97,00 €*
Versandkostenfrei per Post / DHL
Aktuell nicht verfügbar
Part A Mathematical Foundation for One-Factor Problems
Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance.
Part B Mathematical Foundation for Two-Factor Problems
Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks.
Part C The Foundations of the Finite Difference Method (FDM)
Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes.
Part D Advanced Finite Difference Schemes for Two-Factor Problems
Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail.
Part E Test Cases in Computational Finance
Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems.
This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering.
More on computational finance and the author's online courses, see [...]
Part A Mathematical Foundation for One-Factor Problems
Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance.
Part B Mathematical Foundation for Two-Factor Problems
Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks.
Part C The Foundations of the Finite Difference Method (FDM)
Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes.
Part D Advanced Finite Difference Schemes for Two-Factor Problems
Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail.
Part E Test Cases in Computational Finance
Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems.
This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering.
More on computational finance and the author's online courses, see [...]
DANIEL DUFFY, PhD, has BA (Mod), MSc and PhD degrees in pure, applied and numerical mathematics (University of Dublin, Trinity College) and he is active in promoting partial differential equations (PDE) and the Finite Difference Method (FDM) for applications in computational finance. He was responsible for the introduction of the Fractional Step (Soviet Splitting) method and the Alternating Direction Explicit (ADE) method in computational finance. He is the originator of the exponential fitting method for convection-dominated PDEs.
Preface xix
Who Should Read this Book? xxiii
Part A : Mathematical Foundation for One-Factor Problems
Chapter 1 : Real Analysis Foundations for this Book 3
1.1 Introduction and Objectives 3
1.2 Continuous Functions 4
1.2.1 Formal Definition of Continuity 5
1.2.2 An Example 6
1.2.3 Uniform Continuity 6
1.2.4 Classes of Discontinuous Functions 7
1.3 Differential Calculus 8
1.3.1 Taylor's Theorem 9
1.3.2 Big O and Little o Notation 10
1.4 Partial Derivatives 11
1.5 Functions and Implicit Forms 13
1.6 Metric Spaces and Cauchy Sequences 14
1.6.1 Metric Spaces 15
1.6.2 Cauchy Sequences 16
1.6.3 Lipschitz Continuous Functions 17
1.7 Summary and Conclusions 19
Chapter 2 : Ordinary Differential Equations (ODEs), Part 1 21
2.1 Introduction and Objectives 21
2.2 Background and Problem Statement 22
2.2.1 Qualitative Properties of the Solution and Maximum Principle 22
2.2.2 Rationale and Generalisations 24
2.3 Discretisation of Initial Value Problems: Fundamentals 25
2.3.1 Common Schemes 26
2.3.2 Discrete Maximum Principle 28
2.4 Special Schemes 29
2.4.1 Exponential Fitting 29
2.4.2 Scalar Non-Linear Problems and Predictor-Corrector Method 31
2.4.3 Extrapolation 31
2.5 Foundations of Discrete Time Approximations 32
2.6 Stiff ODEs 37
2.7 Intermezzo: Explicit Solutions 39
2.8 Summary and Conclusions 41
Chapter 3 : Ordinary Differential Equations (ODEs), Part 2 43
3.1 Introduction and Objectives 43
3.2 Existence and Uniqueness Results 43
3.2.1 An Example 45
3.3 Other Model Examples 45
3.3.1 Bernoulli ODE 45
3.3.2 Riccati ODE 46
3.3.3 Predator-Prey Models 47
3.3.4 Logistic Function 48
3.4 Existence Theorems for Stochastic Differential Equations (SDEs) 48
3.4.1 Stochastic Differential Equations (SDEs) 49
3.5 Numerical Methods for ODEs 51
3.5.1 Code Samples in Python 52
3.6 The Riccati Equation 55
3.6.1 Finite Difference Schemes 57
3.7 Matrix Differential Equations 59
3.7.1 Transition Rate Matrices and Continuous Time Markov Chains 61
3.8 Summary and Conclusions 62
Chapter 4 : An Introduction to Finite Dimensional Vector Spaces 63
4.1 Short Introduction and Objectives 63
4.1.1 Notation 64
4.2 What Is a Vector Space? 65
4.3 Subspaces 67
4.4 Linear Independence and Bases 68
4.5 Linear Transformations 69
4.5.1 Invariant Subspaces 70
4.5.2 Rank and Nullity 71
4.6 Summary and Conclusions 72
Chapter 5 : Guide to Matrix Theory and Numerical Linear Algebra 73
5.1 Introduction and Objectives 73
5.2 From Vector Spaces to Matrices 73
5.2.1 Sums and Scalar Products of Linear Transformations 73
5.3 Inner Product Spaces 74
5.3.1 Orthonormal Basis 75
5.4 From Vector Spaces to Matrices 76
5.4.1 Some Examples 76
5.5 Fundamental Matrix Properties 77
5.6 Essential Matrix Types 80
5.6.1 Nilpotent and Related Matrices 80
5.6.2 Normal Matrices 81
5.6.3 Unitary and Orthogonal Matrices 82
5.6.4 Positive Definite Matrices 82
5.6.5 Non-Negative Matrices 83
5.6.6 Irreducible Matrices 83
5.6.7 Other Kinds of Matrices 84
5.7 The Cayley Transform 84
5.8 Summary and Conclusions 86
Chapter 6 : Numerical Solutions of Boundary Value Problems 87
6.1 Introduction and Objectives 87
6.2 An Introduction to Numerical Linear Algebra 87
6.2.1 BLAS (Basic Linear Algebra Subprograms) 90
6.3 Direct Methods for Linear Systems 92
6.3.1 LU Decomposition 92
6.3.2 Cholesky Decomposition 94
6.4 Solving Tridiagonal Systems 94
6.4.1 Double Sweep Method 94
6.4.2 Thomas Algorithm 96
6.4.3 Block Tridiagonal Systems 97
6.5 Two-Point Boundary Value Problems 99
6.5.1 Finite Difference Approximation 100
6.5.2 Approximation of Boundary Conditions 102
6.6 Iterative Matrix Solvers 103
6.6.1 Iterative Methods 103
6.6.2 Jacobi Method 104
6.6.3 Gauss-Seidel Method 104
6.6.4 Successive Over-Relaxation (SOR) 105
6.6.5 Other Methods 105
6.7 Example: Iterative Solvers for Elliptic PDEs 106
6.8 Summary and Conclusions 107
Chapter 7 : Black-Scholes Finite Differences for the Impatient 109
7.1 Introduction and Objectives 109
7.2 The Black-Scholes Equation: Fully Implicit and Crank-Nicolson Methods 110
7.2.1 Fully Implicit Method 110
7.2.2 Crank-Nicolson Method 111
7.2.3 Final Remarks 114
7.3 The Black-Scholes Equation: Trinomial Method 115
7.3.1 Comparison with Other Methods 115
7.4 The Heat Equation and Alternating Direction Explicit (ADE) Method 120
7.4.1 Background and Motivation 120
7.5 ADE for Black-Scholes: Some Test Results 121
7.6 Summary and Conclusions 126
Part B : Mathematical Foundation for Two-Factor Problems
Chapter 8 : Classifying and Transforming Partial Differential Equations 129
8.1 Introduction and Objectives 129
8.2 Background and Problem Statement 129
8.3 Introduction to Elliptic Equations 130
8.3.1 What is an Elliptic Operator? 130
8.3.2 Total and Principal Symbols 131
8.3.3 The Adjoint Equation 132
8.3.4 Self-Adjoint Operators and Equations 133
8.3.5 Numerical Approximation of PDEs in Adjoint Form 134
8.3.6 Elliptic Equations with Non-Negative Characteristic Form 135
8.4 Classification of Second-Order Equations 135
8.4.1 Characteristics 136
8.4.2 Model Example 137
8.4.3 Test your Knowledge 138
8.5 Examples of Two-Factor Models from Computational Finance 139
8.5.1 Multi-Asset Options 139
8.5.2 Stochastic Dividend PDE 140
8.6 Summary and Conclusions 141
Chapter 9 : Transforming Partial Differential Equations to a Bounded Domain 143
9.1 Introduction and Objectives 143
9.2 The Domain in Which a PDE Is Defined: Preamble 143
9.2.1 Background and Specific Mappings 144
9.2.2 Initial Examples 146
9.3 Other Examples 147
9.4 Hotspots 148
9.5 What Happened to Domain Truncation? 148
9.6 Another Way to Remove Mixed Derivative Terms 149
9.7 Summary and Conclusions 151
Chapter 10 : Boundary Value Problems for Elliptic and Parabolic Partial Differential Equations 153
10.1 Introduction and Objectives 153
10.2 Notation and Prerequisites 154
10.3 The Laplace Equation 154
10.3.1 Harmonic Functions and the Cauchy-Riemann Equations 154
10.4 Properties of The Laplace Equation 156
10.4.1 Maximum-Minimum Principle for Laplace's Equation 158
10.5 Some Elliptic Boundary Value Problems 159
10.5.1 Some Motivating Examples 159
10.6 Extended Maximum-Minimum Principles 159
10.6.1 An Example 161
10.7 Summary and Conclusions 162
Chapter 11 : Fichera Theory, Energy Inequalities and Integral Relations 163
11.1 Introduction and Objectives 163
11.2 Background and Problem Statement 163
11.2.1 The 'Big Bang': Cauchy-Euler Equation 163
11.3 Well-Posed Problems and Energy Estimates 165
11.3.1 Time to Reflect: What Have We Achieved and What's Next? 167
11.4 The Fichera Theory: Overview 168
11.5 The Fichera Theory: The Core Business 168
11.6 The Fichera Theory: Further Examples and Applications 171
11.6.1 Cox-Ingersoll-Ross (CIR) 171
11.6.2 Heston Model Fundamenals 172
11.6.3 Heston Model by Fichera Theory 176
11.6.4 First-Order Hyperbolic PDE in One and Two Space Variables 177
11.7 Some Useful Theorems 178
11.7.1 Divergence (Gauss-Ostrogradsky) Theorem 179
11.7.2 Green's Theorem/Formula 180
11.7.3 Green's First and Second Identities 180
11.8 Summary and Conclusions 180
Chapter 12 : An Introduction to Time-Dependent Partial Differential Equations 181
12.1 Introduction and Objectives 181
12.2 Notation and Prerequisites 181
12.3 Preamble: Separation of Variables for the Heat Equation 182
12.4 Well-Posed Problems 184
12.4.1 Examples of an ill-posed Problem 185
12.4.2 The Importance of Proving that Problems Are Well-Posed 187
12.5 Variations on Initial Boundary Value Problem for the Heat Equation 188
12.5.1 Smoothness and Compatibility Conditions 188
12.6 Maximum-Minimum Principles for Parabolic PDEs 189
12.7 Parabolic Equations with Time-Dependent Boundaries 190
12.8 Uniqueness Theorems for Boundary Value Problems in Two Dimensions 192
12.8.1 Laplace Equation 192
12.8.2 Heat Equation 193
12.9 Summary and Conclusions 193
Chapter 13 : Stochastics Representations of PDEs and Applications 195
13.1 Introduction and Objectives 195
13.2 Background, Requirements and Problem Statement 196
13.3 An Overview of Stochastic Differential Equations (SDEs) 196
13.4 An Introduction to One-Dimensional Random Processes 196
13.5 An Introduction to the Numerical Approximation of SDEs 199
13.5.1 Euler-Maruyama Method 199
13.5.2 Milstein Method 201
13.5.3 Predictor-Corrector Method 201
13.5.4 Drift-Adjusted Predictor-Corrector Method 202
13.6 Path Evolution and Monte Carlo Option Pricing 203
13.6.1 Monte Carlo Option Pricing 204
13.6.2 Some C++ Code 205
13.7 Two-Factor Problems 209
13.7.1 Spread Options with Stochastic Volatility...
| Erscheinungsjahr: | 2022 |
|---|---|
| Fachbereich: | Betriebswirtschaft |
| Genre: | Wirtschaft |
| Rubrik: | Recht & Wirtschaft |
| Medium: | Buch |
| Inhalt: | 544 S. |
| ISBN-13: | 9781119719670 |
| ISBN-10: | 1119719674 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Duffy, Daniel J |
| Hersteller: | Wiley |
| Maße: | 246 x 174 x 40 mm |
| Von/Mit: | Daniel J Duffy |
| Erscheinungsdatum: | 21.03.2022 |
| Gewicht: | 1,157 kg |
DANIEL DUFFY, PhD, has BA (Mod), MSc and PhD degrees in pure, applied and numerical mathematics (University of Dublin, Trinity College) and he is active in promoting partial differential equations (PDE) and the Finite Difference Method (FDM) for applications in computational finance. He was responsible for the introduction of the Fractional Step (Soviet Splitting) method and the Alternating Direction Explicit (ADE) method in computational finance. He is the originator of the exponential fitting method for convection-dominated PDEs.
Preface xix
Who Should Read this Book? xxiii
Part A : Mathematical Foundation for One-Factor Problems
Chapter 1 : Real Analysis Foundations for this Book 3
1.1 Introduction and Objectives 3
1.2 Continuous Functions 4
1.2.1 Formal Definition of Continuity 5
1.2.2 An Example 6
1.2.3 Uniform Continuity 6
1.2.4 Classes of Discontinuous Functions 7
1.3 Differential Calculus 8
1.3.1 Taylor's Theorem 9
1.3.2 Big O and Little o Notation 10
1.4 Partial Derivatives 11
1.5 Functions and Implicit Forms 13
1.6 Metric Spaces and Cauchy Sequences 14
1.6.1 Metric Spaces 15
1.6.2 Cauchy Sequences 16
1.6.3 Lipschitz Continuous Functions 17
1.7 Summary and Conclusions 19
Chapter 2 : Ordinary Differential Equations (ODEs), Part 1 21
2.1 Introduction and Objectives 21
2.2 Background and Problem Statement 22
2.2.1 Qualitative Properties of the Solution and Maximum Principle 22
2.2.2 Rationale and Generalisations 24
2.3 Discretisation of Initial Value Problems: Fundamentals 25
2.3.1 Common Schemes 26
2.3.2 Discrete Maximum Principle 28
2.4 Special Schemes 29
2.4.1 Exponential Fitting 29
2.4.2 Scalar Non-Linear Problems and Predictor-Corrector Method 31
2.4.3 Extrapolation 31
2.5 Foundations of Discrete Time Approximations 32
2.6 Stiff ODEs 37
2.7 Intermezzo: Explicit Solutions 39
2.8 Summary and Conclusions 41
Chapter 3 : Ordinary Differential Equations (ODEs), Part 2 43
3.1 Introduction and Objectives 43
3.2 Existence and Uniqueness Results 43
3.2.1 An Example 45
3.3 Other Model Examples 45
3.3.1 Bernoulli ODE 45
3.3.2 Riccati ODE 46
3.3.3 Predator-Prey Models 47
3.3.4 Logistic Function 48
3.4 Existence Theorems for Stochastic Differential Equations (SDEs) 48
3.4.1 Stochastic Differential Equations (SDEs) 49
3.5 Numerical Methods for ODEs 51
3.5.1 Code Samples in Python 52
3.6 The Riccati Equation 55
3.6.1 Finite Difference Schemes 57
3.7 Matrix Differential Equations 59
3.7.1 Transition Rate Matrices and Continuous Time Markov Chains 61
3.8 Summary and Conclusions 62
Chapter 4 : An Introduction to Finite Dimensional Vector Spaces 63
4.1 Short Introduction and Objectives 63
4.1.1 Notation 64
4.2 What Is a Vector Space? 65
4.3 Subspaces 67
4.4 Linear Independence and Bases 68
4.5 Linear Transformations 69
4.5.1 Invariant Subspaces 70
4.5.2 Rank and Nullity 71
4.6 Summary and Conclusions 72
Chapter 5 : Guide to Matrix Theory and Numerical Linear Algebra 73
5.1 Introduction and Objectives 73
5.2 From Vector Spaces to Matrices 73
5.2.1 Sums and Scalar Products of Linear Transformations 73
5.3 Inner Product Spaces 74
5.3.1 Orthonormal Basis 75
5.4 From Vector Spaces to Matrices 76
5.4.1 Some Examples 76
5.5 Fundamental Matrix Properties 77
5.6 Essential Matrix Types 80
5.6.1 Nilpotent and Related Matrices 80
5.6.2 Normal Matrices 81
5.6.3 Unitary and Orthogonal Matrices 82
5.6.4 Positive Definite Matrices 82
5.6.5 Non-Negative Matrices 83
5.6.6 Irreducible Matrices 83
5.6.7 Other Kinds of Matrices 84
5.7 The Cayley Transform 84
5.8 Summary and Conclusions 86
Chapter 6 : Numerical Solutions of Boundary Value Problems 87
6.1 Introduction and Objectives 87
6.2 An Introduction to Numerical Linear Algebra 87
6.2.1 BLAS (Basic Linear Algebra Subprograms) 90
6.3 Direct Methods for Linear Systems 92
6.3.1 LU Decomposition 92
6.3.2 Cholesky Decomposition 94
6.4 Solving Tridiagonal Systems 94
6.4.1 Double Sweep Method 94
6.4.2 Thomas Algorithm 96
6.4.3 Block Tridiagonal Systems 97
6.5 Two-Point Boundary Value Problems 99
6.5.1 Finite Difference Approximation 100
6.5.2 Approximation of Boundary Conditions 102
6.6 Iterative Matrix Solvers 103
6.6.1 Iterative Methods 103
6.6.2 Jacobi Method 104
6.6.3 Gauss-Seidel Method 104
6.6.4 Successive Over-Relaxation (SOR) 105
6.6.5 Other Methods 105
6.7 Example: Iterative Solvers for Elliptic PDEs 106
6.8 Summary and Conclusions 107
Chapter 7 : Black-Scholes Finite Differences for the Impatient 109
7.1 Introduction and Objectives 109
7.2 The Black-Scholes Equation: Fully Implicit and Crank-Nicolson Methods 110
7.2.1 Fully Implicit Method 110
7.2.2 Crank-Nicolson Method 111
7.2.3 Final Remarks 114
7.3 The Black-Scholes Equation: Trinomial Method 115
7.3.1 Comparison with Other Methods 115
7.4 The Heat Equation and Alternating Direction Explicit (ADE) Method 120
7.4.1 Background and Motivation 120
7.5 ADE for Black-Scholes: Some Test Results 121
7.6 Summary and Conclusions 126
Part B : Mathematical Foundation for Two-Factor Problems
Chapter 8 : Classifying and Transforming Partial Differential Equations 129
8.1 Introduction and Objectives 129
8.2 Background and Problem Statement 129
8.3 Introduction to Elliptic Equations 130
8.3.1 What is an Elliptic Operator? 130
8.3.2 Total and Principal Symbols 131
8.3.3 The Adjoint Equation 132
8.3.4 Self-Adjoint Operators and Equations 133
8.3.5 Numerical Approximation of PDEs in Adjoint Form 134
8.3.6 Elliptic Equations with Non-Negative Characteristic Form 135
8.4 Classification of Second-Order Equations 135
8.4.1 Characteristics 136
8.4.2 Model Example 137
8.4.3 Test your Knowledge 138
8.5 Examples of Two-Factor Models from Computational Finance 139
8.5.1 Multi-Asset Options 139
8.5.2 Stochastic Dividend PDE 140
8.6 Summary and Conclusions 141
Chapter 9 : Transforming Partial Differential Equations to a Bounded Domain 143
9.1 Introduction and Objectives 143
9.2 The Domain in Which a PDE Is Defined: Preamble 143
9.2.1 Background and Specific Mappings 144
9.2.2 Initial Examples 146
9.3 Other Examples 147
9.4 Hotspots 148
9.5 What Happened to Domain Truncation? 148
9.6 Another Way to Remove Mixed Derivative Terms 149
9.7 Summary and Conclusions 151
Chapter 10 : Boundary Value Problems for Elliptic and Parabolic Partial Differential Equations 153
10.1 Introduction and Objectives 153
10.2 Notation and Prerequisites 154
10.3 The Laplace Equation 154
10.3.1 Harmonic Functions and the Cauchy-Riemann Equations 154
10.4 Properties of The Laplace Equation 156
10.4.1 Maximum-Minimum Principle for Laplace's Equation 158
10.5 Some Elliptic Boundary Value Problems 159
10.5.1 Some Motivating Examples 159
10.6 Extended Maximum-Minimum Principles 159
10.6.1 An Example 161
10.7 Summary and Conclusions 162
Chapter 11 : Fichera Theory, Energy Inequalities and Integral Relations 163
11.1 Introduction and Objectives 163
11.2 Background and Problem Statement 163
11.2.1 The 'Big Bang': Cauchy-Euler Equation 163
11.3 Well-Posed Problems and Energy Estimates 165
11.3.1 Time to Reflect: What Have We Achieved and What's Next? 167
11.4 The Fichera Theory: Overview 168
11.5 The Fichera Theory: The Core Business 168
11.6 The Fichera Theory: Further Examples and Applications 171
11.6.1 Cox-Ingersoll-Ross (CIR) 171
11.6.2 Heston Model Fundamenals 172
11.6.3 Heston Model by Fichera Theory 176
11.6.4 First-Order Hyperbolic PDE in One and Two Space Variables 177
11.7 Some Useful Theorems 178
11.7.1 Divergence (Gauss-Ostrogradsky) Theorem 179
11.7.2 Green's Theorem/Formula 180
11.7.3 Green's First and Second Identities 180
11.8 Summary and Conclusions 180
Chapter 12 : An Introduction to Time-Dependent Partial Differential Equations 181
12.1 Introduction and Objectives 181
12.2 Notation and Prerequisites 181
12.3 Preamble: Separation of Variables for the Heat Equation 182
12.4 Well-Posed Problems 184
12.4.1 Examples of an ill-posed Problem 185
12.4.2 The Importance of Proving that Problems Are Well-Posed 187
12.5 Variations on Initial Boundary Value Problem for the Heat Equation 188
12.5.1 Smoothness and Compatibility Conditions 188
12.6 Maximum-Minimum Principles for Parabolic PDEs 189
12.7 Parabolic Equations with Time-Dependent Boundaries 190
12.8 Uniqueness Theorems for Boundary Value Problems in Two Dimensions 192
12.8.1 Laplace Equation 192
12.8.2 Heat Equation 193
12.9 Summary and Conclusions 193
Chapter 13 : Stochastics Representations of PDEs and Applications 195
13.1 Introduction and Objectives 195
13.2 Background, Requirements and Problem Statement 196
13.3 An Overview of Stochastic Differential Equations (SDEs) 196
13.4 An Introduction to One-Dimensional Random Processes 196
13.5 An Introduction to the Numerical Approximation of SDEs 199
13.5.1 Euler-Maruyama Method 199
13.5.2 Milstein Method 201
13.5.3 Predictor-Corrector Method 201
13.5.4 Drift-Adjusted Predictor-Corrector Method 202
13.6 Path Evolution and Monte Carlo Option Pricing 203
13.6.1 Monte Carlo Option Pricing 204
13.6.2 Some C++ Code 205
13.7 Two-Factor Problems 209
13.7.1 Spread Options with Stochastic Volatility...
| Erscheinungsjahr: | 2022 |
|---|---|
| Fachbereich: | Betriebswirtschaft |
| Genre: | Wirtschaft |
| Rubrik: | Recht & Wirtschaft |
| Medium: | Buch |
| Inhalt: | 544 S. |
| ISBN-13: | 9781119719670 |
| ISBN-10: | 1119719674 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Duffy, Daniel J |
| Hersteller: | Wiley |
| Maße: | 246 x 174 x 40 mm |
| Von/Mit: | Daniel J Duffy |
| Erscheinungsdatum: | 21.03.2022 |
| Gewicht: | 1,157 kg |
Ähnliche Produkte
Lieferzeit 1-2 Wochen
Aktuell nicht verfügbar
Aktuell nicht verfügbar
Aktuell nicht verfügbar
Lieferzeit 2-4 Werktage
Lieferzeit 1-2 Wochen
