DESCRIPTION

The pricing of derivatives has always been time consuming. The use of mathematical models has enabled quicker and more accurate pricing. The author uses a proven mathematical technique to bridge the divide between finance and mathematics. The author describes the processes in a way that is accessible to those without a deep understanding of mathematics. Little understood techniques will assist in the accurate pricing of options. There are centers on practical application of these techniques. The first to explore the application of these particular techniques to the financial markets, it offers a detailed and comprehensive account of the methods involved.

TABLE OF CONTENTS

Preface.

There is a list of symbols.

Preliminaries are part of the first part.

1. Introduction.
2. Some Prototype Models.

There is an optimal price policy.

The black-holes option pricing model is used.

Pricing American options.

There are multi- asset options with a correlation.

The Vasicek Interest Rate Process has a Steady-State Distribution.

2.6 Notes.

3. The Conventional Approach: Finite Differences.

There are general considerations for numerical computation.

There are problems with the ordinary initial value.

The two-point Boundary-Value problems are Ordinary.

There are problems with the initial boundary value.

3.5 Notes.

The second part is about finite elements.

4. Static 1D Problems.

There are basic features of finite element methods.

The method of weighted residuals is one element solutions.

The Ritzational method is used.

The method of weighted residuals is a more general view.

There are 4.5 multi- element solutions.

There are case studies.

There is a convergence.

4.8 Notes.

5. Dynamic 1D Problems.

Derivation of equations.

There are five case studies.

6. Static 2D Problems.

There is an introduction and an overview.

There is a construction of a mesh.

The method is called the Galerkin Method.

There are 6.4 case studies.

6.5 Notes.

7. Dynamic 2D Problems.

Derivation of equations.

There are 7.2 case studies.

8. Static 3D Problems.

The Collocation Method is used for theDerivation of Element Equations.

There are case studies.

8.3 Notes.

9. Dynamic 3D Problems.

The Collocation Method is used for theDerivation of Element Equations.

There are 9.2 case studies.

10. Nonlinear Problems.

There is an introduction.

There are case studies.

There are notes.

The outlook is part III.

11. Future Directions of Research .

Part IV is about assents.

There are some useful results from analysis.

Calculus has important Theorems.

There are basic numerical tools.

The Differential Equations are A.3

There is a Calculus of Variations.

There are some useful results from the Stochastics.

There are some important distributions.

There are some important processes.

There were B.3 results.

B.4 Notes.

There are some useful results from linear math.

There are some basic facts.

There are C.2 Errors and Norms.

Ill-Conditioning is referred to as C.3 Ill-Conditioning.

C.4 is related to Linear Algebraic Systems.

C.5 Notes.

A quick introduction to PDE2D.

There are references.

Index .

AUTHOR INFORMATION

JRGEN TOPPER. d-fine is a company that specializes in financial and commodity risk consulting. He worked for the financial risk management consulting division of Arthur Andersen.