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Numerical partial differential equations in finance explained : an introduction to computational finance /
This book provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs). It provides readers with an easily accessible text explaining main concepts, models, methods and results that arise in this approach. In keeping...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Palgrace Macmillan,
[2017]
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| Colección: | Financial engineering explained.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1 Financial Option Valuation; 1.1 Financial Options; 1.2 The Black-Scholes PDE; 2 Partial Differential Equations; 2.1 Convection-Diffusion-Reaction Equations; 2.2 The Model Equation; 2.3 Boundary Conditions; 2.4 Notes and References; 3 Spatial Discretization I; 3.1 Method of Lines; 3.2 Finite Difference Formulas; 3.3 Stability; 3.4 Notes and References; 4 Spatial Discretization II; 4.1 Boundary Conditions; 4.2 Nonuniform Grids; 4.3 Nonsmooth Initial Data; 4.4 Mixed Central/Upwind Discretization; 4.5 Notes and References; 5 Numerical Study: Space; 5.1 Cell Averaging; 5.2 Nonuniform Grids.
- 5.3 Boundary Conditions6 The Greeks; 6.1 The Greeks; 6.2 Numerical Study; 6.3 Notes and References; 7 Temporal Discretization; 7.1 The -Methods; 7.2 Stability and Convergence; 7.3 Maximum Norm and Positivity; 7.4 Notes and References; 8 Numerical Study: Time; 8.1 Explicit Method; 8.2 Implicit Methods; 8.3 Notes and References; 9 Cash-or-Nothing Options; 10 Barrier Options; 11 American-Style Options; 11.1 American-Style Options; 11.2 LCP Solution Methods; 11.3 Numerical Study; 11.4 Notes and References; 12 Merton Model; 12.1 Merton Model; 12.2 Spatial Discretization; 12.3 IMEX Schemes.
- 12.4 Numerical Study12.5 Notes and References; 13 Two-Asset Options; 13.1 Two-Asset Options; 13.2 Spatial Discretization; 13.3 ADI Schemes; 13.4 Numerical Study; 13.5 Notes and References; Appendix A: Wiener Process; Appendix B: Feynman-Kac Theorem; Appendix C: Down-and-Out Put Option Value; Appendix D: Max-of-Two-Assets Call Option Value; Bibliography; Index.