Options, Futures, and Other Derivatives

Cover
Title Page
Copyright Page
Contents in Brief
Contents
List of Business Snapshots
List of Technical Notes
Preface
Chapter 1.Introduction
	1.1 Exchange-traded markets
	1.2 Over-the-counter markets
	1.3 Forward contracts
	1.4 Futures contracts
	1.5 Options
	1.6 Types of traders
	1.7 Hedgers
	1.8 Speculators
	1.9 Arbitrageurs
	1.10 Dangers
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 2.Mechanics of futures markets
	2.1 Background
	2.2 Specification of a futures contract
	2.3 Convergence of futures price to spot price
	2.4 The operation of margin accounts
	2.5 OTC markets
	2.6 Market quotes
	2.7 Delivery
	2.8 Types of traders and types of orders
	2.9 Regulation
	2.10 Accounting and tax
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 3.Hedging strategies using futures
	3.1 Basic principles
	3.2 Arguments for and against hedging
	3.3 Basis risk
	3.4 Cross hedging
	3.5 Stock index futures
	3.6 Stack and roll
	Summary
	Further reading
	Practice questions
	Further questions
	Appendix: Capital asset pricing model
Chapter 4.Interest rates
	4.1 Types of rates
	4.2 Measuring interest rates
	4.3 Zero rates
	4.4 Bond pricing
	4.5 Determining Treasury zero rates
	4.6 Forward rates
	4.7 Forward rate agreements
	4.8 Duration
	4.9 Convexity
	4.10 Theories of the term structure of interest rates
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 5.Determination of forward and futures prices
	5.1 Investment assets vs. consumption assets
	5.2 Short selling
	5.3 Assumptions and notation
	5.4 Forward price for an investment asset
	5.5 Known income
	5.6 Known yield
	5.7 Valuing forward contracts
	5.8 Are forward prices and futures prices equal?
	5.9 Futures prices of stock indices
	5.10 Forward and futures contracts on currencies
	5.11 Futures on commodities
	5.12 The cost of carry
	5.13 Delivery options
	5.14 Futures prices and expected future spot prices
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 6.Interest rate futures
	6.1 Day count and quotation conventions
	6.2 Treasury bond futures
	6.3 Eurodollar futures
	6.4 Duration-based hedging strategies using futures
	6.5 Hedging portfolios of assets and liabilities
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 7.Swaps
	7.1 Mechanics of interest rate swaps
	7.2 Day count issues
	7.3 Confirmations
	7.4 The comparative-advantage argument
	7.5 The nature of swap rates
	7.6 Determining LIBOR/swap zero rates
	7.7 Valuation of interest rate swaps
	7.8 Term structure effects
	7.9 Fixed-for-fixed currency swaps
	7.10 Valuation of fixed-for-fixed currency swaps
	7.11 Other currency swaps
	7.12 Credit risk
	7.13 Other types of swaps
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 8.Securitization and the credit crisis of 2007
	8.1 Securitization
	8.2 The US housing market
	8.3 What went wrong?
	8.4 The aftermath
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 9.OIS discounting, credit issues, and funding costs
	9.1 The risk-free rate
	9.2 The OIS rate
	9.3 Valuing swaps and FRAs with OIS discounting
	9.4 OIS vs. LIBOR: Which is correct?
	9.5 Credit risk: CVA and DVA
	9.6 Funding costs
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 10.Mechanics of options markets
	10.1 Types of options
	10.2 Option positions
	10.3 Underlying assets
	10.4 Specification of stock options
	10.5 Trading
	10.6 Commissions
	10.7 Margin requirements
	10.8 The options clearing corporation
	10.9 Regulation
	10.10 Taxation
	10.11 Warrants, employee stock options, and convertibles
	10.12 Over-the-counter options markets
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 11.Properties of stock options
	11.1 Factors affecting option prices
	11.2 Assumptions and notation
	11.3 Upper and lower bounds for option prices
	11.4 Put–call parity
	11.5 Calls on a non-dividend-paying stock
	11.6 Puts on a non-dividend-paying stock
	11.7 Effect of dividends
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 12.Trading strategies involving options
	12.1 Principal-protected notes
	12.2 Trading an option and the underlying asset
	12.3 Spreads
	12.4 Combinations
	12.5 Other payoffs
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 13.Binomial trees
	13.1 A one-step binomial model and a no-arbitrage argument
	13.2 Risk-neutral valuation
	13.3 Two-step binomial trees
	13.4 A put example
	13.5 American options
	13.6 Delta
	13.7 Matching volatility with u and d
	13.8 The binomial tree formulas
	13.9 Increasing the number of steps
	13.10 Using DerivaGem
	13.11 Options on other assets
	Summary
	Further reading
	Practice questions
	Further questions
	Appendix: Derivation of the Black–Scholes–Merton option-pricing formula from a binomial tree
Chapter 14.Wiener processes and Itô’s lemma
	14.1 The Markov property
	14.2 Continuous-time stochastic processes
	14.3 The process for a stock price
	14.4 The parameters
	14.5 Correlated processes
	14.6 Itô’s lemma
	14.7 The lognormal property
	Summary
	Further reading
	Practice questions
	Further questions
	Appendix: Derivation of Itô’s lemma
Chapter 15.The Black–Scholes–Merton model
	15.1 Lognormal property of stock prices
	15.2 The distribution of the rate of return
	15.3 The expected return
	15.4 Volatility
	15.5 The idea underlying the Black–Scholes–Merton differential equation
	15.6 Derivation of the Black–Scholes–Merton differential equation
	15.7 Risk-neutral valuation
	15.8 Black–Scholes–Merton pricing formulas
	15.9 Cumulative normal distribution function
	15.10 Warrants and employee stock options
	15.11 Implied volatilities
	15.12 Dividends
	Summary
	Further reading
	Practice questions
	Further questions
	Appendix: Proof of Black–Scholes–Merton formula using risk-neutral valuation
Chapter 16.Employee stock options
	16.1 Contractual arrangements
	16.2 Do options align the interests of shareholders and managers?
	16.3 Accounting issues
	16.4 Valuation
	16.5 Backdating scandals
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 17.Options on stock indices and currencies
	17.1 Options on stock indices
	17.2 Currency options
	17.3 Options on stocks paying known dividend yields
	17.4 Valuation of European stock index options
	17.5 Valuation of European currency options
	17.6 American options
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 18.Futures options
	18.1 Nature of futures options
	18.2 Reasons for the popularity of futures options
	18.3 European spot and futures options
	18.4 Put–call parity
	18.5 Bounds for futures options
	18.6 Valuation of futures options using binomial trees
	18.7 Drift of a futures price in a risk-neutral world
	18.8 Black’s model for valuing futures options
	18.9 American futures options vs. American spot options
	18.10 Futures-style options
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 19.The Greek letters
	19.1 Illustration
	19.2 Naked and covered positions
	19.3 A stop-loss strategy
	19.4 Delta hedging
	19.5 Theta
	19.6 Gamma
	19.7 Relationship between delta, theta, and gamma
	19.8 Vega
	19.9 Rho
	19.10 The realities of hedging
	19.11 Scenario analysis
	19.12 Extension of formulas
	19.13 Portfolio insurance
	19.14 Stock market volatility
	Summary
	Further reading
	Practice questions
	Further questions
	Appendix: Taylor series expansions and hedge parameters
Chapter 20.Volatility smiles
	20.1 Why the volatility smile is the same for calls and puts
	20.2 Foreign currency options
	20.3 Equity options
	20.4 Alternative ways of characterizing the volatility smile
	20.5 The volatility term structure and volatility surfaces
	20.6 Greek letters
	20.7 The role of the model
	20.8 When a single large jump is anticipated
	Summary
	Further reading
	Practice questions
	Further questions
	Appendix: Determining implied risk-neutral distributions from volatility smiles
Chapter 21.Basic numerical procedures
	21.1 Binomial trees
	21.2 Using the binomial tree for options on indices, currencies, and futures contracts
	21.3 Binomial model for a dividend-paying stock
	21.4 Alternative procedures for constructing trees
	21.5 Time-dependent parameters
	21.6 Monte Carlo simulation
	21.7 Variance reduction procedures
	21.8 Finite difference methods
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 22.Value at risk
	22.1 The VaR measure
	22.2 Historical simulation
	22.3 Model-building approach
	22.4 The linear model
	22.5 The quadratic model
	22.6 Monte Carlo simulation
	22.7 Comparison of approaches
	22.8 Stress testing and back testing
	22.9 Principal components analysis
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 23.Estimating volatilities and correlations
	23.1 Estimating volatility
	23.2 The exponentially weighted moving average model
	23.3 The GARCH (1,1) model
	23.4 Choosing between the models
	23.5 Maximum likelihood methods
	23.6 Using GARCH (1,1) to forecast future volatility
	23.7 Correlations
	23.8 Application of EWMA to four-index example
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 24.Credit risk
	24.1 Credit ratings
	24.2 Historical default probabilities
	24.3 Recovery rates
	24.4 Estimating default probabilities from bond yield spreads
	24.5 Comparison of default probability estimates
	24.6 Using equity prices to estimate default probabilities
	24.7 Credit risk in derivatives transactions
	24.8 Default correlation
	24.9 Credit VaR
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 25.Credit derivatives
	25.1 Credit default swaps
	25.2 Valuation of credit default swaps
	25.3 Credit indices
	25.4 The use of ?xed coupons
	25.5 CDS forwards and options
	25.6 Basket credit default swaps
	25.7 Total return swaps
	25.8 Collateralized debt obligations
	25.9 Role of correlation in a basket CDS and CDO
	25.10 Valuation of a synthetic CDO
	25.11 Alternatives to the standard market model
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 26.Exoticoptions
	26.1 Packages
	26.2 Perpetual American call and put options
	26.3 Nonstandard American options
	26.4 Gap options
	26.5 Forward start options
	26.6 Cliquet options
	26.7 Compound options
	26.8 Chooser options
	26.9 Barrier options
	26.10 Binary options
	26.11 Lookback options
	26.12 Shout options
	26.13 Asian options
	26.14 Options to exchange one asset for another
	26.15 Options involving several assets
	26.16 Volatility and variance swaps
	26.17 Static options replication
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 27.More on models and numerical procedures
	27.1 Alternatives to Black–Scholes–Merton
	27.2 Stochastic volatility models
	27.3 The IVF model
	27.4 Convertible bonds
	27.5 Path-dependent derivatives
	27.6 Barrier options
	27.7 Options on two correlated assets
	27.8 Monte Carlo simulation and American options
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 28.Martingales and measures
	28.1 The market price of risk
	28.2 Several state variables
	28.3 Martingales
	28.4 Alternative choices for the numeraire
	28.5 Extension to several factors
	28.6 Black’s model revisited
	28.7 Option to exchange one asset for another
	28.8 Change of numeraire
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 29.Interest rate derivatives: The standard market models
	29.1 Bond options
	29.2 Interest rate caps and ?oors
	29.3 European swap options
	29.4 OIS discounting
	29.5 Hedging interest rate derivatives
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 30.Convexity, timing, and quanto adjustments
	30.1 Convexity adjustments
	30.2 Timing adjustments
	30.3 Quantos
	Summary
	Further reading
	Practice questions
	Further questions
	Appendix: Proof of the convexity adjustment formula
Chapter 31.Interest rate derivatives: Models of the short rate
	31.1 Background
	31.2 Equilibrium models
	31.3 No-arbitrage models
	31.4 Options on bonds
	31.5 Volatility structures
	31.6 Interest rate trees
	31.7 A general tree-building procedure
	31.8 Calibration
	31.9 Hedging using a one-factor model
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 32.HJM, LMM, and multiple zero curves
	32.1 The Heath, Jarrow, and Morton model
	32.2 The LIBOR market model
	32.3 Handling multiple zero curves
	32.4 Agency mortgage-backed securities
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 33.Swaps Revisited
	33.1 Variations on the vanilla deal
	33.2 Compounding swaps
	33.3 Currency swaps
	33.4 More complex swaps
	33.5 Equity swaps
	33.6 Swaps with embedded options
	33.7 Other swaps
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 34.Energy and commodity derivatives
	34.1 Agricultural commodities
	34.2 Metals
	34.3 Energy products
	34.4 Modeling commodity prices
	34.5 Weather derivatives
	34.6 Insurance derivatives
	34.7 Pricing weather and insurance derivatives
	34.8 How an energy producer can hedge risks
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 35.Real options
	35.1 Capital investment appraisal
	35.2 Extension of the risk-neutral valuation framework
	35.3 Estimating the market price of risk
	35.4 Application to the valuation of a business
	35.5 Evaluating options in an investment opportunity
	Summary
	Further reading
	Practice questions
	Further questions
Chapter 36.Derivatives mishaps and what we can learn from them
	36.1 Lessons for all users of derivatives
	36.2 Lessons for financial institutions
	36.3 Lessons for nonfinancial corporations
	Summary
	Further reading
DerivaGem software
Major exchanges trading futures and options
Tables for N(x)
Author index
Subject index