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Finite Difference Methods in Financial Engineering [2006]
- 1
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Goals of this Book and Global Overview
- 5
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An Introduction to Ordinary Differential Equations
- 13
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An Introduction to Partial Differential Equations
- 25
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Second‐Order Parabolic Differential Equations
- 38
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An Introduction to the Heat Equation in One Dimension
- 47
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An Introduction to the Method of Characteristics
- 61
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An Introduction to the Finite Difference Method
- 79
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An Introduction to the Method of Lines
- 91
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General Theory of the Finite Difference Method
- 103
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Finite Difference Schemes for First‐Order Partial Differential Equations
- 117
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FDM for the One‐Dimensional Convection–Diffusion Equation
- 123
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Exponentially Fitted Finite Difference Schemes
- 135
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Exact Solutions and Explicit Finite Difference Method for One‐Factor Models
- 147
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An Introduction to the Trinomial Method
- 153
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Exponentially Fitted Difference Schemes for Barrier Options
- 165
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Advanced Issues in Barrier and Lookback Option Modelling
- 175
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The Meshless (Meshfree) Method in Financial Engineering
- 183
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Extending the Black–Scholes Model: Jump Processes
- 193
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Finite Difference Schemes for Multidimensional Problems
- 209
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An Introduction to Alternating Direction Implicit and Splitting Methods
- 223
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Advanced Operator Splitting Methods: Fractional Steps
- 229
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Modern Splitting Methods
- 237
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Options with Stochastic Volatility: The Heston Model
- 249
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Finite Difference Methods for Asian Options and Other ‘Mixed’ Problems
- 257
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Multi‐Asset Options
- 273
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Finite Difference Methods for Fixed‐Income Problems
- 285
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Background to Free and Moving Boundary Value Problems
- 295
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Numerical Methods for Free Boundary Value Problems: Front‐Fixing Methods
- 307
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Viscosity Solutions and Penalty Methods for American Option Problems
- 315
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Variational Formulation of American Option Problems
- 325
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Finding the Appropriate Finite Difference Schemes for your Financial Engineering Problem
- 337
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Design and Implementation of First‐Order Problems
- 353
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Moving to Black–Scholes
- 363
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C++ Class Hierarchies for One‐Factor and Two‐Factor Payoffs
- 375
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Appendix 1: An introduction to Integral and Partial Integro‐Differential Equations
- 393
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Appendix 2: An Introduction to the Finite Element Method
- 409
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Bibliography
- 417
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Index
- i
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Front Matter