Fixed Income Mathematics

Fixed Income Mathematics

by Robert Zipf
Released June 2003
Publisher(s): Academic Press
ISBN: 9780080506555

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Book description

An introduction to common fixed income instruments and mathematics, this book offers explanations, exercises, and examples without demanding sophisticated mathematics. Not only does the author use his business and teaching experience to highlight the fundamentals of investment and management decision-making, but he also offers questions and exercises that suggest the applicability of fixed income mathematics. Written for the reader with a general mathematics background, this self-teaching book is suffused with examples that also make it a handy reference guide. It should serve as a gateway to financial mathematics and to increased competence in business analysis.

* An easy-to-understand introduction to the mathematics of common fixed income instruments
* Offers students explanations, exercises, and examples without demanding sophisticated mathematics
* Uses international comparisons to illustrate how interest is compounded

Table of contents

  1. Front Cover
  2. Fixed Income Mathematics
  3. Copyright Page
  4. Contents (1/2)
  5. Contents (2/2)
  6. Chapter 1. Introduction—Who this Book is for and What it Hopes to Accomplish
    1. Historical Background—The Big Change in Investment, Loan, and Money Management
    2. What this Book Hopes to Accomplish
    3. What Sort of Problems Might this Book Help You to Solve?
    4. Who this Book is Meant to Address
    5. The Mathematical Knowledge Required for this Book
    6. The Role of Examples and Problems in this Book
  7. Chapter 2. Interest, Its Calculation, and Return on Investment
    1. A General Introduction to Interest
    2. How to Compute Interest
    3. Notation
    4. Percentage Rate and Time Period
    5. Return on Investment
    6. Analysis of Investments or Returns without Explicit Money Values, and Intangible Investments and Returns
    7. Chapter Summary
  8. Chapter 3. Compound Interest
    1. What is Compound Interest?
    2. Using Compound Interest Tables
    3. Looking at the Compound Interest Tables
    4. Compounding within a Period
    5. The Equations for Compound Interest–Compounding within a Period
    6. Continuous Compounding: How it Works and When it Applies
    7. The Derivation of the Equations for Continuous Compounding
    8. What is a Mathematical Model?
    9. Some Famous Mathematical Models
    10. Reasons for Using Continuous Functions in Financial Models
    11. A Business Example of Use of Continuous Functions
    12. Further Reflections on Approach 3
    13. Computing i, Given S, Snt, T, and N
    14. Accuracy Requirements
    15. Legal Requirements for Accuracy
    16. An Example from Compound Interest
    17. Using Tables and Interpolating between Values
    18. The Rule of 72
    19. A Zero Interest Rate?
    20. Negative Interest Rates?
    21. Real and Nominal Rates
    22. Chapter Summary
    23. Suggestions for Further Study (1/2)
    24. Suggestions for Further Study (2/2)
  9. Chapter 4. Present Values
    1. What is Present Value?
    2. The Equation for Present Value
    3. The General Equation for Present Value
    4. The Present Value Tables
    5. Using Present Values to Make Project Decisions
    6. Example of Project Analysis
    7. Using Different Interest Rates in the Analysis
    8. The Equations for Flow of Funds Analysis
    9. The Various Number Systems and What They Mean
    10. Solving Polynomial Equations
    11. Practical Considerations in Using Calculators and Computers to Solve Polynomial Equations
    12. Using the Bisection Method to Find Real Solutions
    13. What if the Exponents are not Integers?
    14. Chapter Summary
    15. Suggestions for Further Study (1/2)
    16. Suggestions for Further Study (2/2)
  10. Chapter 5. Annuities Certain
    1. What is an Annuity Certain?
    2. Examples of Annuities Certain
    3. Why Annuities Certain are Important
    4. The Equation for the Present Value of an Annuity Certain
    5. A Look at the Tables for an Annuity Certain
    6. Solving for the Interest Rate, Given the Annuity Certain and Its Cost
    7. The Perpetuity
    8. The Annuity Due
    9. Further Comments
    10. Analysis and Calculation of Some Combination Annuities Certain
    11. Chapter Summary
  11. Chapter 6. Bond Price Calculation
    1. What is a Bond?
    2. How Bonds are Described
    3. How to Read a Bond Market Report
    4. What is a Call Feature?
    5. What is a Put Option?
    6. Discount Securities
    7. The General Equation for Computing a Bond Price, Given the Yield
    8. A Note on Yield
    9. A Note on Accrued Days in the Settlement Period (A in Equation 6.1) and Dated Date
    10. Analysis of the Equation
    11. Standards of Accuracy
    12. Pricing Zero Coupon Bonds
    13. Pricing to a Call Feature
    14. Examples of Bond Price Calculations
    15. Amortization of Premium and Accrual of Discount
    16. Accrual of Discount
    17. Amortization of Premium
    18. A Portfolio Management Interlude
    19. Pricing a Bond to a Call
    20. A Look at a Basis Book
    21. Basic Rules for Prices and Yields
    22. The Shape of the Price-Yield Curve
    23. Dirty Price and Clean Price
    24. Chapter Summary
    25. Suggestion for Further Study
  12. Chapter 7. The Future Value (or Amount) of an Annuity
    1. Uses of the Future Value of an Annuity
    2. The Equation for the Future Value of an Annuity
    3. The Tables for Amount of Annuity
    4. Some Investment Policy Implications
    5. Chapter Summary
  13. Chapter 8. Accrued Interest
    1. What is Accrued Interest?
    2. Bonds that Accrue Interest
    3. The Equation for Accrued Interest
    4. Chapter Summary
  14. Chapter 9. Discount Yield
    1. Discount Yield
    2. Calculation of the Discount and Price for Discount Securities
    3. What is a Treasury Bill?
    4. The Day-Count Conventions for T-Bills
    5. Price Calculations for Discount Municipal Securities
    6. Bond Equivalent Yield (BEY) What It Means and How to Compute It
    7. Derivation of the Bond Equivalent Yield Equations
    8. Why We Care about Bond Equivalent Yield (BEY)
    9. A Historical Note
    10. Taxation of Income from Treasury Bills
    11. Chapter Summary
  15. Chapter 10. Calculations for Other Securities
    1. Certificates of Deposit
    2. Repurchase Agreements
    3. Uses of Repos and Reverse Repos
    4. Pricing Repos
    5. Chapter Summary
    6. Class Project
  16. Chapter 11. Quotations and Bond Market Reports
    1. Long-Term Instruments
    2. Discount Instruments
    3. Chapter Summary
  17. Chapter 12. Types of Yields
    1. Nominal (or Coupon) Yield
    2. Discount Yield
    3. Current Yield
    4. True (or Bond) Yield
    5. A Method to Compute Approximate Bond Yield, Given Price
    6. Chapter Summary
  18. Chapter 13. Sources of Return, Total Return, and Interest on Interest
    1. Examples
    2. Sources of Return
    3. How to Analyze this Problem
    4. Some Observations on These Examples
    5. Problems
  19. Chapter 14. Volatility and Its Measures
    1. What is Volatility?
    2. Why do We Care about Volatility?
    3. What Volatility Measures Can do for You
    4. Measures of Volatility
    5. Properties of Volatility
    6. Bond Investment Management Interlude
    7. Measuring Volatility by Measuring Price Change per Unit Change in Yield
    8. Chapter Summary
  20. Chapter 15. Duration
    1. Historical Background
    2. How Long will a Flow of Funds be Outstanding?
    3. Modified Duration
    4. Payback Interlude
    5. A Plea for Payback
    6. Calculation of Macaulay Duration and Modified Duration
    7. Using Modified Duration to Predict Price Change
    8. Dollar Duration
    9. A Pictorial View of Duration
    10. A Misconception about Duration
    11. Portfolio Duration
    12. Computing Portfolio Duration
    13. Using Duration as a Portfolio Management Tool
    14. Duration for Bonds with Embedded Options
    15. Negative Duration
    16. Problems with Duration as a Measure
    17. Chapter Summary
  21. Chapter 16. Convexity
    1. Convexity
    2. Convexity Calculation
    3. Addition for Convexity
    4. Modified Prices for Convexity
    5. Dollar Convexity
    6. Meaning of Convexity
    7. A Misconception about Convexity
    8. Portfolio Convexity
    9. Chapter Summary
  22. Chapter 17. The Mathematical Development of Duration, Convexity, and the Equation to Predict New Bond Prices, Given Yield Changes
    1. Derivation of Duration
    2. Negative Duration
    3. Derivation of Convexity
    4. Negative Convexity
    5. Taylor’s Series Expansion
    6. Reasons for the Equations and Additional Factors Introduced in the Previous Two Chapters
  23. Chapter 18. Probability and Some Applications to Finance
    1. Elementary Concepts in Probability: A Review
    2. Examples of Probabilities
    3. Independent Events
    4. The Gambler’s Fallacy
    5. Probability as a Mathematical Model
    6. Use of the Word “Population”
    7. Sources of Probabilities
    8. Probability Distribution Functions
    9. The Binomial Distribution
    10. Continuous Probability Distributions
    11. The Normal Distribution
    12. Statistics and Statistical Analysis
    13. Measures of Central Tendency
    14. Measure of Dispersions
    15. Applications to Insurance
    16. Chapter Summary
    17. Suggestions for Further Reading and Study
  24. Chapter 19. The Term Structure of Interest Rates, the Expectations Hypothesis, and Implied Forward Rates
    1. The Term Structure of Interest Rates
    2. Shapes of Yield Curves
    3. The Expectations Hypothesis
    4. Implied Spot Rates and Bootstrapping a Spot Yield Curve
    5. Computing the Spot Rates
    6. Calculation of Spot Rates
    7. Using the Treasury Spot Rate in the Treasury Market
    8. Using Spot Rates with Other Bonds
    9. Implied Future Forward Rates
    10. Other Term Structure Hypotheses
    11. Risk Premium Hypothesis
    12. Liquidity Preference Hypothesis
    13. Market Segmentation Hypothesis
    14. Discussion of the Various Hypotheses
    15. Chapter Summary
    16. Suggestions for Further Study
  25. Chapter 20. Variable and Uncertain Cash Flows
    1. Valuing a Varying Series of Cash Flows Using the Same Interest Rate, Varying Interest Rates, and Probabilities
    2. Sources of the Probabilities You Use
    3. Sources of the Interest Rates You Use
    4. Applying Probability Concepts to Value a Variable or Uncertain Flow of Funds
    5. Different Size Payments with Different Probabilities of Being Paid at the Same Time
    6. Applying These Concepts to Life Insurance
    7. Discussion of the Life Insurance Application
    8. Using Different Interest Rates
    9. How to Compute an Annual Premium for the Insurance
    10. Calculating Life Insurance Company Reserves
    11. Explanation of Year 2 Income and Expenses
    12. Applying These Totals to Actual Insurance Company Operations
    13. Reserves for Other Insurance Companies
    14. Computing the Value of a Pension
    15. Applications to Project Analysis
    16. Applications to Bonds: Weighted Average Duration and Effective Duration
    17. The Advantages and Disadvantages of Effective Duration
    18. Chapter Summary
    19. Suggestions for Further Study
  26. Chapter 21. Mortgage-Backed Securities
    1. What is a Mortgage?
    2. How a Level-Payment Self-Amortizing Mortgage Works
    3. The Equation for Level-Payment, Self-Amortizing Mortgages
    4. Variable Rate Mortgages
    5. Points
    6. Mortgage Pools
    7. Pass-Through Securities
    8. Pay-Through Securities (Collateralized Mortgage Obligations (CMOS))
    9. Cash Flows for Mortgages
    10. Prepayment Models
    11. Mortgage-Backed Investment Management: Application of Duration and Probability Concepts
  27. Chapter 22. Futures Contracts
    1. Cash, Forward, and Futures Trades
    2. The Cross Hedge
    3. The Need for Hedging Management
    4. The Futures Contract
    5. Settlement of a Futures Contract
    6. Financial Futures
    7. Hedging with Financial Futures
    8. Cost of Carry
    9. Conversion Factors
    10. Conversion Factor Equation CBOT U.S. 2-Year Treasury Note
    11. Conversion Factor Equation CBOT U.S. 5-Year Treasury Note
    12. Conversion Factor Equation CBOT U.S. 10-Year Treasury Note
    13. Conversion Factor Equation CBOT U.S. 30-Year Treasury Bond
    14. Understanding the Equations for Computing Conversion Factors
    15. Understanding Deliverable Grades of Treasury Securities
    16. Web Sites
    17. Chapter Summary
  28. Chapter 23. Options
    1. What is an Option?
    2. Purposes of Options
    3. Factors that Determine Option Prices
    4. Black-Scholes Options Pricing Model
    5. The Assumptions for Black-Scholes
    6. Understanding These Assumptions
    7. An Immediate Problem with Black-Scholes for Bonds
    8. Hedging and Hedging Ratios (The Greeks)
    9. The Put-Call Parity Relationship
    10. Hedging Ratios (The Greeks)
    11. Another Mathematical Approach to Continuous Functions, as Part of the Development of the Black-Scholes Model
    12. Other Approaches Fractal Analysis
    13. Chapter Summary
    14. Suggestions for Further Study
  29. Index (1/2)
  30. Index (2/2)

Product information

  • Title: Fixed Income Mathematics
  • Author(s): Robert Zipf
  • Release date: June 2003
  • Publisher(s): Academic Press
  • ISBN: 9780080506555