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• Copyright
• Contents
• Preface
• Acknowledgments
• Part I: Basics
• Chapter 1: An Introduction to Fixed Income Markets
• Introduction
• The Complexity of Fixed Income Markets
• No Arbitrage and the Law of One Price
• The Government Debt Markets
• Zero Coupon Bonds
• Floating Rate Coupon Bonds
• The Municipal Debt Market
• The Money Market
• Federal Funds Rate
• Eurodollar Rate
• LIBOR
• The Repo Market
• General Collateral Rate and Special Repos
• What if the T-bond Is Not Delivered?
• The Mortgage Backed Securities Market and Asset-Backed Securities Market
• The Derivatives Market
• Swaps
• Futures and Forwards
• Options
• Roadmap of Future Chapters
• Summary
• Chapter 2: Basics of fixed Income Securities
• Discount Factors
• Discount Factors across Maturities
• Discount Factors over Time
• Interest Rates
• Discount Factors, Interest Rates, and Compounding Frequencies
• The Relation between Discounts Factors and Interest Rates
• The Term Structure of Interest Rates
• The Term Structure of Interest Rates over Time
• Coupon Bonds
• From Zero Coupon Bonds to Coupon Bonds
• From Coupon Bonds to Zero Coupon Bonds
• Expected Return and the Yield to Maturity
• Quoting Conventions
• Floating Rate Bonds
• The Pricing of Floating Rate Bonds
• Complications
• Summary
• Exercises
• Case Study: Orange County Inverse Floaters
• Decomposing Inverse Floaters into a Portfolio of Basic Securities
• Calculating the Term Structure of Interest Rates from Coupon Bonds
• Calculating the Price of the Inverse Floater
• Leveraged Inverse Floaters
• Appendix: Extracting the Discount Factors Z(0, T) from Coupon Bonds
• Bootstrap Again
• Regressions
• Curve Fitting
• Curve Fitting with Splines
• Chapter 3: Basics of interest Rate Risk Management
• The Variation in Interest Rates
• The Savings and Loan Debacle
• The Bankruptcy of Orange County
• Duration
• Duration of a Zero Coupon Bond
• Duration of a Portfolio
• Duration of a Coupon Bond
• Duration and Average Time of Cash Flow Payments
• Properties of Duration
• Traditional Definitions of Duration
• The Duration of Zero Investment Portfolios: Dollar Duration
• Duration and Value-at-Risk
• Duration and Expected Shortfall
• Interest Rate Risk Management
• Cash Flow Matching and Immunization
• Immunization versus Simpler Investment Strategies
• Why Does the Immunization Strategy Work?
• Asset-Liability Management
• Summary
• Exercises
• Case Study: The 1994 Bankruptcy of Orange County
• Benchmark: What if Orange County was Invested in Zero Coupon Bonds Only?
• The Risk in Leverage
• The Risk in Inverse Floaters
• The Risk in Leveraged Inverse Floaters
• What Can We Infer about the Orange County Portfolio?
• Conclusion
• Case Analysis: The Ex-Ante Risk in Orange County’s Portfolio
• The Importance of the Sampling Period
• Conclusion
• Appendix: Expected Shortfall under the Normal Distribution
• Chapter 4: Basic Refinements in Interest Rate Risk Management
• Convexity
• The Convexity of Zero Coupon Bonds
• The Convexity of a Portfolio of Securities
• The Convexity of a Coupon Bond
• Positive Convexity: Good News for Average Returns
• A Common Pitfall
• Convexity and Risk Management
• Convexity Trading and the Passage of Time
• Slope and Curvature
• Implications for Risk Management
• Factor Models and Factor Neutrality
• Factor Duration
• Factor Neutrality
• Estimation of the Factor Model
• Summary
• Exercises
• Case Study: Factor Structure in Orange County’s Portfolio
• Factor Estimation
• Factor Duration of the Orange County Portfolio
• The Value-at-Risk of the Orange County Portfolio with Multiple Factors
• Appendix: Principal Component Analysis
• Benefits from PCA
• The Implementation of PCA
• Chapter 5: Interest Rate Derivatives: Forwards and Swaps
• Forward Rates and Forward Discount Factors
• Forward Rates by No Arbitrage
• The Forward Curve
• Extracting the Spot Rate Curve from Forward Rates
• Forward Rate Agreements
• The Value of a Forward Rate Agreement
• Forward Contracts
• A No Arbitrage Argument
• Forward Contracts on Treasury Bonds
• The Value of a Forward Contract
• Interest Rate Swaps
• The Value of a Swap
• The Swap Rate
• The Swap Curve
• The LIBOR Yield Curve and the Swap Spread
• The Forward Swap Contract and the Forward Swap Rate
• Payment Frequency and Day Count Conventions
• Interest Rate Risk Management using Derivative Securities
• Summary
• Exercises
• Case Study: PiVe Capital Swap Spread Trades
• Setting Up the Trade
• The Quarterly Cash Flow
• Unwinding the Position?
• Conclusion
• Chapter 6: Interest Rate Derivatives: Futures and Options
• Interest Rate Futures
• Standardization
• Margins and Mark-to-Market
• The Convergence Property of Futures Prices
• Futures versus Forwards
• Hedging with Futures or Forwards?
• Options
• Options as Insurance Contracts
• Option Strategies
• Put-Call Parity
• Hedging with Futures or with Options?
• Summary
• Exercises
• Appendix: Liquidity and the LIBOR Curve
• Chapter 7: Inflation, Monetary Policy, and The Federal Funds Rate
• The Federal Reserve
• Monetary Policy, Economic Growth, and Inflation
• The Tools of Monetary Policy
• The Federal Funds Rate
• Predicting the Future Fed Funds Rate
• Fed Funds Rate, Inflation and Employment Growth
• Long-Term Fed Funds Rate Forecasts
• Fed Funds Rate Predictions Using Fed Funds Futures
• Understanding the Term Structure of Interest Rates
• Why Does the Term Structure Slope up in Average?
• The Expectation Hypothesis
• Predicting Excess Returns
• Conclusion
• Coping with Inflation Risk: Treasury Inflation-Protected Securities
• TIPS Mechanics
• Real Bonds and the Real Term Structure of Interest Rates
• Real Bonds and TIPS
• Fitting the Real Yield Curve
• The Relation between Nominal and Real Rates
• Summary
• Exercises
• Case Study: Monetary Policy during the Subprime Crisis of 2007 – 2008
• Problems on the Horizon
• August 17, 2007: Fed Lowers the Discount Rate
• September – December 2007: The Fed Decreases Rates and Starts TAF
• January 2008: The Fed Cuts the Fed Funds Target and Discount Rates
• March 2008: Bearn Stearns Collapses and the Fed Bolsters Liquidity Support to Primary Dealers
• September – October 2008: Fannie Mae, Freddie Mac, Lehman Brothers, and AIG Collapse
• Appendix: Derivation of Expected Return Relation
• Chapter 8: Basics of Residential Mortgage Backed Securities
• Securitization
• The Main Players in the RMBS Market
• Private Labels and the 2007 – 2009 Credit Crisis
• Default Risk and Prepayment in Agency RMBSs
• Mortgages and the Prepayment Option
• The Risk in the Prepayment Option
• Mortgage Prepayment
• Mortgage Backed Securities
• Measures of Prepayment Speed
• Pass-Through Securities
• The Effective Duration of Pass-Through Securities
• The Negative Effective Convexity of Pass-Through Securities
• The TBA Market
• Collateralized Mortgage Obligations
• CMO Sequential Structure
• CMO Planned Amortization Class (PAC)
• Interest Only and Principal Only Strips.
• Summary
• Exercises
• Case Study: PiVe Investment Group and the Hedging of Pass-Through Securities
• Three Measures of Duration and Convexity
• PSA-Adjusted Effective Duration and Convexity
• Empirical Estimate of Duration and Convexity
• The Hedge Ratio
• Appendix: Effective Convexity
• Part II: Term Structure Models: Trees
• Chapter 9: One Step Binomial Trees
• A one-step interest rate binomial tree
• Continuous Compounding
• The Binomial Tree for a Two-Period Zero Coupon Bond
• No Arbitrage on a Binomial Tree
• The Replicating Portfolio Via No Arbitrage
• Where Is the Probability p?
• Derivative Pricing as Present Discounted Values of Future Cash Flows
• Risk Premia in Interest Rate Securities
• The Market Price of Interest Rate Risk
• An Interest Rate Security Pricing Formula
• What If We Do Not Know p?
• Risk Neutral Pricing
• Risk Neutral Probability
• The Price of Interest Rate Securities
• Risk Neutral Pricing and Dynamic Replication
• Risk Neutral Expectation of Future Interest Rates
• Summary
• Exercises
• Chapter 10: Multi-Step Binomial Trees
• A Two-Step Binomial Tree
• Risk Neutral Pricing
• Risk Neutral Pricing by Backward Induction
• Dynamic Replication
• Matching the Term Structure
• Multi-step Trees
• Building a Binomial Tree from Expected Future Rates
• Risk Neutral Pricing
• Pricing and Risk Assessment: The Spot Rate Duration
• Summary
• Exercises
• Chapter 11: Risk Neutral Trees and Derivative Pricing
• Risk Neutral Trees
• The Ho-Lee Model
• The Simple Black, Derman, and Toy (BDT) Model
• Comparison of the Two Models
• Risk Neutral Trees and Future Interest Rates
• Using Risk Neutral Trees
• Intermediate Cash Flows
• Caps and Floors
• Swaps
• Swaptions
• Implied Volatilities and the Black, Derman, and Toy Model
• Flat and Forward Implied Volatility
• Forward Volatility and the Black, Derman, and Toy Model
• Risk Neutral Trees for Futures Prices
• Eurodollar Futures
• T-Note and T-Bond Futures
• Implied Trees: Final Remarks
• Summary
• Exercises
• Chapter 12: American Options
• Callable Bonds
• An Application to U.S. Treasury Bonds
• The Negative Convexity in Callable Bonds
• The Option Adjusted Spread
• Dynamic Replication of Callable Bonds
• American Swaptions
• Mortgages and Residential Mortgage Backed Securities
• Mortgages and the Prepayment Option
• The Pricing of Residential Mortgage Backed Securities
• The Spot Rate Duration of MBS
• Summary
• Exercises
• Chapter 13: Monte Carlo Simulations on trees
• Monte Carlo Simulations on a One-step Binomial Tree
• Monte Carlo Simulations on a Two-step Binomial Tree
• Example: Non-Recombining Trees in Asian Interest Rate Options
• Monte Carlo Simulations for Asian Interest Rate Options
• Monte Carlo Simulations on Multi-step Binomial Trees
• Does This Procedure Work?
• Illustrative Example: Long-Term Interest Rate Options
• How Many Simulations are Enough?
• Pricing Path Dependent Options
• Illustrative Example: Long-Term Asian Options
• Illustrative Example: Index Amortizing Swaps
• Spot Rate Duration by Monte Carlo Simulations
• Pricing Residential Mortgage Backed Securities
• Simulating the Prepayment Decision
• Additional Factors Affecting the Prepayment Decision
• Residential Mortgage Backed Securities
• Prepayment Models
• Summary
• Exercises
• Part III: Term Structure Models: Trees
• Chapter 14: Interest Rate Models in continuous Time
• Brownian Motions
• Properties of the Brownian Motion
• Notation
• Differential Equations
• Continuous Time Stochastic Processes
• Ito’s Lemma
• Illustrative Examples
• Summary
• Exercises
• Appendix: Rules of Stochastic Calculus
• Chapter 15: No Arbitrage and The Pricing of Interest Rate Securities
• Bond Pricing with Deterministic Interest Rate
• Interest Rate Security Pricing in the Vasicek Model
• The Long/Short Portfolio
• The Fundamental Pricing Equation
• The Vasicek Bond Pricing Formula
• Parameter Estimation
• Derivative Security Pricing
• Zero Coupon Bond Options
• Options on Coupon Bonds
• The Three Steps to Derivative Pricing
• No Arbitrage Pricing in a General Interest Rate Model
• The Cox, Ingersoll, and Ross Model
• Bond Prices under the Cox, Ingersoll, and Ross Model
• Summary
• Exercises
• Appendix: Derivations
• Derivation of the Pricing Formula in Equation 15.4
• The Derivation of the Vasicek Pricing Formula
• The CIR Model
• Chapter 16: Dynamic Hedging and Relative Value Trades
• The Replicating Portfolio
• Rebalancing
• Application 1: Relative Value Trades on the Yield Curve
• Relative Pricing Errors Discovery
• Setting Up the Arbitrage Trade
• Application 2: Hedging Derivative Exposure
• Hedging and Dynamic Replication
• Trading on Mispricing and Relative Value Trades
• The Theta – Gamma Relation
• Summary
• Exercises
• Case Study: Relative Value Trades on the Yield Curve
• Finding the Relative Value Trade
• Setting Up the Trade
• Does It Work? Simulations
• Does It Work? Data
• Conclusion
• Appendix: Derivation of Delta for Call Options
• Chapter 17: Risk Neutral Pricing and Monte Carlo Simulations
• Risk Neutral Pricing
• Feynman-Kac Theorem
• Application of Risk Neutral Pricing: Monte Carlo Simulations
• Simulating a Diffusion Process
• Simulating the Payoff
• Standard Errors
• Example: Pricing a Range Floater
• Hedging with Monte Carlo Simulations
• Convexity by Monte Carlo Simulations
• Summary
• Exercises
• Case Study: Procter & Gamble / Bankers Trust Leveraged Swap
• Parameter Estimates
• Pricing by Monte Carlo Simulations
• Chapter 18: The Risk and Return of Interest Rate Securities
• Expected Return and the Market Price Risk
• The Market Price of Risk in a General Interest Rate Model
• Risk Analysis: Risk Natural Monte Carlo Simulations
• Delta Approximation Errors
• A Macroeconomic Model of the Term Structure
• Market Participants
• Equilibrium Nominal Bond Prices
• Conclusion
• Case Analysis: The Risk in the P&G Leveraged Swap
• Summary
• Exercises
• Appendix: Proof of Pricing Formula in Macroeconomic Model
• Chapter 19: No Arbitrage Models and Standard Derivatives
• No Arbitrage Models
• The Ho-Lee Model Revisited
• Consistent Derivative Pricing
• The Term Structure of Volatility in the Ho-Lee Model
• The Hull-White Model
• The Option Price
• Standard Derivatives under the “Normal” Model
• Options on Coupon Bonds
• Caps and Floors
• Caps and Floors Implied Volatility
• European Swaptions
• Swaptions’ Implied Volatility
• The “Lognormal” Model
• The Black, Derman, and Toy Model
• The Black and Karasinski Model
• Generalized Affine Term Structure Models
• Summary
• Exercises
• Appendix: Proofs
• Proof of the Ho-Lee Pricing Formula
• Proof of the Expression in Equation 19.13
• Proof of the Hull-White Pricing Formula
• Proof of the Expression in Equation 19.28
• Proof of the Expressions in Equations 19.41 and 19.42
• Chapter 20: The Market Model for Standard Derivatives
• The Black Formula for Caps and Floors Pricing
• Flat and Forward Volatilities
• Extracting Forward Volatilities from Flat Volatilities
• The Behavior of the Implied Forward Volatility
• Forward Volatilities and the Black, Derman, and Toy Model
• The Black Formula for Swaption Pricing
• Summary
• Exercises
• Chapter 21: Forward Risk Neutral Pricing and the LIBOR Market Model
• One Difficulty with Risk Neutral Pricing
• Change of Numeraire and the Forward Risk Neutral Dynamics
• Two Important Results
• Generalizations
• The Option Pricing Formula in “Normal” Models
• The LIBOR Market Model
• The Black Formula for Caps and Floors
• Valuing Fixed Income Securities that Depend on a Single LIBOR Rate
• The LIBOR Market Model for More Complex Securities
• Extracting the Volatility of Forward Rates from Caplets’ Forward Volatilities
• Pricing Fixed Income Securities by Monte Carlo Simulations
• Forward Risk Neutral Pricing and the Black Formula for Swaptions
• Remarks: Forward Risk Neutral Pricing and No Arbitrage
• The Heath, Jarrow, and Morton Framework
• Futures and Forwards
• Unnatural Lag and Convexity Adjustment
• Unnatural Lag and Convexity
• A Convexity Adjustment
• Summary
• Exercises
• Appendix: Derivations
• Derivation of the Partial Differential Equation in the Forward Risk Neutral Dynamics
• Derivation of the Call Option Pricing Formula (Equations 21.11)
• Derivation of the Formula in Equations 21.27 and 21.31
• Derivation of the Formula in Equation 21.21
• Derivation of the Formula in Equation 21.37
• Chapter 22: Multifactor Models
• Multifactor Ito’s Lemma with Independent Factors
• No Arbitrage with Independent Factors
• A Two-Factor Vasicek Model
• A Dynamic Model for the Short and Long Yield
• Long-Term Spot Rate Volatility
• Options on Zero Coupon Bonds
• Correlated Factors
• The Two-Factor Vasicek Model with Correlated Factors
• Zero Coupon Bond Options
• The Two-Factor Hull–White Model
• The Feynman-Kac Theorem
• Application: Yield Curve Steepener
• Simulating Correlated Brownian Motions
• Forward Risk Neutral Pricing
• Application: Options on Coupon Bonds
• The Multifactor LIBOR Market Model
• Level, Slope, and Curvature Factors for Forward Rates
• Affine and Quadratic Term Structure Models
• Affine Models
• Quadratic Models
• Summary
• Exercises
• Appendix
• The Coefficients of the Joint Process for Short- and Long-Term Rates
• The Two-Factor Hull-White Model
• References
• Index