The Time-Discrete Method of Lines for Options and Bonds 9814619671, 9789814619677, 9789814619691, 9789814619684
Few financial mathematical books have discussed mathematically acceptable boundary conditions for the degenerate diffusi
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English Pages C, XV, 269 Year 2015
Table of contents :
Cover
S Title
The Time-Discrete Method of Lines for Options and Bonds: A PDE Approach
Copyright © 2015 by World Scientific Publishing
ISBN 978-981-4619-67-7
Preface
Contents
Acknowledgment
Chapter 1 Comments on the Pricing Equations in Finance
1.1 Solutions and their properties
1.2 Boundary conditions for the pricing equations
1.2.1 The Fichera function for degenerate equations
1.2.2 The boundary condition at “infinity”
1.2.3 The Venttsel boundary conditions on “far but finite” boundaries
1.2.4 Free boundaries
Chapter 2 The Method of Lines (MOL) for the Diffusion Equation
2.1 The method of lines with continuous time (the vertical MOL)
2.2 The method of lines with continuous x (the horizontal MOL)
2.3 The method of lines with continuous x for multidimensional problems
Appendix 2.3 Convergence of the line Gauss Seidel iteration for a model problem
2.4 Free boundaries and the MOL in two dimensions
Chapter 3 The Riccati Transformation Method for Linear Two Point Boundary Value Problems
3.1 The Riccati transformation on a fixed interval
3.2 The Riccati transformation for a free boundary problem
3.3 The numerical solution of the sweep equations
Appendix 3.3 Connection between the Riccati transformation, Gaussian elimination and the Brennan-Schwartz method
Chapter 4 European Options
Chapter 5 American Puts and Calls
Chapter 6 Bonds and Options for One-Factor Interest Rate Models
Chapter 7 Two-Dimensional Diffusion Problems in Finance
7.1 Front tracking in Cartesian coordinates
7.2 American calls and puts in polar coordinates
7.3 A three-dimensional problem
Bibliography
Index
About the Author
Cover
S Title
The Time-Discrete Method of Lines for Options and Bonds: A PDE Approach
Copyright © 2015 by World Scientific Publishing
ISBN 978-981-4619-67-7
Preface
Contents
Acknowledgment
Chapter 1 Comments on the Pricing Equations in Finance
1.1 Solutions and their properties
1.2 Boundary conditions for the pricing equations
1.2.1 The Fichera function for degenerate equations
1.2.2 The boundary condition at “infinity”
1.2.3 The Venttsel boundary conditions on “far but finite” boundaries
1.2.4 Free boundaries
Chapter 2 The Method of Lines (MOL) for the Diffusion Equation
2.1 The method of lines with continuous time (the vertical MOL)
2.2 The method of lines with continuous x (the horizontal MOL)
2.3 The method of lines with continuous x for multidimensional problems
Appendix 2.3 Convergence of the line Gauss Seidel iteration for a model problem
2.4 Free boundaries and the MOL in two dimensions
Chapter 3 The Riccati Transformation Method for Linear Two Point Boundary Value Problems
3.1 The Riccati transformation on a fixed interval
3.2 The Riccati transformation for a free boundary problem
3.3 The numerical solution of the sweep equations
Appendix 3.3 Connection between the Riccati transformation, Gaussian elimination and the Brennan-Schwartz method
Chapter 4 European Options
Chapter 5 American Puts and Calls
Chapter 6 Bonds and Options for One-Factor Interest Rate Models
Chapter 7 Two-Dimensional Diffusion Problems in Finance
7.1 Front tracking in Cartesian coordinates
7.2 American calls and puts in polar coordinates
7.3 A three-dimensional problem
Bibliography
Index
About the Author
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