Verfügbarkeit: Implementing models in quantitative finance

Implementing models in quantitative finance: methods and cases

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Bibliographische Detailangaben
Beteiligte Personen:	Fusai, Gianluca (VerfasserIn), Roncoroni, Andrea (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2008
Schriftenreihe:	Springer finance
Schlagwörter:	Quantitative Methode Wertpapieranalyse Finanzmathematik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014183745&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XXIII, 607 S. Ill., graph. Darst.
ISBN:	9783540223481

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Datensatz im Suchindex

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adam_text	Contents Introduction . xv Parti Methods 1 Static Monte Carlo . 3 1.1 Motivation and Issues . 3 1.1.1 Issue 1: Monte Carlo Estimation . 5 1.1.2 Issue 2: Efficiency and Sample Size . 7 1.1.3 Issue 3: How to Simulate Samples . 8 1.1.4 Issue 4: How to Evaluate Financial Derivatives . 9 1.1.5 The Monte Carlo Simulation Algorithm . 11 1.2 Simulation of Random Variables . 11 1.2.1 Uniform Numbers Generation . 12 1.2.2 Transformation Methods . 14 1.2.3 Acceptance-Rejection Methods . 20 1.2.4 Hazard Rate Function Method . 23 1.2.5 Special Methods . 24 1.3 Variance Reduction . 31 1.3.1 Antithetic Variables . 31 1.3.2 Control Variables . 33 1.3.3 Importance Sampling . 35 1.4 Comments . 39 2 Dynamic Monte Carlo . 41 2.1 Main Issues . 41 2.2 Continuous Diffusions . 45 2.2.1 Method I: Exact Transition . 45 2.2.2 Method II: Exact Solution . 46 2.2.3 Method III: Approximate Dynamics . 46 2.2.4 Example: Option Valuation under Alternative Simulation Schemes . 48 2.3 Jump Processes . 49 2.3.1 Compound Jump Processes . 49 2.3.2 Modelling via Jump Intensity . 51 2.3.3 Simulation with Constant Intensity . 53 2.3.4 Simulation with Deterministic Intensity . 54 2.4 Mixed-Jump Diffusions . 56 2.4.1 Statement of the Problem . 56 2.4.2 Method I: Transition Probability . 58 2.4.3 Method II: Exact Solution . 58 2.4.4 Method Ш.А: Approximate Dynamics with Deterministic Intensity . 59 2.4.5 Method Ш.В: Approximate Dynamics with Random Intensity 60 2.5 Gaussian Processes . 62 2.6 Comments . 66 Dynamic Programming for Stochastic Optimization . 69 3.1 Controlled Dynamical Systems . 69 3.2 The Optimal Control Problem . 71 3.3 The Bellman Principle of Optimality . 73 3.4 Dynamic Programming . 74 3.5 Stochastic Dynamic Programming . 76 3.6 Applications . 77 3.6.1 American Option Pricing . 77 3.6.2 Optimal Investment Problem . 79 3.7 Comments . 81 Finite Difference Methods . 83 4.1 Introduction . 83 4.1.1 Security Pricing and Partial Differential Equations . 83 4.1.2 Classification of PDEs . 84 4.2 From Black-Scholes to the Heat Equation . 87 4.2.1 Changing the Time Origin . 88 4.2.2 Undiscounted Prices . 88 4.2.3 From Prices to Returns . 89 4.2.4 Heat Equation . 89 4.2.5 Extending Transformations to Other Processes . 90 4.3 Discretization Setting . 91 4.3.1 Finite-Difference Approximations . 91 4.3.2 Grid . 93 4.3.3 Explicit Scheme . 94 4.3.4 Implicit Scheme . 101 4.3.5 Crank-Nicolson Scheme . 103 4.3.6 Computing the Greeks . 109 їх 4.4 Consistency, Convergence and Stability . 110 4.5 General Linear Parabolic PDEs . 115 4.5.1 Explicit Scheme . 116 4.5.2 Implicit Scheme . 117 4.5.3 Crank-Nicolson Scheme . 118 4.6 A VBA Code for Solving General Linear Parabolic PDEs . 119 4.7 Comments . 119 Numerical Solution of Linear Systems . 121 5.1 Direct Methods: The LU Decomposition . 122 5.2 Iterative Methods . 127 5.2.1 Jacobi Iteration: Simultaneous Displacements . 128 5.2.2 Gauss-Seidel Iteration (Successive Displacements) . 130 5.2.3 SOR (Successive Over-Relaxation Method) . 131 5.2.4 Conjugate Gradient Method (CGM) . 133 5.2.5 Convergence of Iterative Methods . 135 5.3 Code for the Solution of Linear Systems . 140 5.3.1 VBA Code . 140 5.3.2 MATLAB Code . 141 5.4 Illustrative Examples . 143 5.4.1 Pricing a Plain Vanilla Call in the Black-Scholes Model (VBA) . 144 5.4.2 Pricing a Plain Vanilla Call in the Square-Root Model (VBA) 145 5.4.3 Pricing American Options with the CN Scheme (VBA) _ 147 5.4.4 Pricing a Double Barrier Call in the BS Model (MATLAB and VBA) . 149 5.4.5 Pricing an Option on a Coupon Bond in the Cox-Ingersoll- Ross Model (MATLAB) . 152 5.5 Comments . 155 Quadrature Methods . 157 6.1 Quadrature Rules . 158 6.2 Newton-Cotes Formulae . 159 6.2.1 Composite Newton-Cotes Formula . 162 6.3 Gaussian Quadrature Formulae . 173 6.4 Matlab Code . 180 6.4.1 Trapezoidal Rule . 180 6.4.2 Simpson Rule . 180 6.4.3 Romberg Extrapolation . 181 6.5 VBA Code . 181 6.6 Adaptive Quadrature . 182 6.7 Examples . 185 6.7.1 Vanilla Options in the Black-Scholes Model . 186 6.7.2 Vanilla Options in the Square-Root Model . 188 6.7.3 Bond Options in the Cox-Ingersoll-Ross Model . 190 6.7.4 Discretely Monitored Barrier Options . 193 6.8 Pricing Using Characteristic Functions . 197 6.8.1 MATLAB and VBA Algorithms . 202 6.8.2 Options Pricing with Levy Processes . 206 6.9 Comments . 211 7 The Laplace Transform . 213 7.1 Definition and Properties . 213 7.2 Numerical Inversion . 216 7.3 The Fourier Series Method . 218 7.4 Applications to Quantitative Finance . 219 7.4.1 Example . 219 7.4.2 Example . 225 7.5 Comments . 228 8 Structuring Dependence using Copula Functions . 231 8.1 Copula Functions . 231 8.2 Concordance and Dependence . 233 8.2.1 Fréchet-Hoeffding Bounds . 233 8.2.2 Measures of Concordance . 234 8.2.3 Measures of Dependence . 235 8.2.4 Comparison with the Linear Correlation . 236 8.2.5 Other Notions of Dependence . 238 8.3 Elliptical Copula Functions . 240 8.4 Archimedean Copulas . 245 8.5 Statistical Inference for Copulas . 25 1 8.5.1 Exact Maximum Likelihood . 253 8.5.2 Inference Functions for Margins . 254 8.5.3 Kernel-based Nonparametric Estimation . 255 8.6 Monte Carlo Simulation . 257 8.6.1 Distributional Method . 257 8.6.2 Conditional Sampling . 259 8.6.3 Compound Copula Simulation . 263 8.7 Comments . 265 Partii Problems Portfolio Management and Trading . 271 9 Portfolio Selection: "Optimizing" an Error . 273 9.1 Problem Statement . 274 9.2 Model and Solution Methodology . 276 9.3 Implementation and Algorithm . 278 9.4 Results and Comments . 280 9.4.1 In-sample Analysis . 281 9.4.2 Out-of-sample Simulation. 285 10 Alpha, Beta and Beyond . 289 10.1 Problem Statement . 290 10.2 Solution Methodology . 291 10.2.1 Constant Beta: OLS Estimation . 292 10.2.2 Constant Beta: Robust Estimation . 293 10.2.3 Constant Beta: Shrinkage Estimation . 295 10.2.4 Constant Beta: Bayesian Estimation . 296 10.2.5 Time-Varying Beta: Exponential Smoothing . 299 10.2.6 Time-Varying Beta: The Kalman Filter . 300 10.2.7 Comparing the models . 304 10.3 Implementation and Algorithm . 306 10.4 Results and Comments . 309 11 Automatic Trading: Winning or Losing in a kBit . 311 11.1 Problem Statement . 312 11.2 Model and Solution Methodology . 314 11.2.1 Measuring Trading System Performance . 314 11.2.2 Statistical Testing . 315 11.3 Code . 317 11.4 Results and Comments . 322 Vanüla Options . 329 12 Estimating the Risk-Neutral Density . 331 12.1 Problem Statement . 332 12.2 Solution Methodology . 332 12.3 Implementation and Algorithm . 335 12.4 Results and Comments . 338 13 An "American" Monte Carlo . 345 13.1 Problem Statement . 346 13.2 Model and Solution Methodology . 347 13.3 Implementation and Algorithm . 348 13.4 Results and Comments . 349 14 Fixing Volatile Volatility . 353 14.1 Problem Statement . 354 14.2 Model and Solution Methodology . 356 14.2.1 Analytical Transforms . 356 14.2.2 Model Calibration . 358 14.3 Implementation and Algorithm . 360 14.3.1 Code Description . 361 14.4 Results and Comments . 362 Exotic Derivatives . 371 15 An Average Problem . 373 15.1 Problem Statement . 374 15.2 Model and Solution Methodology . 374 15.2.1 Moment Matching . 375 15.2.2 Upper and Lower Price Bounds . 378 15.2.3 Numerical Solution of the Pricing PDE . 379 15.2.4 Transform Approach . 382 15.3 Implementation and Algorithm . 386 15.4 Results and Comments . 390 16 Quasi-Monte Carlo: An Asian Bet . 395 16.1 Problem Statement . 396 16.2 Solution Metodology . 398 16.2.1 Stratification and Latin Hypercube Sampling . 399 16.2.2 Low Discrepancy Sequences . 401 16.2.3 Digital Nets . 402 16.2.4 The Sobol' Sequence . 403 16.2.5 Scrambling Techniques . 404 16.3 Implementation and Algorithm . 406 16.4 Results and Comments . 407 17 Lookback Options: A Discrete Problem . 411 17.1 Problem Statement . 412 17.2 Model and Solution Methodology . 414 17.2.1 Analytical Approach . 414 17.2.2 Finite Difference Method . 417 17.2.3 Monte Carlo Simulation . 419 17.2.4 Continuous Monitoring Formula . 419 17.3 Implementation and Algorithm . 420 17.4 Results and Comments . 421 18 Electrifying the Price of Power . 427 18.1 Problem Statement . 429 18.1.1 TheDemandSide . 429 18.1.2 The Bid Side . 429 18.1.3 The Bid Cost Function . 430 18.1.4 The Bid Strategy . 432 18.1.5 A Multi-Period Extension . 433 18.2 Solution Methodology . 433 18.3 Implementation and Experimental Results . 435 19 A Sparkling Option . 441 19.1 Problem Statement . 441 19.2 Model and Solution Methodology . 444 19.3 Implementation and Algorithm . 450 19.4 Results and Comments . 453 20 Swinging on a Tree . 457 20.1 Problem Statement . 458 20.2 Model and Solution Methodology . 460 20.3 Implementation and Algorithm . 461 20.3.1 Gas Price Tree . 461 20.3.2 Backward Recursion . 463 20.3.3 Code . 464 20.4 Results and Comments . 464 Interest-Rate and Credit Derivatives . 469 21 Floating Mortgages . 471 21.1 Problem Statement and Solution Method . 473 21.1.1 Fixed-Rate Mortgage . 473 21.1.2 Flexible-Rate Mortgage . 474 21.2 Implementation and Algorithm . 476 21.2.1 Markov Control Policies . 476 21.2.2 Dynamic Programming Algorithm . 477 21.2.3 Transaction Costs . 480 21.2.4 Code . 480 21.3 Results and Comments . 482 22 Basket Default Swaps . 487 22.1 Problem Statement . 487 22.2 Models and Solution Methodologies . 489 22.2.1 Pricing nth-to-default Homogeneous Basket Swaps . 489 22.2.2 Modelling Default Times . 490 22.2.3 Monte Carlo Method . 491 22.2.4 A One-Factor Gaussian Model . 491 22.2.5 Convolutions, Characteristic Functions and Fourier Transforms . 493 22.2.6 The Hull and White Recursion . 495 22.3 Implementation and Algorithm . 495 22.3.1 Monte Carlo Method . 496 22.3.2 Fast Fourier Transform . 496 22.3.3 Hull-White Recursion . 497 22.3.4 Code . 497 22.4 Results and Comments . 497 23 Scenario Simulation Using Principal Components . 505 23.1 Problem Statement and Solution Methodology . 506 23.2 Implementation and Algorithm . 508 23.2.1 Principal Components Analysis . 508 XIV 23.2.2 Code . 511 23.3 Results and Comments . 511 Financial Econometrics . 515 24 Parametric Estimation of Jump-Diffusions . 519 24.1 Problem Statement . 520 24.2 Solution Methodology . 520 24.3 Implementation and Algorithm . 522 24.3.1 The Continuous Square-Root Model . 523 24.3.2 The Mixed-Jump Square-Root Model . 525 24.4 Results and Comments . 528 24.4.1 Estimating a Continuous Square-Root Model . 528 24.4.2 Estimating a Mixed-Jump Square-Root Model . 530 25 Nonparametric Estimation of Jump-Diffusions . 531 25.1 Problem Statement . 532 25.2 Solution Methodology . 533 25.3 Implementation and Algorithm . 535 25.4 Results and Comments . 537 26 A Smiling GARCH . 543 26.1 Problem Statement . 543 26.2 Model and Solution Methodology . 545 26.3 Implementation and Algorithm . 547 26.3.1 Code Description . 551 26.4 Results and Comments . 554 A Appendix: Proof of the Thinning Algorithm . 557 В Appendix: Sample Problems for Monte Carlo . 559 С Appendix: The Matlab Solver . 563 D Appendix: Optimal Control . 569 D.I Setting up the Optimal Stopping Problem . 569 D.2 Proof of the Bellman Principle of Optimality . 570 D.3 Proof of the Dynamic Programming Algorithm . 570 Bibliography . 573 Index . 599
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spellingShingle	Fusai, Gianluca Roncoroni, Andrea Implementing models in quantitative finance methods and cases Quantitative Methode (DE-588)4232139-6 gnd Wertpapieranalyse (DE-588)4124458-8 gnd Finanzmathematik (DE-588)4017195-4 gnd
subject_GND	(DE-588)4232139-6 (DE-588)4124458-8 (DE-588)4017195-4
title	Implementing models in quantitative finance methods and cases
title_auth	Implementing models in quantitative finance methods and cases
title_exact_search	Implementing models in quantitative finance methods and cases
title_full	Implementing models in quantitative finance methods and cases Gianluca Fusai ; Andrea Roncoroni
title_fullStr	Implementing models in quantitative finance methods and cases Gianluca Fusai ; Andrea Roncoroni
title_full_unstemmed	Implementing models in quantitative finance methods and cases Gianluca Fusai ; Andrea Roncoroni
title_short	Implementing models in quantitative finance
title_sort	implementing models in quantitative finance methods and cases
title_sub	methods and cases
topic	Quantitative Methode (DE-588)4232139-6 gnd Wertpapieranalyse (DE-588)4124458-8 gnd Finanzmathematik (DE-588)4017195-4 gnd
topic_facet	Quantitative Methode Wertpapieranalyse Finanzmathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014183745&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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