Derivatives : Principles and Practice

Tittle
Contents
1 Introduction
	1.1 Forward and Futures Contracts
	1.2 Options
	1.3 Swaps
	1.4 Using Derivatives: Some Comments
	1.5 The Structure of this Book
	1.6 Exercises
PART ONE Futures and Forwards
	2 Futures Markets
		2.1 Introduction
		2.2 The Changing Face of Futures Markets
		2.3 The Functioning of Futures Exchanges
		2.4 The Standardization of Futures Contracts
		2.5 Closing Out Positions
		2.6 Margin Requirements and Default Risk
		2.7 Case Studies in Futures Markets
		2.8 Exercises
		Appendix 2A Futures Trading and US Regulation: A Brief History
	Chapter
	3 Pricing Forwards and Futures I: The Basic Theory
		3.1 Introduction
		3.2 Pricing Forwards by Replication
		3.3 Examples
		3.4 Forward Pricing on Currencies and Related Assets
		3.5 Forward-Rate Agreements
		3.6 Concept Check
		3.7 The Marked-to-Market Value of a Forward Contract
		3.8 Futures Prices
		3.9 Exercises
		Appendix 3A Compounding Frequency
		Appendix 3B Forward and Futures Prices with Constant Interest Rates
		Appendix 3C Rolling Over Futures Contracts
	4 Pricing Forwards and Futures II: Building on the Foundations
		4.1 Introduction
		4.2 From Theory to Reality
		4.3 The Implied Repo Rate
		4.4 Transactions Costs
		4.5 Forward Prices and Future Spot Prices
		4.6 Index Arbitrage
		4.7 Exercises
		Appendix 4A Forward Prices with Convenience Yields
	5 Hedging with Futures and Forwards
		5.1 Introduction
		5.2 A Guide to the Main Results
		5.3 The Cash Flow from a Hedged Position
		5.4 The Case of No Basis Risk
		5.5 The Minimum-Variance Hedge Ratio
		5.6 Examples
		5.7 Implementation
		5.8 Further Issues in Implementation
		5.9 Index Futures and Changing Equity Risk
		5.10 Fixed-Income Futures and Duration-Based Hedging
		5.11 Exercises
		Appendix 5A Derivation of the Optimal Tailed Hedge Ratio h∗∗
	6 Interest-Rate Forwards and Futures
		6.1 Introduction
		6.2 Eurodollars and Libor Rates
		6.3 Forward-Rate Agreements
		6.4 Eurodollar Futures
		6.5 Treasury Bond Futures
		6.6 Treasury Note Futures
		6.7 Treasury Bill Futures
		6.8 Duration-Based Hedging
		6.9 Exercises
		Appendix 6A Deriving the Arbitrage-Free FRA Rate
		Appendix 6B PVBP-Based Hedging Using Eurodollar Futures
		Appendix 6C Calculating the Conversion Factor
		Appendix 6D Duration as a Sensitivity Measure
		Appendix 6E The Duration of a Futures Contract
PART TWO Options
	7 Options Markets
		7.1 Introduction
		7.2 Definitions and Terminology
		7.3 Options as Financial Insurance
		7.4 Naked Option Positions
		7.5 Options as Views on Market Direction and Volatility
		7.6 Exercises
		Appendix 7A Options Markets
	8 Options: Payoffs and Trading Strategies
		8.1 Introduction
		8.2 Trading Strategies I: Covered Calls and Protective Puts
		8.3 Trading Strategies II: Spreads
		8.4 Trading Strategies III: Combinations
		8.5 Trading Strategies IV: Other Strategies
		8.6 Which Strategies Are the Most Widely Used?
		8.7 The Barings Case
		8.8 Exercises
		Appendix 8A Asymmetric Butterfly Spreads
	9 No-Arbitrage Restrictions on Option Prices
		9.1 Introduction
		9.2 Motivating Examples
		9.3 Notation and Other Preliminaries
		9.4 Maximum and Minimum Prices for Options
		9.5 The Insurance Value of an Option
		9.6 Option Prices and Contract Parameters
		9.7 Numerical Examples
		9.8 Exercises
	10 Early Exercise and Put-Call Parity
		10.1 Introduction
		10.2 A Decomposition of Option Prices
		10.3 The Optimality of Early Exercise
		10.4 Put-Call Parity
		10.5 Exercises
	11 Option Pricing: An Introduction
		11.1 Overview
		11.2 The Binomial Model
		11.3 Pricing by Replication in a One-Period Binomial Model
		11.4 Comments
		11.5 Riskless Hedge Portfolios
		11.6 Pricing Using Risk-Neutral Probabilities
		11.7 The One-Period Model in General Notation
		11.8 The Delta of an Option
		11.9 An Application: Portfolio Insurance
		11.10 Exercises
		Appendix 11A Riskless Hedge Portfolios and Option Pricing
		Appendix 11B Risk-Neutral Probabilities and Arrow Security Prices
		Appendix 11C The Risk-Neutral Probability, No-Arbitrage, and Market Completeness
		Appendix 11D Equivalent Martingale Measures
	12 Binomial Option Pricing
		12.1 Introduction
		12.2 The Two-Period Binomial Tree
		12.3 Pricing Two-Period European Options
		12.4 European Option Pricing in General n-Period Trees
		12.5 Pricing American Options: Preliminary Comments
		12.6 American Puts on Non-Dividend-Paying Stocks
		12.7 Cash Dividends in the Binomial Tree
		12.8 An Alternative Approach to Cash Dividends
		12.9 Dividend Yields in Binomial Trees
		12.10 Exercises
		Appendix 12A A General Representation of European Option Prices
	13 Implementing the Binomial Model
		13.1 Introduction
		13.2 The Lognormal Distribution
		13.3 Binomial Approximations of the Lognormal
		13.4 Computer Implementation of the Binomial Model
		13.5 Exercises
		Appendix 13A Estimating Historical Volatility
	14 The Black-Scholes Model
		14.1 Introduction
		14.2 Option Pricing in the Black-Scholes Setting
		14.3 Remarks on the Formula
		14.4 Working with the Formulae I: Plotting Option Prices
		14.5 Working with the Formulae II: Algebraic Manipulation
		14.6 Dividends in the Black-Scholes Model
		14.7 Options on Indices, Currencies, and Futures
		14.8 Testing the Black-Scholes Model: Implied Volatility
		14.9 The VIX and Its Derivatives
		14.10 Exercises
		Appendix 14A Further Properties of the Black-Scholes Delta
		Appendix 14B Variance and Volatility Swaps
	15 The Mathematics of Black-Scholes
		15.1 Introduction
		15.2 Geometric Brownian Motion Defined
		15.3 The Black-Scholes Formula via Replication
		15.4 The Black-Scholes Formula via Risk-Neutral Pricing
		15.5 The Black-Scholes Formula via CAPM
		15.6 Exercises
	16 Options Modeling: Beyond Black-Scholes
		16.1 Introduction
		16.2 Jump-Diffusion Models
		16.3 Stochastic Volatility
		16.4 GARCH Models
		16.5 Other Approaches
		16.6 Implied Binomial Trees/Local Volatility Models
		16.7 Summary
		16.8 Exercises
		Appendix 16A Program Code for Jump- Diffusions
		Appendix 16B Program Code for a Stochastic Volatility Model
		Appendix 16C Heuristic Comments on Option Pricing under Stochastic Volatility
		Appendix 16D Program Code for Simulating GARCH Stock Prices Distributions
		Appendix 16E Local Volatility Models: The Fourth Period of the Example
	17 Sensitivity Analysis: The Option “Greeks”
		17.1 Introduction
		17.2 Interpreting the Greeks: A Snapshot View
		17.3 The Option Delta
		17.4 The Option Gamma
		17.5 The Option Theta
		17.6 The Option Vega
		17.7 The Option Rho
		17.8 Portfolio Greeks
		17.9 Exercises
		Appendix 17A Deriving the Black-Scholes Option Greeks
	18 Exotic Options I: Path-Independent Options
		18.1 Introduction
		18.2 Forward Start Options
		18.3 Binary Options
		18.4 Chooser Options
		18.5 Compound Options
		18.6 Exchange Options
		18.7 Quanto Options
		18.8 Variants on the Exchange Option Theme
		18.9 Exercises
	19 Exotic Options II: Path-Dependent Options
		19.1 Path-Dependent Exotic Options
		19.2 Barrier Options
		19.3 Asian Options
		19.4 Lookback Options
		19.5 Cliquets
		19.6 Shout Options
		19.7 Exercises
		Appendix 19A Barrier Option Pricing Formulae
	20 Value-at-Risk
		20.1 Introduction
		20.2 Value-at-Risk
		20.3 Risk Decomposition
		20.4 Coherent Risk Measures
		20.5 Exercises
	21 Convertible Bonds
		21.1 Introduction
		21.2 Convertible Bond Terminology
		21.3 Main Features of Convertible Bonds
		21.4 Breakeven Analysis
		21.5 Pricing Convertibles: A First Pass
		21.6 Incorporating Credit Risk
		21.7 Convertible Greeks
		21.8 Convertible Arbitrage
		21.9 Summary
		21.10 Exercises
		Appendix 21A Octave Code for the Blended Discount Rate Valuation Tree
		Appendix 21B Octave Code for the Simplified Das-Sundaram Model
	22 Real Options
		22.1 Introduction
		22.2 Preliminary Analysis and Examples
		22.3 A Real Options “Case Study”
		22.4 Creating the State Space
		22.5 Applications of Real Options
		22.6 Summary
		22.7 Exercises
		Appendix 22A Derivation of Cash-Flow Value in the “Waiting-to-Invest” Example
PART THREE Swaps
	23 Interest Rate Swaps and Floating-Rate Products
		23.1 Introduction
		23.2 Floating-Rate Notes
		23.3 Interest Rate Swaps
		23.4 Uses of Swaps
		23.5 Swap Payoffs
		23.6 Valuing and Pricing Swaps
		23.7 Extending the Pricing Arguments
		23.8 Case Study: The Procter & Gamble–Bankers Trust “5/30” Swap
		23.9 Case Study: A Long-Term Capital Management “Convergence Trade”
		23.10 Credit Risk and Credit Exposure
		23.11 Hedging Swaps
		23.12 Caps, Floors, and Swaptions
		23.13 The Black Model for Pricing Caps, Floors, and Swaptions
		23.14 Summary
		23.15 Exercises
	24 Equity Swaps
		24.1 Introduction
		24.2 Uses of Equity Swaps
		24.3 Payoffs from Equity Swaps
		24.4 Valuation and Pricing of Equity Swaps
		24.5 Summary
		24.6 Exercises
	25 Currency and Commodity Swaps
		25.1 Introduction
		25.2 Currency Swaps
		25.3 Commodity Swaps
		25.4 Summary
		25.5 Exercises
PART FOUR Interest Rate Modeling
	26 The Term Structure of Interest Rates: Concepts
		26.1 Introduction
		26.2 The Yield-to-Maturity
		26.3 The Term Structure of Interest Rates
		26.4 Discount Functions
		26.5 Zero-Coupon Rates
		26.6 Forward Rates
		26.7 Yield-to-Maturity, Zero-Coupon Rates, and Forward Rates
		26.8 Constructing the Yield-to-Maturity Curve: An Empirical Illustration
		26.9 Summary
		26.10 Exercises
		Appendix 26A The Raw YTM Data
	27 Estimating the Yield Curve
		27.1 Introduction
		27.2 Bootstrapping
		27.3 Splines
		27.4 Polynomial Splines
		27.5 Exponential Splines
		27.6 Implementation Issues with Splines
		27.7 The Nelson-Siegel-Svensson Approach
		27.8 Summary
		27.9 Exercises
		Appendix 27A Bootstrapping by Matrix Inversion
		Appendix 27B Implementation with Exponential Splines
	28 Modeling Term-Structure Movements
		28.1 Introduction
		28.2 Interest-Rate Modeling versus Equity Modeling
		28.3 Arbitrage Violations: A Simple Example
		28.4 A Gentle Introduction to No-Arbitrage Modeling
		28.5 “No-Arbitrage” and “Equilibrium” Models
		28.6 Summary
		28.7 Exercises
	29 Factor Models of the Term Structure
		29.1 Overview
		29.2 The Black-Derman-Toy Model
		29.3 The Ho-Lee Model
		29.4 One-Factor Models in Continuous Time
		29.5 Multifactor Models
		29.6 Affine Factor Models
		29.7 Summary
		29.8 Exercises
		Appendix 29A Deriving the Fundamental PDE in Factor Models
	30 The Heath-Jarrow-Morton and Libor Market Models
		30.1 Overview
		30.2 The HJM Framework: Preliminary Comments
		30.3 A One-Factor HJM Model
		30.4 A Two-Factor HJM Setting
		30.5 The HJM Risk-Neutral Drifts: An Algebraic Derivation
		30.6 Libor Market Models
		30.7 Mathematical Excursion: Martingales
		30.8 Libor Rates: Notation
		30.9 Risk-Neutral Pricing in the LMM
		30.10 Simulation of the Market Model
		30.11 Calibration
		30.12 Swap Market Models
		30.13 Swaptions
		30.14 Summary
		30.15 Exercises
		Appendix 30A Risk-Neutral Drifts and Volatilities in HJM
PART FIVE Credit Risk
	31 Credit Derivative Products
		31.1 Introduction
		31.2 Total Return Swaps
		31.3 Credit Spread Options/Forwards
		31.4 Credit Default Swaps
		31.5 Credit-Linked Notes
		31.6 Correlation Products
		31.7 Summary
		31.8 Exercises
		Appendix 31A The CDS Big Bang
	32 Structural Models of Default Risk
		32.1 Introduction
		32.2 The Merton (1974) Model
		32.3 Issues in Implementation
		32.4 A Practitioner Model
		32.5 Extensions of the Merton Model
		32.6 Evaluation of the Structural Model Approach
		32.7 Summary
		32.8 Exercises
		Appendix 32A The Delianedis-Geske Model
	33 Reduced-Form Models of Default Risk
		33.1 Introduction
		33.2 Modeling Default I: Intensity Processes
		33.3 Modeling Default II: Recovery Rate Conventions
		33.4 The Litterman-Iben Model
		33.5 The Duffie-Singleton Result
		33.6 Defaultable HJM Models
		33.7 Ratings-Based Modeling: The JLT Model
		33.8 An Application of Reduced-Form Models: Pricing CDS
		33.9 Summary
		33.10 Exercises
		Appendix 33A Duffie-Singleton in Discrete Time
		Appendix 33B Derivation of the Drift-Volatility Relationship
	34 Modeling Correlated Default
		34.1 Introduction
		34.2 Examples of Correlated Default Products
		34.3 Simple Correlated Default Math
		34.4 Structural Models Based on Asset Values
		34.5 Reduced-Form Models
		34.6 Multiperiod Correlated Default
		34.7 Fast Computation of Credit Portfolio Loss Distributions without Simulation
		34.8 Copula Functions
		34.9 Top-Down Modeling of Credit Portfolio Loss
		34.10 Summary
		34.11 Exercises
Bibliography
Name Index
Subject Index