Skip to Content
The Mathematics of Derivatives: Tools for Designing Numerical Algorithms
book

The Mathematics of Derivatives: Tools for Designing Numerical Algorithms

by Robert L. Navin
December 2006
Intermediate to advanced content levelIntermediate to advanced
205 pages
4h 26m
English
Wiley
Content preview from The Mathematics of Derivatives: Tools for Designing Numerical Algorithms

Contents

Preface

Acknowledgments

PART I   The Models

CHAPTER 1

Introduction to the Techniques of Derivative Modeling

1.1 Introduction

1.2 Models

1.2.1 What Is a Derivative?

1.2.2 What Is a Model?

1.2.3 Two Initial Methods for Modeling Derivatives

1.2.4 Price Processes

1.2.5 The Archetypal Security Process: Normal Returns

1.2.6 Book Outline

CHAPTER 2

Preliminary Mathematical Tools

2.1 Probability Distributions

2.2 n-Dimensional Jacobians and n-Form Algebra

2.3 Functional Analysis and Fourier Transforms

2.4 Normal (Central) Limit Theorem

2.5 Random Walks

2.6 Correlation

2.7 Functions of Two/More Variables: Path Integrals

2.8 Differential Forms

CHAPTER 3

Stochastic Calculus

3.1 Wiener Process

3.2 Ito’s Lemma

3.3 Variable Changes to Get the Martingale

3.4 Other Processes: Multivariable Correlations

CHAPTER 4

Applications of Stochastic Calculus to Finance

4.1 Risk Premium Derivation

4.2 Analytic Formula for the Expected Payoff of a European Option

CHAPTER 5

From Stochastic Processes Formalism to Differential Equation Formalism

5.1 Backward and Forward Kolmogorov Equations

5.2 Derivation of Black-Scholes Equation, Risk-Neutral Pricing

5.3 Risks and Trading Strategies

CHAPTER 6

Understanding the Black-Scholes Equation

6.1 Black-Scholes Equation: A Type of Backward Kolmogorov Equation

6.1.1 Forward Price

6.2 Black-Scholes Equation: Risk-Neutral Pricing

6.3 Black-Scholes Equation: Relation to Risk Premium Definition

6.4 Black-Scholes Equation Applies to Currency Options: Hidden Symmetry ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Numerical Simulation, An Art of Prediction 1

Numerical Simulation, An Art of Prediction 1

Jean-François Sigrist
Modern Computational Finance

Modern Computational Finance

Antoine Savine, Leif Andersen
Learning Cocoa with Objective-C, 4th Edition

Learning Cocoa with Objective-C, 4th Edition

Paris Buttfield-Addison, Jonathon Manning, Tim Nugent

Publisher Resources

ISBN: 9780470047255Purchase book