Numerical Partial Differential Equations in Finance Explained An Introduction to Computational Finance 1st Edition by Karel int Hout ISBN 1137435690 9781137435699

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ISBN 10:  1137435690 
ISBN 13: 9781137435699
Author: Karel in ‘t Hout

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.

Numerical Partial Differential Equations in Finance Explained An Introduction to Computational Finance 1st Table of contents:

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 Conditions

6 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 Study

12.5 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

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Karel int Hout,Numerical Partial,Differential Equations,Finance Explained,Introduction,Computational Finance