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 decisionmaking, 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 selfteaching 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 easytounderstand 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
 Front Cover
 Fixed Income Mathematics
 Copyright Page
 Contents (1/2)
 Contents (2/2)

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

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 (1/2)
 Suggestions for Further Study (2/2)

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 (1/2)
 Suggestions for Further Study (2/2)

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 PriceYield Curve
 Dirty Price and Clean Price
 Chapter Summary
 Suggestion for Further Study
 Chapter 7. The Future Value (or Amount) of an Annuity
 Chapter 8. Accrued Interest

Chapter 9. Discount Yield
 Discount Yield
 Calculation of the Discount and Price for Discount Securities
 What is a Treasury Bill?
 The DayCount Conventions for TBills
 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
 Chapter 11. Quotations and Bond Market Reports
 Chapter 12. Types of Yields
 Chapter 13. Sources of Return, Total Return, and Interest on Interest
 Chapter 14. Volatility and Its Measures

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
 Chapter 17. The Mathematical Development of Duration, Convexity, and the Equation to Predict New Bond Prices, Given Yield Changes

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. MortgageBacked Securities
 What is a Mortgage?
 How a LevelPayment SelfAmortizing Mortgage Works
 The Equation for LevelPayment, SelfAmortizing Mortgages
 Variable Rate Mortgages
 Points
 Mortgage Pools
 PassThrough Securities
 PayThrough Securities (Collateralized Mortgage Obligations (CMOS))
 Cash Flows for Mortgages
 Prepayment Models
 MortgageBacked Investment Management: Application of Duration and Probability Concepts

Chapter 22. Futures Contracts
 Cash, Forward, and Futures Trades
 The Cross Hedge
 The Need for Hedging Management
 The Futures Contract
 Settlement of a Futures Contract
 Financial Futures
 Hedging with Financial Futures
 Cost of Carry
 Conversion Factors
 Conversion Factor Equation CBOT U.S. 2Year Treasury Note
 Conversion Factor Equation CBOT U.S. 5Year Treasury Note
 Conversion Factor Equation CBOT U.S. 10Year Treasury Note
 Conversion Factor Equation CBOT U.S. 30Year Treasury Bond
 Understanding the Equations for Computing Conversion Factors
 Understanding Deliverable Grades of Treasury Securities
 Web Sites
 Chapter Summary

Chapter 23. Options
 What is an Option?
 Purposes of Options
 Factors that Determine Option Prices
 BlackScholes Options Pricing Model
 The Assumptions for BlackScholes
 Understanding These Assumptions
 An Immediate Problem with BlackScholes for Bonds
 Hedging and Hedging Ratios (The Greeks)
 The PutCall Parity Relationship
 Hedging Ratios (The Greeks)
 Another Mathematical Approach to Continuous Functions, as Part of the Development of the BlackScholes Model
 Other Approaches Fractal Analysis
 Chapter Summary
 Suggestions for Further Study
 Index (1/2)
 Index (2/2)
Product information
 Title: Fixed Income Mathematics
 Author(s):
 Release date: June 2003
 Publisher(s): Academic Press
 ISBN: 9780080506555
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