| |
| |
| |
| The measurement of interest | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The accumulation and amount functions | |
| |
| |
| |
| The effective rate of interest | |
| |
| |
| |
| Simple interest | |
| |
| |
| |
| Compound interest | |
| |
| |
| |
| Present value | |
| |
| |
| |
| The effective rate of discount | |
| |
| |
| |
| Nominal rates of interest and discount | |
| |
| |
| |
| Forces of interest and discount | |
| |
| |
| |
| Varying interest | |
| |
| |
| |
| Summary of results | |
| |
| |
| Appendix 1 | |
| |
| |
| Simple interest for fractional periods | |
| |
| |
| Compound interest for fractional periods | |
| |
| |
| Exercises | |
| |
| |
| |
| Solution of problems in interest | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The basic problem | |
| |
| |
| |
| Equations of value | |
| |
| |
| |
| Unknown time | |
| |
| |
| |
| Unknown rate of interest | |
| |
| |
| |
| Determining time periods | |
| |
| |
| |
| Practical examples | |
| |
| |
| Appendix 2 | |
| |
| |
| Derivation involving method of equated time | |
| |
| |
| Exercises | |
| |
| |
| |
| Basic annuities | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Annuity-immediate | |
| |
| |
| |
| Annuity-due | |
| |
| |
| |
| Annuity values on any date | |
| |
| |
| |
| Perpetuities | |
| |
| |
| |
| Unknown time | |
| |
| |
| |
| Unknown rate of interest | |
| |
| |
| |
| Varying interest | |
| |
| |
| |
| Annuities not involving compound interest | |
| |
| |
| Appendix 3 | |
| |
| |
| Approximate formula for unknown rate of interest | |
| |
| |
| Exercises | |
| |
| |
| |
| More general annuities | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Differing payment and interest conversion periods | |
| |
| |
| |
| Annuities payable less frequently than interest is convertible | |
| |
| |
| |
| Annuities payable more frequently than interest is convertible | |
| |
| |
| |
| Continuous annuities | |
| |
| |
| |
| Payments varying in arithmetic progression | |
| |
| |
| |
| Payments varying in geometric progression | |
| |
| |
| |
| More general varying annuities | |
| |
| |
| |
| Continuous varying annuities | |
| |
| |
| |
| Summary of results | |
| |
| |
| Appendix 4 | |
| |
| |
| Other formulas for annuities payable more frequently than interest is convertible | |
| |
| |
| Alternative approach for payments varying in arithmetic progression | |
| |
| |
| Exercises | |
| |
| |
| |
| Amortization schedules and sinking funds | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Finding the outstanding loan balance | |
| |
| |
| |
| Amortization schedules | |
| |
| |
| |
| Sinking funds | |
| |
| |
| |
| Differing payment periods and interest conversion periods | |
| |
| |
| |
| Varying series of payments | |
| |
| |
| |
| Amorization with continuous payments | |
| |
| |
| |
| Step-rate amounts of principal | |
| |
| |
| Exercises | |
| |
| |
| |
| Bonds and other securities | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Types of securities | |
| |
| |
| |
| Price of a bond | |
| |
| |
| |
| Premium and discount | |
| |
| |
| |
| Valuation between coupon payment dates | |
| |
| |
| |
| Determination of yield rates | |
| |
| |
| |
| Callable and putable bonds | |
| |
| |
| |
| Serial bonds | |
| |
| |
| |
| Some generalizations | |
| |
| |
| |
| Other securities | |
| |
| |
| |
| Valuation of securities | |
| |
| |
| Appendix 6 | |
| |
| |
| Derivation of the bond salesman's formula | |
| |
| |
| Exercises | |
| |
| |
| |
| Yield rates | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Discounted cash flow analysis | |
| |
| |
| |
| Uniqueness of the yield rate | |
| |
| |
| |
| Reinvestment rates | |
| |
| |
| |
| Interest measurement of a fund | |
| |
| |
| |
| Time-weighted rates of interest | |
| |
| |
| |
| Portfolio methods and investment year methods | |
| |
| |
| |
| Short sales | |
| |
| |
| |
| Capital budgeting - basic techniques | |
| |
| |
| |
| Capital budgeting - other techniques | |
| |
| |
| Appendix 7 | |
| |
| |
| Uniqueness of the yield rate | |
| |
| |
| Further analysis of the simple interest assumption in Section 7.5 | |
| |
| |
| Interest measurement using continuous functions | |
| |
| |
| Exercises | |
| |
| |
| |
| Practical applications | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Truth in lending | |
| |
| |
| |
| Automobile financing | |
| |
| |
| |
| Real estate mortgages | |
| |
| |
| |
| Approximate methods | |
| |
| |
| |
| Depreciation methods | |
| |
| |
| |
| Capitalized cost | |
| |
| |
| |
| Modern financial instruments | |
| |
| |
| Exercises | |
| |
| |
| |
| More advanced financial analysis | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| An economic rationale for interest | |
| |
| |
| |
| Determinants of the level of interest rates | |
| |
| |
| |
| Recognition of inflation | |
| |
| |
| |
| Consideration of expenses | |
| |
| |
| |
| Effect of taxes | |
| |
| |
| |
| Currency exchange rates | |
| |
| |
| |
| Reflecting risk and uncertainty | |
| |
| |
| |
| Interest rate assumptions | |
| |
| |
| Exercises | |
| |
| |
| |
| The term structure of interest rates | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Yield curves | |
| |
| |
| |
| Spot rates | |
| |
| |
| |
| Relationship with bond yields | |
| |
| |
| |
| Forward rates | |
| |
| |
| |
| Arbitrage | |
| |
| |
| |
| A continuous model | |
| |
| |
| Exercises | |
| |
| |
| |
| Duration, convexity and immunization | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Duration | |
| |
| |
| |
| Convexity | |
| |
| |
| |
| Interest sensitive cash flows | |
| |
| |
| |
| Analysis of portfolios | |
| |
| |
| |
| Matching assets and liabilities | |
| |
| |
| |
| Immunization | |
| |
| |
| |
| Full immunization | |
| |
| |
| |
| A more general model | |
| |
| |
| Appendix 11 | |
| |
| |
| Further analysis of varying annuities | |
| |
| |
| Exercises | |
| |
| |
| |
| Stochastic approaches to interest | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Independent rates of interest | |
| |
| |
| |
| The lognormal model | |
| |
| |
| |
| Time series models | |
| |
| |
| |
| Binomial lattices | |
| |
| |
| |
| Continuous stochastic models | |
| |
| |
| |
| Scenario testing | |
| |
| |
| |
| More advanced models | |
| |
| |
| Appendix 12 | |
| |
| |
| Derivation of the variance of annuity | |
| |
| |
| Exercises | |
| |
| |
| |
| Options and other derivatives | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Definitions and concepts | |
| |
| |
| |
| Position and profit diagrams | |
| |
| |
| |
| Determinants of option value | |
| |
| |
| |
| Combination positions | |
| |
| |
| |
| Binomial lattices | |
| |
| |
| |
| Black-Scholes formula | |
| |
| |
| |
| Some extensions | |
| |
| |
| Appendix 13 | |
| |
| |
| Derivation of the Black-Scholes formula | |
| |
| |
| Exercises | |
| |
| |
| |
| Table numbering the days of the year | |
| |
| |
| |
| Illustrative mortgage loan amortization schedule | |
| |
| |
| |
| Basic mathematical review | |
| |
| |
| |
| Statistical background | |
| |
| |
| |
| Iteration methods | |
| |
| |
| Answers to the exercises | |
| |
| |
| Glossary of notation | |
| |
| |
| Index | |