Mathematical Finance

CONTENTS

Preface

UNIT I    MATHEMATICAL INTRODUCTION

1  Numbers, Exponents, and Logarithms

  1.1.  Numbers

  1.2.  Fractions

  1.3.  Decimals

  1.4.  Repe tends

  1.5.  Percentages

  1.6.  Base Amount, Percentage Rate, and Percentage Amount

  1.7.  Ratios

  1.8.  Proportions

  1.9.  Aliquots

1.10.  Exponents

1.11.  Laws of Exponents

1.12.  Exponential Function

1.13.  Natural Exponential Function

1.14.  Laws of Natural Exponents

1.15.  Scientific Notation

1.16.  Logarithms

1.17.  Laws of Logarithms

1.18.  Characteristic, Mantissa, and Antilogarithm

1.19.  Logarithmic Function

2  Mathematical Progressions

2.1.  Arithmetic Progression

2.2.  Geometric Progression

2.3.  Recursive Progression

2.4.  Infinite Geometric Progression

2.5.  Growth and Decay Curves

2.6.  Growth and Decay Functions with a Natural Logarithmic Base

3  Statistical Measures

  3.1.  Basic Combinatorial Rules and Concepts

  3.2.  Permutation

  3.3.  Combination

  3.4.  Probability

  3.5.  Mathematical Expectation and Expected Value

  3.6.  Variance

  3.7.  Standard Deviation

  3.8.  Covariance

  3.9.  Correlation

3.10.  Normal Distribution

Unit I Summary

List of Formulas

Exercises for Unit I

UNIT II    MATHEMATICS OF THE TIME VALUE OF MONEY

Introduction

1  Simple Interest

  1.1.  Total Interest

  1.2.  Rate of Interest

  1.3.  Term of Maturity

  1.4.  Current Value

  1.5.  Future Value

  1.6.  Finding n and r When the Current and Future Values are Both Known

  1.7.  Simple Discount

  1.8.  Calculating the Term in ...