective function, 570 variants, 399 OIS, see Overnight Index Swap On-demand self-service, 510 1D diffusion process, 292 OpenMP, 418, 419 Operational risk, 148–149 Operational Risk Consortium (ORIC), 149 Operations Per Second (OPS), 416 Operator overloading, 20 OPS, see Operations Per Second Optimal execution algorithms, 77, 78 Optimal feedback controls, 81–82 Optimal liquidation problem, 80–81 Optimal number of samples, 206, 220 606 Optimization, 562; see also Reinsurance Contract Optimization (RCO) convex, 326 distributed portfolio, 531–533 model, 397 portfolio optimization models, 26, 34, 422 problem, 83 QUBO, 562, 564 robust optimization problem, 85 Option payoffs, Option pricing problems, 344 Option value, 175, 251, 267, 344 Ordered records, 539 Orders of convergence, 209, 215, 219–220 ORIC, see Operational Risk Consortium ORSA, see Own risk and solvency assessment Orthogonal Chebyshev polynomial basis, 158, 159 Orthonormality, 257 OTC, see Over-the-counter Out-of-sample Monte Carlo projection, 304–308 Over-and under-collateralization, Overloading for custom active data type, 321 Overnight Index Swap (OIS), 463 Over-the-counter (OTC), 5, 291, 466, 548 Own risk and solvency assessment (ORSA), 120 P P2P lending, 554–555 PaaS, see Platform as a Service Packages, 491 Parallel application, 418 Parallel computing problem, 513 taxonomy of, 513–515 Parallel edges, 321 Parallelism, 383 Parallelism and execution, 480 data structures, 482–484 logical threading models, 480–481 physical execution models, 481–482 Parallelism and performance, 477 Index Amdahl’s law, 477–478 data parallel, 480 Gustafson’s law, 478 instruction parallel, 479–480 Little’s law, 479 task parallel, 479 Parallelism imperative, 473 Dennard scaling, 474 Moore’s law, 473 performance, 474–475 Parallelization, 421, 429, 433–434, 437 of code, 419 interfaces, 418–420 schema, 298 Parallel version, 384–389 Parameter calibrations, 121, 142 Parameter estimation method, 290 Parametric integration, 198 Pareto-event-driven compound Poisson (PEDCP), 149, 150 compound Poisson empirical distribution function, 151 density function, 154–157 distribution function, 152–153 finite-element representation, 154, 155 histogram, 151 Pareto Type I events, 150 regularized finite-element representation, 157 Pareto frontier, 387, 388 Parseval’s identity, 258 Parsimonious models, 52 Partial differential equations (PDEs), 175, 251, 290, 328, 422; see also Medium-and high-dimensional derivative pricing PDEs bond pricing, 292 discretization method, PDE/HV approach, 193 Partial freezing, 184 Partial-integro differential equation, 5–6 Partnership for Advanced Computing in Europe (PRACE), 426 Passive inputs, 317 Passive outputs, 317 Path-dependent jump rate, 224 Path-dependent rates, MLMC for, 224–226 Index Path generation, 495–497 Pathwise derivative method, 344 LMM simulation, 345–349 Pathwise sensitivity analysis, 239 approach, 216 conditional Monte Carlo for, 218–219 Payoff, 4, 5, 211, 212 coefficients, 252, 254, 260, 264–265 function, 217, 233, 251 PBIL, 377–379 PCI Express (PCIe), 445, 449, 456 PDEs, see Partial differential equations PEDCP, see Pareto-event-driven compound Poisson Penalty function, 84, 85 Per unit of limit, 373 Pervasiveness of cloud computing, 511 Peta FLOPS, 416 P-forecasting measure, 128 Physical execution models, 481–482 Piecewise linear interpolation, 207 analysis, 233–235 PImpact, 33 Pipeline depth, 460–461 Plain vanilla payoff coefficients, 254, 260 Plain vanilla products, 120 Plancharel equality, Platform as a Service (PaaS), 143 P-measure, 121 PnL attribution, 11 Point-wise entropy, 62 Pointwise ε-optimality, 106–107 Poisson process, 224, 225 Polynomial separation algorithm, 39 Portfolio backtesting, 528–529 Portfolio liquidation, 78 optimal depth for ambiguity neutral agent, 82 reference model, 79–82 Portfolio optimization models, 26, 34, 422 Portfolio simulation, 527 Portfolio strategies, 43, 44 PoS, see Proof of stake Positive homogeneity, 119 POSIX threads (Pthreads), 418, 419 Potential computing bottleneck, 529 PoW, see Proof of work 607 PPC, see Price per CPU core PPI, see Price per instance PRA, see Prudential Regulatory Authority PRACE, see Partnership for Advanced Computing in Europe Preaccumulation, 327 Pre-analysis, 31 Precision, 582, 586 Price per CPU core (PPC), 524 Price per instance (PPI), 524 Pricing, 517–518 formulas, model and cost, 525 multiple strikes, 254–255, 266 phase, 500–501 Step, 358, 360 Pricing basket options using C++ and MPI, 427 approach, 428 combination technique, 428–429 decomposition, 428 implementation, 429 parallelization, 429 problem, 427–428 results, 429–431 Pricing of credit derivatives, 5–7, 357 calibration step, 358–359 Pricing with MLMC, 206 barrier options, 211–214 conditional Monte Carlo, 211 digital options, 214–215 Euler–Maruyama scheme, 207–209 Milstein scheme, 209–211 orders of convergence, 209, 215 Primal code, 317 Primal function, 317 Private banks, 538, 552 Private cloud, 516 Probability density function, 217, 250, 268 Probability indicator, 54, 62–64 Processors performance, 442 Product specification and design, 497–498 Profitable trading, hallmarks of, 52–53 Programming languages, 418–420 Proof of stake (PoS), 540 Proof of work (PoW), 540 608 Proprietary supercomputers, 426 Prudential Regulatory Authority (PRA), 118 Pseudo-random normal deviates, 144 Pseudo-square root, 488–489 Pthreads, see POSIX threads Public cloud, 516 computing, 443, 447–448 Python, 418, 420 Q 1QBit, 562 1QBit SDK, 570 QGMs, see Quadratic Gaussian models QL code, see QuantLib code Q-measure, 121 QMLE, see Quasi-maximum likelihood estimation Quadratic Gaussian models (QGMs), 279n5 Quadratic inventory penalization, 90 Quadratic objective function, 574, 585 Quadratic unconstrained binary optimization (QUBO), 562, 564 as established approach, 564–565 feature selection, 570, 579–580, 582–584 feature selection in 1QBit SDK, 570 Quality assurance, unified platform for, 520–521 Quantitative analyst, 472 Quantitative Easing program, 54 Quantitative trading, 519 Quantity of interest, 7, 131, 176 QuantLib code (QL code), 502, 503 Quantum annealer, 586 binarizing, scaling, and correlating German credit data, 569 classification, 568 coding feature selector, 570–573 comparison of QUBO feature selection and recursive feature elimination, 582–584 credit scoring and classification as business problem, 562–564 credit scoring and classification problem formulation, 565–566 establishing zero-rule and other baseline properties, 574–579 Index evaluation metrics, 573–574 experimental results, 574 feature selection, 566–568 implementation, 585 potentially missed subsets, comparison with, 584–585 previously reported results, comparison with, 585–586 QUBO as established approach, 564–565 QUBO feature selection with logistic regression, 579–580 recursive feature elimination with logistic regression, 580–582 Quantum annealing process, 572 Quantum effects, 473 Quantum hardware, 562, 570 Quantum ready SDK, 562, 587 Quasi-maximum likelihood estimation (QMLE), 290, 297 parameter estimation, 287 Quasi-Monte Carlo methods, 240 QUBO, see Quadratic unconstrained binary optimization R Rack Unit (U), 446n1 Radial basis functions, 176, 266 Radon–Nikodym derivative, 83, 85 Random fields, 84 Random market effects, 237 Rank-1 lattice rule, 240 Rapid elasticity, 511 Rate of convergence, 268–269 Rate on line, see Per unit of limit Rates on line (ROL), 375–376 Rating transition risk, 354 RCO, see Reinsurance Contract Optimization RCR, see Regulatory capital requirements Real-code (RPBIL), 378 Real-time counterparty credit risk management, 349 adjoint algorithmic differentiation and, 352–354 counterparty credit risk management, 350–352 results, 354–357 Index Real-Time Gross Settlement system, 549 Real-time risk management AAD, 341–343 of flow credit products, 357–368 of interest rate products, 344–349 real-time counterparty credit risk management, 349–357 Real-world ESG (rESG), 125 Recall, 582, 586 Recursive feature elimination (RFE), 564, 580–584 Recursive feature elimination cross-validation (RFECV), 564 Red Hat Linux 64-bit operating system, 383 Reference distribution, revision of, 28–29, 35–36 Reference model, 79 dynamics, 79–80 feedback controls, 81–82 optimal liquidation problem, 80–81 Registers, 476 Regression-based method, 486 Regularization methods, 532 “Regulation T”, 39 Regulator Supervisory Report, 120 Regulatory capital requirements (RCR), 11, 13 calculation of market risk capital, 12 capital value adjustment, 13–14 credit risk capital, 12–13 Regulatory supervisor, 121 Rehypothecate collateral, 10 Rehypothecation, 549–550 Reinsurance costs, 373–374 recoveries, 374–375 Reinsurance Contract Optimization (RCO), 372 case study, 382 EAs, 376–382 metrics, 382–383 modeling RCO problem, 373 parallel version, 384–389 reinsurance costs, 373–374 reinsurance recoveries, 374–375 results, 383 609 risk value and optimization problem, 375–376 Relative predictive power, 569 Relative strength index (RSI), 37 asset filter relative strength index, 37–38 Replicating portfolio of matching assets, 122n8 Repomarket for derivatives, 10 Reporting, 518–519 rESG, see Real-world ESG Resource manager, 516 Resource pooling, 510 Reverse accumulation, 19, 20 Reverse mode AD, see Adjoint(s)—mode AD Revised Basel III framework (2010), 11 RFE, see Recursive feature elimination RFECV, see Recursive feature elimination cross-validation R framework, 31 Ricatti equation, 280 Riesz basis, 257 Risk, 535 assessment, 276 calculation, of derivatives, 5–7 hedging strategies, 371 management, 340, 518–519 and premium flow, 372 risk transfer contracts, tendency for, 372 value and optimization problem, 375–376 RiskAnalytics DFE implementation, 465 RiskIntegrity suite, 126 Risk-neutral option valuation formula, 251 pricing, 121n6 Risk scenario generator (RSG), 124, 131, 143; see also Economic scenario generators (ESG) co-dependency structures and simulation, 144–147 lapse and surrender risk, 148 mortality and longevity risk, 147 operational risk, 148–149 Rmetrics’ R package fOptions, 162 Robust calibration technique, 141 610 Robust long-term yield curve model, 275 calculation of log-likelihood function, 309–310 EFM, 275 empirical evaluation of model in-and out-of-sample, 299–308 HPC approaches to calibrating Black models, 288, 290–295 multifactor yield curve models and drawbacks, 276–283 nonlinear black correction for EFM model, 283–288, 289 UKF EM algorithm HPC implementation, 295–298 Robust optimization problem, 85 ROL, see Rates on line Root mean square error, 303 RPBIL, see Real-code R’s ecdf() function, 151 RSG, see Risk scenario generator RSI, see Relative strength index R’s runif() function, 151 runif.sobol() function, 162 S S&P 502 realized mean runtime, 430 SABR-LMM model, 138 SA-CCR approaches, 11, 12 SA-CVA approaches, 11 SAPS, see Self-administered pension scheme Scalable problem, 513 “Scaled” tail, 34 Scaled long/short formulation of achievement-maximization problem, 34 Scale-free networks, 59 Scale-up to process larger models, 41–42 Scaling function, 256 Scaling laws, 54, 72 distributions, 59 emergence of, 58–59 Scenario generation, challenges in challenge of negative nominal interest rates, 116 ESG, 124–143 ESG and solvency 2, 117–124 examples, 149 Index layout, 124 objectives, 116–117 PEDCP representation, 150–157 RSG, 143–149 SVJD model, 157–165 Scenario simulation, 276 SCR, see Solvency capital requirement SDEs, see Stochastic differential equations SDK, see Software development kit Secondary trading, 548 Second derivatives, 318–319 Second-order cumulant approximation, 294 Second-order polynomials, 491 Second-order stochastic dominance model (SSD model), 26, 29 asset allocation optimization model, 31 backtesting, 40 data, 30 density curves, 36 enhanced indexation applying SSD criterion, 26–28 guided tour, 29 impact measure for news, 32–34 information flow and computational architecture, 31 long–short discrete optimization model, 34–35 models, 32–36 money management via “volatility pumping”, 29 performance measures, 44 results, 42–45 revising reference distribution, 28–29 revision of reference distribution, 35–36 scale-up to process larger models, 41–42 solution method and processing requirement, 39–42 solution methods for SIP models, 29 solution of LP and SIP models, 39–40 system architecture, 31 trading strategies, 36–39 Seeding, 318 Self-administered pension scheme (SAPS), 147 Index Sentiment score, 32 Separation algorithm, 41 Server–worker nodes, 516 SHA-258, 544 Shadow rates, 278 models, 275 process, 292 Shadow short rate, 287, 292 Shannon scaling function, 261 Shannon wavelet inverse Fourier technique (SWIFT), 250, 261, 267; see also Multilevel Monte Carlo methods (MLMC methods) density coefficients, 263–264 payoff coefficients, 264–265 pricing multiple strikes, 266 Shannon wavelets, 250, 255, 261 Shared computing resources, 510 Shaw–Brickman algorithm, 495 Short-term models, 53 Short rate models, 133 ShuffleSplit, 570 Sign reversal, 231 SIMD, see Single Instruction Multiple Data SIMM, see Standard initial margin model Simple Live CPU (SLiC), 451 library, 456 Single bank, 553 Single Instruction Multiple Data (SIMD), 442 Single-level checkpointing schemes, 324 Single period SP, 29 SIP model, see Stochastic integer programming model Sklar’s theorem, 144, 145 SLiC, see Simple Live CPU Small fixed cost, 352–353 Smooth density functions, 261 Smoothing, 326 SMs, see Streaming Multiprocessors Sobol numbers generation, 495 SoC, see Systems on Chip Software development kit (SDK), 562 1QBit, 570 QuadraticBinaryPolynomialBuilder class, 571 611 Solid-State Drive, 448n2 Solvency 2, 117–124 Solvency and Financial Condition Report, 120 Solvency capital requirement (SCR), 118 Source code transformation, 20 Sparse grids, 176 SPDE applications, 237 Spearman correlation, 575 Speed comparisons and numerical results, 501–504 Speedup, 383, 386 Split pathwise sensitivity, 219–220 Splitting, 219, 220 Spot LIBOR measure, 487 Spot-starting interest rate swap, Square Chimera graph, 572, 573 SSD model, see Second-order stochastic dominance model SST, see Swiss Solvency Test Standard initial margin model (SIMM), 18, 467–469 Standard methods, 22 State-measurement cross-covariance matrix, 296 State–space form, 286, 292 Stochastic asset price process, 250 Stochastic differential equations (SDEs), 125, 127, 201, 202–203, 278 Stochastic integer programming model (SIP model), 26 solution, 39–40 solution methods for, 29 Stochastic partial differential equations, 237 Stochastic volatility and jump diffusion model (SVJD model), 149, 157 bar plots of coefficients, 165 and combined equity asset shock, 160–161 distributional representation, 158–160 unconditional equity asset shock distribution, 161–165 Stochastic volatility process, 137 StratifiedShuffleSplit, 570, 575, 586 Streaming Multiprocessors (SMs), 477, 482 612 Structural models, 138 Stylized properties of Black models, 288, 289 Sub-additivity, 119 Sun-Gard’s Prophet Asset Liability Strategy, 117 Sun Grid Engine, 521 Sunway TaihuLight, 414, 415 Supercomputers, 414 advantages and disadvantages, 421–422 current landscape, and upcoming trends, 416–417 exponential performance development and projection, 415 for financial applications, 422–426 with MPP architecture, 414 optimizing life cycle investment decisions, 431–436 pricing basket options using C++ and MPI, 427–431 programming languages and parallelization interfaces, 418–420 SuperDerivatives, 137 SuperMUC supercomputer, 426 Superposition dimension, 176 Supplementary material, 74 Support vector machines (SVMs), 565 Surprise of event-based price curve, 62 Surrender risk, 148 SVJD model, see Stochastic volatility and jump diffusion model SVMs, see Support vector machines Swap rate, 133 SWIFT, see Shannon wavelet inverse Fourier technique Swiss Piz Daint, 417 Swiss Solvency Test (SST), 118 System memory, 476 Systems on Chip (SoC), 417 T Tail-Value at Risk (TVaR), 29, 375 Tangent-over-adjoint mode AD tangent mode, 319 Tangent-over-tangent mode AD tangent mode, 318–319 Index Tangent mode AD, 318 Task parallel, 479 backtesting algorithm, 515 problem, 513 Taxonomy of parallel computing, 513–515 Taylor-like ANOVA decomposition, 428–430 TCO, see Total cost of ownership T -copula, 144–146 Techila-enabled computing tools, 529 Techila high-level architecture, 522 Techila Middleware, 521, 530 with MATLAB, 521–522 Techila SDK, 529 Tensor approach, 176 Tesla K20, 484 Tesla K20c, 492 Textures, 494 cache, 482 Thinning, 224 Thomson Reuters, 530 Thomson Reuters Data Stream platform, 43 Threads, 476, 493–495 Three-dimension (3D) equations, 181 parabolic quasi-linear PDE, 292 Three-factor affine short rate models, 280–281 basic EFM model, 284–285 Black model calibration, 290–291 extended Vasicek model, 281 state variables, 286 “Three-stage feature selection fusion” technique, 586 Threshold, 64 Tianhe-1A, 416 Tikhonov-regularized least squares, 533 Time-consuming process, 276 Time-dependent exponential correlation, 190, 191 Time-dependent simple correlation, 189–190 Time-dependent volatilities exponential correlation, 191–192 simple correlation, 190–191, 192 Time frequency analysis, 261 Time-reversed Brownian motion, 231 613 Index Time-series data, 26 Time-shared functional unit, 444 Time value of guarantees (TVOG), 122 Titan’s performance of 17.6 Peta FLOPS, 416–417 Title deeds, 543 TOP500 supercomputers, 420 Top right plot, 236 Total cost of ownership (TCO), 517 Total offset ratio, 405 TpS, see Transactions per second Tracking error, 26–27 Trade/trading, 14–15 clearing, 548–549 execution, 548–549 finance, 549–550 settlement, 548–549 Trading models, 52, 53, 72 algorithm, 50, 51 anatomy and performance, 53–56 and complexity, 59–60 Trading strategies, 36 base strategy, 37 dynamic strategy using money management, 38–39 using RSI and impact as filters, 38 using RSI as filter, 37–38 Transaction costs reducing, 399 Transactions per second (TpS), 546 Transition equation, 286 Translational invariance, 119 Truncated Pareto event–driven compound Poisson distribution, 149 Truncated series expansions, 238–239 Tsunamis, 535 TVaR, see Tail-Value at Risk TVOG, see Time value of guarantees Two-dimension (2D) arrays, 483 equations, 181 Two-level approach, 239 t-year VaR, 119 U UCI, see University of California, Irvine UKF, see Unscented Kalman filter UKF EM algorithm HPC implementation, 295–298 HPC implementation, 297–298 quasi-maximum likelihood estimation, 297 technical implementation, 297 UKF for Black EFM model, 295–297 Uncollateralized derivative transactions, 10 Unconditional equity asset shock distribution, 161–165 Unified platform for quality assurance, 520–521 University of California, Irvine (UCI), 564 Unscented Kalman filter (UKF), 275, 290 for Black EFM model, 295–297 likelihood, 302 V Valuation, 276, 517–518 CVA, 7–9 derivatives pricing and risk, 5–7 DVA, 7–9 FVA, 10 requirements, Value-at-Risk measurement (VaR measurement), 12, 29, 118–120, 375, 463–464 Variable coefficients, 184, 186–187 Variance reduction (VR), 356 VaR measurement, see Value-at-Risk measurement VAR models, see Vector autoregression models Vasicek dynamic model, 134, 135 Vasicek implied yield curve, 135 Vasicek model, 125–126 Vector autoregression models (VAR models), 281 Verification theorem, 87 Vibrato Monte Carlo, 220–222 Vieta’s formula, 263 Virtualization, 516 Viscosity solution, 155 Visualization code, 530n7 Volatility, 54, 176 Volatility pumping, 26, 29, 38 money management via, 29 614 Volume credit products, 340 VR, see Variance reduction W WA(a,b) method, 256, 267 density coefficients, 258–260 plain vanilla payoff coefficients, 260 robustness of, 267–268 Wall clock time (WCT), 517 Walltime, 426 War of the Austrian Succession, 541 Warps, 493 Wavelet series, 255–256 WCT, see Wall clock time Weak speedup, 383 Wealth, 80 Willis Towers Watson’s MoSes HPC, 124 Willis Towers Watson’s Replica, Igloo, and MoSes solutions, 117 Willis Towers Watson’s Star ESG, 124 Index Winning propositions, 38 Workload, 517 Work variables, 19 Wrong way risk, X X-Road, 547 xVA, 14–15, 320, 518 Y Yield curve, 131–133 bootstrapping, 300 Z Zero-correlation approximation, 184 Zero coupon bond prices, 280, 292 Zero lower bound (ZLB), 275 Zero-rule classifier, 574 Zero-rule establishment, 574–579 .. .High- Performance Computing in Finance Problems, Methods, and Solutions High- Performance Computing in Finance Problems, Methods, and Solutions Edited by M A H Dempster Juho Kanniainen John... the Use of Cloud Computing in Finance Binghuan Lin, Rainer Wehkamp, and Juho Kanniainen 509 Contents 18 Blockchains and Distributed Ledgers in Retrospective and Perspective Alexander Lipton ix... Finance, SC’15 The International Conference for High Performance Computing, Networking, Storage and Analysis New York: ACM Which appeared originally in Recent Developments in Computational Finance,