An Introduction to the Mathematics of Finance

An Introduction to the Mathematics of Finance

A Deterministic Approach

2nd Edition - May 28, 2013

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  • Author: Stephen Garrett
  • Paperback ISBN: 9780081013021
  • eBook ISBN: 9780080982755

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Description

An Introduction to the Mathematics of Finance: A Deterministic Approach, Second edition, offers a highly illustrated introduction to mathematical finance, with a special emphasis on interest rates. This revision of the McCutcheon-Scott classic follows the core subjects covered by the first professional exam required of UK actuaries, the CT1 exam. It realigns the table of contents with the CT1 exam and includes sample questions from past exams of both The Actuarial Profession and the CFA Institute. With a wealth of solved problems and interesting applications, An Introduction to the Mathematics of Finance stands alone in its ability to address the needs of its primary target audience, the actuarial student.

Key Features

  • Closely follows the syllabus for the CT1 exam of The Institute and Faculty of Actuaries
  • Features new content and more examples
  • Online supplements available: http://booksite.elsevier.com/9780080982403/
  • Includes past exam questions from The Institute and Faculty of Actuaries and the CFA Institute

Readership

Upper-division undergraduates and graduate students in the UK studying financial mathematics. They will typically be taking courses such as "Principles of Finance" and "Actuarial Finance." Upper-division undergraduates and graduate students studying financial mathematics

Table of Contents

  • Chapter 1. Introduction

    1.1 The Concept of Interest

    1.2 Simple Interest

    1.3 Compound Interest

    1.4 Some Practical Illustrations

    Summary

    Chapter 2. Theory of Interest Rates

    2.1 The Rate of Interest

    2.2 Nominal Rates of Interest

    2.3 Accumulation Factors

    2.4 The Force of Interest

    2.5 Present Values

    2.6 Present Values of Cash Flows

    2.7 Valuing Cash Flows

    2.8 Interest Income

    2.9 Capital Gains and Losses, and Taxation

    Summary

    Exercises

    Chapter 3. The Basic Compound Interest Functions

    3.1 Interest Rate Quantities

    3.2 The Equation of Value

    3.3 Annuities-certain: Present Values and Accumulations

    3.4 Deferred Annuities

    3.5 Continuously Payable Annuities

    3.6 Varying Annuities

    3.7 Uncertain Payments

    Summary

    Exercises

    Chapter 4. Further Compound Interest Functions

    4.1 Interest Payable pthly

    4.2 Annuities Payable pthly: Present Values and Accumulations

    4.3 Annuities Payable at Intervals of Time r, Where r > 1

    4.4 Definition of for Non-integer Values of n

    Summary

    Exercises

    Chapter 5. Loan Repayment Schedules

    5.1 The General Loan Schedule

    5.2 The Loan Schedule for a Level Annuity

    5.3 The Loan Schedule for a pthly Annuity

    5.4 Consumer Credit Legislation

    Summary

    Exercises

    Chapter 6. Project Appraisal and Investment Performance

    6.1 Net Cash Flows

    6.2 Net Present Values and Yields

    6.3 The Comparison of Two Investment Projects

    6.4 Different Interest Rates for Lending and Borrowing

    6.5 Payback Periods

    6.6 The Effects of Inflation

    6.7 Measurement of Investment Fund Performance

    Summary

    Exercises

    Chapter 7. The Valuation of Securities

    7.1 Fixed-Interest Securities

    7.2 Related Assets

    7.3 Prices and Yields

    7.4 Perpetuities

    7.5 Makeham’s Formula

    7.6 The Effect of the Term to Redemption on the Yield

    7.7 Optional Redemption Dates

    7.8 Valuation between Two Interest Dates: More Complicated Examples

    7.9 Real Returns and Index-linked Stocks

    Summary

    Exercises

    Chapter 8. Capital Gains Tax

    8.1 Valuing a Loan with Allowance for Capital Gains Tax

    8.2 Capital Gains Tax When the Redemption Price or the Rate of Tax Is Not Constant

    8.3 Finding the Yield When There Is Capital Gains Tax

    8.4 Optional Redemption Dates

    8.5 Offsetting Capital Losses Against Capital Gains

    Summary

    Exercises

    Chapter 9. Term Structures and Immunization

    9.1 Spot and Forward Rates

    9.2 Theories of the Term Structure of Interest Rates

    9.3 The Discounted Mean Term of a Project

    9.4 Volatility

    9.5 The Volatility of Particular Fixed-interest Securities

    9.6 The Matching of Assets and Liabilities

    9.7 Redington’s Theory of Immunization

    9.8 Full Immunization

    Summary

    Exercises

    Chapter 10. An Introduction to Derivative Pricing: Forwards and Futures

    10.1 Futures Contracts

    10.2 Margins and Clearinghouses

    10.3 Uses of Futures

    10.4 Forwards

    10.5 Arbitrage

    10.6 Calculating the Forward Price

    10.7 Calculating the Value of a Forward Contract Prior to Maturity

    10.8 Eliminating the Risk to the Short Position

    Summary

    Exercises

    Chapter 11. Further Derivatives: Swaps and Options

    11.1 Swaps

    11.2 Options

    11.3 Option Payoff and Profit

    11.4 An Introduction to European Option Pricing

    11.5 The Black–Scholes Model

    11.6 Trading Strategies Involving European Options

    Summary

    Exercises

    Chapter 12. An Introduction to Stochastic Interest Rate Models

    12.1 Introductory Examples

    12.2 Independent Annual Rates of Return

    12.3 The Log-Normal Distribution

    12.4 Simulation Techniques

    12.5 Random Number Generation

    12.6 Dependent Annual Rates of Return

    12.7 An Introduction to the Application of Brownian Motion

    Summary

    Exercises

Product details

  • No. of pages: 464
  • Language: English
  • Copyright: © Butterworth-Heinemann 2013
  • Published: May 28, 2013
  • Imprint: Butterworth-Heinemann
  • Paperback ISBN: 9780081013021
  • eBook ISBN: 9780080982755

About the Author

Stephen Garrett

Prof. Stephen Garrett is Professor of Mathematical Sciences at the University of Leicester in the UK. He is currently Head of Actuarial Science in the Department of Mathematics, and also Head of the Thermofluids Research Group in the Department of Engineering. These two distinct responsibilities reflect his background and achievements in both actuarial science education and fluid mechanics research. Stephen is a Fellow of the Royal Aeronautical Society, the highest grade attainable in the world's foremost aerospace institution.

Affiliations and Expertise

Professor of Mathematical Sciences, University of Leicester, UK

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