Introduction
Acknowledgments
The Relative Pricing of Fixed Income Securities with Fixed Cash Flows
Bond Prices, Discount Factors, and Arbitrage
The Time Value of Money
Treasury Bond Quotations
Discount Factors The Law of One Price
Arbitrage and the Law of One Price.Treasury STRIPS
Deriving the Replicating Portfolio
Application: Treasury Triplets and High Coupon Bonds
Bond Prices, Spot Rates, and Forward Rates
Semiannual Compounding
Spot Rates
Forward Rates
Maturity and Bond Price Maturity and Bond return
Treasury STRIPS, Continued
The Relation between Spot and Forward Rates and the Slope of the Term Structure
Yield-to-Maturity
Definition and Interpretation
Yield-to-Maturity and Spot Rates
Yield-to-Maturity and Relative Value: The Coupon Effect
Yield-to-Maturity and Realized return
Generalizations and Curve Fitting
Accrued Interest
Compounding Conventions
Yield and Compounding Conventions
Bad Days
Introduction to Curve Fitting
Piecewise Cubics
Application: Fitting the Term Structure in the U.S. Treasury Market on February 15, 2001
Trading Case Study: A 7s-8s-9s Butterfly
Continuous Compounding
A Simple Cubic Spline
Measures of Price Sensitivity and Hedging
One-Factor Measures of Price Sensitivity DV01
A Hedging Example, Part I: Hedging a Call Option
Duration
Convexity
A Hedging Example, Part II: A Short Convexity Position
Estimating Price Changes and Returns with DV01, Duration, and Convexity
Convexity in the Investment and Asset-Liability Management Contexts
Measuring the Price Sensitivity of Portfolios
A Hedging Example, Part III: The Negative Convexity of Callable Bonds
Measures of Price Sensitivity Based on Parallel Yield Shifts
Yield-Based DV01
Modified and Macaulay Duration
Zero Coupon Bonds and a Reinterpretation of Duration
Par Bonds and Perpetuities
Duration, DV01, Maturity, and Coupon: A Graphical Analysis
Duration, DV01, and Yield
Yield-Based Convexity
Yield-Based Convexity of Zero Coupon Bonds
The Barbell versus the Bullet
Key Rate and Bucket Exposures
Key Rate Shifts
Key Rate 01s and Key Rate Durations
Hedging with Key Rate Exposures
Choosing Key Rates
Bucket Shifts and Exposures
Immunization
Multi-Factor Exposures and Risk Management
Regression-Based Hedging
Volatility-Weighted Hedging
One-Variable Regression-Based Hedging
Two-Variable Regression-Based Hedging
Trading Case Study: The Pricing of the 20-Year U.S. Treasury Sector
A Comment on Level Regressions
Term Structure Models
The Science of Term Structure Models
Rate and Price Trees
Arbitrage Pricing of Derivatives
Risk-Neutral Pricing
Arbitrage Pricing in a Multi-Period Setting
Example: Pricing a CMT Swap
Reducing the Time Step
Fixed Income versus Equity Derivatives
The Short-Rate Process and the Shape of the Term Structure
Expectations
Volatility and Convexity
Risk Premium
A Mathematical Description of Expectations, Convexity, and Risk Premium
Application: Expectations, Convexity, and Risk Premium in the U.S. Treasury Market on February 15, 2001
Proofs of Equations (10.19) and (10.25)
The Art of Term Structure Models: Drift
Normally Distributed Rates, Zero Drift: Model 1
Drift and Risk Premium: Model 2
Time-Dependent Drift: The Ho-Lee Model
Desirability of Fitting to the Term Structure
Mean Reversion: The Vasicek (1977) Model
The Art of Term Structure Models: Volatility and Distribution
Time-Dependent Volatility: Model 3
Volatility as a Function of the Short Rate: The Cox-Ingersoll-Ross and Lognormal Models
Tree for the Original Salomon Brothers Model
A Lognormal Model with Mean Reversion: The Black-Karasinski Model
Selected List of One-Factor Term Structure Models
Closed-Form Solutions for Spot Rates
Multi-Factor Term Structure Models
Motivation from Principal Components
A Two-Factor Model
Tree Implementation
Properties of the Two-Factor Model
Other Two-Factor and Multi-Factor Modeling Approaches
Closed-Form Solution for Spot Rates in the Two-Factor Model
Trading with Term Structure Models
Example Revisited: Pricing a CMT Swap
Option-Adjusted Spread
Profit and Loss (P&L) Attribution
P&L Attributions for a Position in the CMT Swap
Trading Case Study: Trading 2s-5s-10s in Swaps with a Two-Factor Model
Fitting Model Parameters
Hedging to the Model versus Hedging to the Market
Selected Securities
Repo
Repurchase Agreements and Cash Management
Repurchase Agreements and Financing Long Positions
Reverse Repurchase Agreements and Short Positions Carry
General Collateral and Specials
Special Repo Rates and the Auction Cycle
Liquidity Premiums of Recent Issues
Application: Valuing a Bond Trading Special in Repo
Application: Disruption in the Specials Market after September 11, 2001
Forward Contracts
Definitions
Forward Price of a Deposit or a Zero Coupon Bond
Using Forwards to Hedge Borrowing Costs or Loan Proceeds
Forward Price of a Coupon Bond
Forward Yield and Forward DV01
Forward Prices with Intermediate Coupon Payments
Value of a Forward Contract
Forward Prices in a Term Structure Model
Eurodollar and Fed Funds Futures
LIBOR and Eurodollar Futures
Hedging with Eurodollar Futures
Tails: A Closer Look at Hedging with Futures
Futures on Prices in a Term Structure Model
Futures on Rates in a Term Structure Model
The Futures-Forward Difference
TED Spreads
Application: Trading TED Spreads
Fed Funds
Fed Funds Futures
Application: Fed Funds Contracts and Predicted Fed Action
Hedging to Dates Not Matching Fed Funds and Eurodollar Futures Expirations
Interest Rate Swaps
Swap Cash Flows
Valuation of Swaps
Floating Rate Notes
Valuation of Swaps, Continued
Note on the Measurement of Fixed and Floating Interest Rate Risk
Swap Spreads
Major Uses of Interest Rate Swaps
Asset Swap Spreads and Asset Swaps
Trading Case Study: 30-Year FNMA Asset Swap Spreads
On the Credit Risk of Swap Agreements
Trading Case Study: Five-Year On-the-Run/Off-the-Run Spread of Spreads
Fixed Income Options
Definitions and Review
Pricing American and Bermudan Bond Options in a Term Structure Model
Application: FNMA 6.25s of July 19, 2011, and the Pricing of Callable Bonds
Graphical Analysis of Callable Bond Pricing
A Note on Yield-to-Call
Swaptions, Caps, and Floors
Quoting Prices with Volatility Measures in Fixed Income Options Markets
Smile and Skew
Note and Bond Futures
Mechanics
Cost of Delivery and the Determination of the Final Settlement Price
Motivations for a Delivery Basket and Conversion Factors
Imperfection of Conversion Factors and the Delivery Option at Expiration
Gross and Net Basis
Quality Option before Delivery
Some Notes on Pricing the Quality Option in Term Structure Models
Measures of Rate Sensitivity
Timing Option
End-of-Month Option
Trading Case Study: November '08 Basis into TYM0
Mortgage-Backed Securities
Basic Mortgage Mathematics
Prepayment Option
Overview of Mortgage Pricing Models
Implementing Prepayment Models
Price-Rate Curve of a Mortgage Pass-Through
Application: Mortgage Hedging and the Directionality of Swap Spreads
Mortgage Derivatives, IOs, and Pos
Exercises
References And Suggestions For Further Reading
Index