Implementing models in quantitative finance: methods and cases
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
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| Schriftenreihe: | Springer finance
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| Schlagworte: | |
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| Beschreibung: | XXIII, 607 S. Ill., graph. Darst. |
| ISBN: | 9783540223481 |
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| 008 | 051109s2008 xx ad|| |||| 00||| eng d | ||
| 020 | |a 9783540223481 |9 978-3-540-22348-1 | ||
| 035 | |a (OCoLC)230136286 | ||
| 035 | |a (DE-599)BVBBV020862210 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
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| 100 | 1 | |a Fusai, Gianluca |e Verfasser |0 (DE-588)133874680 |4 aut | |
| 245 | 1 | 0 | |a Implementing models in quantitative finance |b methods and cases |c Gianluca Fusai ; Andrea Roncoroni |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XXIII, 607 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer finance | |
| 650 | 0 | 7 | |a Quantitative Methode |0 (DE-588)4232139-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wertpapieranalyse |0 (DE-588)4124458-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Finanzmathematik |0 (DE-588)4017195-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Wertpapieranalyse |0 (DE-588)4124458-8 |D s |
| 689 | 1 | 1 | |a Quantitative Methode |0 (DE-588)4232139-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Roncoroni, Andrea |e Verfasser |0 (DE-588)133874702 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-014183745 | |
Datensatz im Suchindex
| _version_ | 1820776908423430144 |
|---|---|
| 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 |
| adam_txt |
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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Fusai, Gianluca Roncoroni, Andrea |
| author_GND | (DE-588)133874680 (DE-588)133874702 |
| author_facet | Fusai, Gianluca Roncoroni, Andrea |
| author_role | aut aut |
| author_sort | Fusai, Gianluca |
| author_variant | g f gf a r ar |
| building | Verbundindex |
| bvnumber | BV020862210 |
| classification_rvk | QP 890 SK 980 |
| classification_tum | WIR 160f |
| ctrlnum | (OCoLC)230136286 (DE-599)BVBBV020862210 |
| dewey-full | 332.0151 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.0151 |
| dewey-search | 332.0151 |
| dewey-sort | 3332.0151 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV020862210 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:23:22Z |
| indexdate | 2025-01-09T13:09:33Z |
| institution | BVB |
| isbn | 9783540223481 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014183745 |
| oclc_num | 230136286 |
| open_access_boolean | |
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| physical | XXIII, 607 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer finance |
| spelling | Fusai, Gianluca Verfasser (DE-588)133874680 aut Implementing models in quantitative finance methods and cases Gianluca Fusai ; Andrea Roncoroni Berlin [u.a.] Springer 2008 XXIII, 607 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer finance Quantitative Methode (DE-588)4232139-6 gnd rswk-swf Wertpapieranalyse (DE-588)4124458-8 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s DE-604 Wertpapieranalyse (DE-588)4124458-8 s Quantitative Methode (DE-588)4232139-6 s Roncoroni, Andrea Verfasser (DE-588)133874702 aut Digitalisierung UB Regensburg application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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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