Introduction to financial mathematics

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Contents Preface........................................................... v Contents........................................................ vii 1 Simple Interest and Day-Count Conventions ................... 1 1.1 Motivation and Basic Concepts .......................... 1 1.2 Simple Interest Approach ............................... 2 1.2.1 Application: Certificate of Deposit ............... 7 1.2.2 Application: Savings Account ...................... 8 1.3 Day-Count Conventions .................................. 9 1.4 Discount .............................................. 14 1.4.1 Application: Treasury Bill ....................... 16 1.4.2 Application: Bill of Exchange..................... 19 1.5 Questions and Exercises................................ 21 2 Compound interest .......................................... 25 2.1 Compound Interest Approach............................. 25 2.2 Effective Rate......................................... 31 2.3 Continuous Compounding .................... 32 2.4 Combination of Simple and Compound Interest ........... 36 2.5 Inflation and Taxes ................................... 40 vii viii___________________________________________________________Contents 2.5.1 Real Rate of Interest ............................. 40 2.5.2 Consumer Price Index (CPI)......................... 41 2.5.3 Taxes.............................................. 43 2.6 Questions and Exercises.................................. 44 3 Cash Flows, Net Present Value and Internal Rate of Return .... 51 3.1 Cash Flows .............................................. 51 3.2 Net Present Value........................................ 52 3.3 Internal Rate of Return.................................. 57 3.3.1 Application: Index Fund............................ 62 3.4 Payback Period .......................................... 63 3.5 Questions and Exercises.................................. 66 4 Annuities .................................................... 73 4.1 Basic Annuities.......................................... 73 4.1.1 Ordinary Annuity................................... 74 4.1.2 Annuity Due ....................................... 79 4.1.3 Varying Annuity.................................... 81 4.1.4 Perpetuity ........................................ 82 4.2 General Annuities........................................ 83 4.2.1 Application: A Pension Problem .................... 86 4.3 Questions and Exercises.................................. 87 5 Amortization Schedules ....................................... 93 5.1 Constant Principal and Interest Payments ................ 93 5.2 Varying Payments......................................... 98 5.3 Annual Percentage Rate of Charge ....................... 102 5.4 Questions and Exercises................................. 103 6 Bonds ....................................................... 109 2017 T. Funioková Contents ix 6.1 Bond Valuation Process ...................... HO 6.1.1 Bond Valuation on a Coupon Date.................. Hl 6.1.2 Bond Valuation between two Coupon Dates.......... 120 6.2 Duration .............................................. 129 6.2.1 Application: Bond Portfolio Immunization.......... 135 6.3 Term Structure of Interest Rates ..................... 142 6.4 Questions and Exercises................................ 148 7 Stocks ...................................................... 155 7.1 Stock Valuation Process ............................... 156 7.1.1 Dividend Discount Model .......................... 156 7.1.2 Price/Earnings Model ............................ 158 7.2 Rates of Return........................................ 161 7.3 Risk Valuation Process................................. 164 7.3.1 Application: Stock Price Volatility............... 167 7.4 Stock Portfolio........................................ 169 7.4.1 Application: Two-stock Portfolio Diversification ... 175 7.5 Capital Asset Pricing Model ........................... 179 7.6 Questions and Exercises................................ 183 Bibliography ..................................................... 159 Index ............................................................ 191 Summary........................................................... 197 Introduction to Financial Mathematics