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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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:
  • Includes past exam questions from The Institute and Faculty of Actuaries and the CFA Institute


Upper-division undergraduates and graduate students in the UK studying financial mathematics, Upper-division undergraduates and graduate students studying financial mathematics

Table of Contents

  • 1. Introduction
    1.1 The Concept of Interest
    1.2 Simple Interest
    1.3 Compound Interest
    1.4 Some Practical Illustrations

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

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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