Numerical partial differential equations in finance explained : an introduction to computational finance / Karel in 't Hout.
In 'T Hout, Karel.
2017
HF5691 .H68 2017eb
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Title Numerical partial differential equations in finance explained : an introduction to computational finance / Karel in 't Hout.
Author In 'T Hout, Karel.
Edition 1ST ED. 2017.
ISBN 9781137435699 (electronic book)
1137435690 (electronic book)
1137435682
9781137435682
Publication Details [S.l.] : PALGRAVE MACMILLAN, 2017.
Language English
Description 1 online resource.
Call Number HF5691 .H68 2017eb
Dewey Decimal Classification 650.01/51
Summary 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 with the series style, emphasis is placed on intuition as opposed to full rigor, and a relatively basic understanding of mathematics is sufficient. The book provides a wealth of examples, and ample numerical experiments are givento illustrate the theory. The main focus is on one-dimensional financial PDEs, notably the Black-Scholes equation. The book concludes with a detailed discussion of the important step towards two-dimensional PDEs in finance.
Access Note Access limited to authorized users.
Series Financial Engineering Explained.
Available in Other Form Print version: 9781137435682
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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

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