Front Cover -- Fixed Income Mathematics -- Copyright Page -- Contents -- Chapter 1. Introduction-Who this Book is for and What it Hopes to Accomplish -- Historical Background-The Big Change in Investment, Loan, and Money Management -- What this Book Hopes to Accomplish -- What Sort of Problems Might this Book Help You to Solve? -- Who this Book is Meant to Address -- The Mathematical Knowledge Required for this Book -- The Role of Examples and Problems in this Book -- Chapter 2. Interest, Its Calculation, and Return on Investment -- A General Introduction to Interest -- How to Compute Interest -- Notation -- Percentage Rate and Time Period -- Return on Investment -- Analysis of Investments or Returns without Explicit Money Values, and Intangible Investments and Returns -- Chapter Summary -- Chapter 3. Compound Interest -- What is Compound Interest? -- Using Compound Interest Tables -- Looking at the Compound Interest Tables -- Compounding within a Period -- The Equations for Compound Interest-Compounding within a Period -- Continuous Compounding: How it Works and When it Applies -- The Derivation of the Equations for Continuous Compounding -- What is a Mathematical Model? -- Some Famous Mathematical Models -- Reasons for Using Continuous Functions in Financial Models -- A Business Example of Use of Continuous Functions -- Further Reflections on Approach 3 -- Computing i, Given S, Snt, T, and N -- Accuracy Requirements -- Legal Requirements for Accuracy -- An Example from Compound Interest -- Using Tables and Interpolating between Values -- The Rule of 72 -- A Zero Interest Rate? -- Negative Interest Rates? -- Real and Nominal Rates -- Chapter Summary -- Suggestions for Further Study -- Chapter 4. Present Values -- What is Present Value? -- The Equation for Present Value -- The General Equation for Present Value -- The Present Value Tables.

Using Present Values to Make Project Decisions -- Example of Project Analysis -- Using Different Interest Rates in the Analysis -- The Equations for Flow of Funds Analysis -- The Various Number Systems and What They Mean -- Solving Polynomial Equations -- Practical Considerations in Using Calculators and Computers to Solve Polynomial Equations -- Using the Bisection Method to Find Real Solutions -- What if the Exponents are not Integers? -- Chapter Summary -- Suggestions for Further Study -- Chapter 5. Annuities Certain -- What is an Annuity Certain? -- Examples of Annuities Certain -- Why Annuities Certain are Important -- The Equation for the Present Value of an Annuity Certain -- A Look at the Tables for an Annuity Certain -- Solving for the Interest Rate, Given the Annuity Certain and Its Cost -- The Perpetuity -- The Annuity Due -- Further Comments -- Analysis and Calculation of Some Combination Annuities Certain -- Chapter Summary -- Chapter 6. Bond Price Calculation -- What is a Bond? -- How Bonds are Described -- How to Read a Bond Market Report -- What is a Call Feature? -- What is a Put Option? -- Discount Securities -- The General Equation for Computing a Bond Price, Given the Yield -- A Note on Yield -- A Note on Accrued Days in the Settlement Period (A in Equation 6.1) and Dated Date -- Analysis of the Equation -- Standards of Accuracy -- Pricing Zero Coupon Bonds -- Pricing to a Call Feature -- Examples of Bond Price Calculations -- Amortization of Premium and Accrual of Discount -- Accrual of Discount -- Amortization of Premium -- A Portfolio Management Interlude -- Pricing a Bond to a Call -- A Look at a Basis Book -- Basic Rules for Prices and Yields -- The Shape of the Price-Yield Curve -- Dirty Price and Clean Price -- Chapter Summary -- Suggestion for Further Study -- Chapter 7. The Future Value (or Amount) of an Annuity.

Uses of the Future Value of an Annuity -- The Equation for the Future Value of an Annuity -- The Tables for Amount of Annuity -- Some Investment Policy Implications -- Chapter Summary -- Chapter 8. Accrued Interest -- What is Accrued Interest? -- Bonds that Accrue Interest -- The Equation for Accrued Interest -- Chapter Summary -- Chapter 9. Discount Yield -- Discount Yield -- Calculation of the Discount and Price for Discount Securities -- What is a Treasury Bill? -- The Day-Count Conventions for T-Bills -- Price Calculations for Discount Municipal Securities -- Bond Equivalent Yield (BEY) What It Means and How to Compute It -- Derivation of the Bond Equivalent Yield Equations -- Why We Care about Bond Equivalent Yield (BEY) -- A Historical Note -- Taxation of Income from Treasury Bills -- Chapter Summary -- Chapter 10. Calculations for Other Securities -- Certificates of Deposit -- Repurchase Agreements -- Uses of Repos and Reverse Repos -- Pricing Repos -- Chapter Summary -- Class Project -- Chapter 11. Quotations and Bond Market Reports -- Long-Term Instruments -- Discount Instruments -- Chapter Summary -- Chapter 12. Types of Yields -- Nominal (or Coupon) Yield -- Discount Yield -- Current Yield -- True (or Bond) Yield -- A Method to Compute Approximate Bond Yield, Given Price -- Chapter Summary -- Chapter 13. Sources of Return, Total Return, and Interest on Interest -- Examples -- Sources of Return -- How to Analyze this Problem -- Some Observations on These Examples -- Problems -- Chapter 14. Volatility and Its Measures -- What is Volatility? -- Why do We Care about Volatility? -- What Volatility Measures Can do for You -- Measures of Volatility -- Properties of Volatility -- Bond Investment Management Interlude -- Measuring Volatility by Measuring Price Change per Unit Change in Yield -- Chapter Summary -- Chapter 15. Duration.

Historical Background -- How Long will a Flow of Funds be Outstanding? -- Modified Duration -- Payback Interlude -- A Plea for Payback -- Calculation of Macaulay Duration and Modified Duration -- Using Modified Duration to Predict Price Change -- Dollar Duration -- A Pictorial View of Duration -- A Misconception about Duration -- Portfolio Duration -- Computing Portfolio Duration -- Using Duration as a Portfolio Management Tool -- Duration for Bonds with Embedded Options -- Negative Duration -- Problems with Duration as a Measure -- Chapter Summary -- Chapter 16. Convexity -- Convexity -- Convexity Calculation -- Addition for Convexity -- Modified Prices for Convexity -- Dollar Convexity -- Meaning of Convexity -- A Misconception about Convexity -- Portfolio Convexity -- Chapter Summary -- Chapter 17. The Mathematical Development of Duration, Convexity, and the Equation to Predict New Bond Prices, Given Yield Changes -- Derivation of Duration -- Negative Duration -- Derivation of Convexity -- Negative Convexity -- Taylor's Series Expansion -- Reasons for the Equations and Additional Factors Introduced in the Previous Two Chapters -- Chapter 18. Probability and Some Applications to Finance -- Elementary Concepts in Probability: A Review -- Examples of Probabilities -- Independent Events -- The Gambler's Fallacy -- Probability as a Mathematical Model -- Use of the Word "Population" -- Sources of Probabilities -- Probability Distribution Functions -- The Binomial Distribution -- Continuous Probability Distributions -- The Normal Distribution -- Statistics and Statistical Analysis -- Measures of Central Tendency -- Measure of Dispersions -- Applications to Insurance -- Chapter Summary -- Suggestions for Further Reading and Study -- Chapter 19. The Term Structure of Interest Rates, the Expectations Hypothesis, and Implied Forward Rates.

The Term Structure of Interest Rates -- Shapes of Yield Curves -- The Expectations Hypothesis -- Implied Spot Rates and Bootstrapping a Spot Yield Curve -- Computing the Spot Rates -- Calculation of Spot Rates -- Using the Treasury Spot Rate in the Treasury Market -- Using Spot Rates with Other Bonds -- Implied Future Forward Rates -- Other Term Structure Hypotheses -- Risk Premium Hypothesis -- Liquidity Preference Hypothesis -- Market Segmentation Hypothesis -- Discussion of the Various Hypotheses -- Chapter Summary -- Suggestions for Further Study -- Chapter 20. Variable and Uncertain Cash Flows -- Valuing a Varying Series of Cash Flows Using the Same Interest Rate, Varying Interest Rates, and Probabilities -- Sources of the Probabilities You Use -- Sources of the Interest Rates You Use -- Applying Probability Concepts to Value a Variable or Uncertain Flow of Funds -- Different Size Payments with Different Probabilities of Being Paid at the Same Time -- Applying These Concepts to Life Insurance -- Discussion of the Life Insurance Application -- Using Different Interest Rates -- How to Compute an Annual Premium for the Insurance -- Calculating Life Insurance Company Reserves -- Explanation of Year 2 Income and Expenses -- Applying These Totals to Actual Insurance Company Operations -- Reserves for Other Insurance Companies -- Computing the Value of a Pension -- Applications to Project Analysis -- Applications to Bonds: Weighted Average Duration and Effective Duration -- The Advantages and Disadvantages of Effective Duration -- Chapter Summary -- Suggestions for Further Study -- Chapter 21. Mortgage-Backed Securities -- What is a Mortgage? -- How a Level-Payment Self-Amortizing Mortgage Works -- The Equation for Level-Payment, Self-Amortizing Mortgages -- Variable Rate Mortgages -- Points -- Mortgage Pools -- Pass-Through Securities.

Pay-Through Securities (Collateralized Mortgage Obligations (CMOS)).