Description
Options, Futures, and Other Derivatives Edition 10 by John C. Hull EBOOK PDF Instant Download
Table of Contents
Options, Futures, and Other Derivatives
Options, Futures, and Other Derivatives
Contents In Brief
Contents
BUSINESS SNAPSHOTS
TECHNICAL NOTES
Preface
What’s New in the Tenth Edition?
Software
Slides
Solutions Manual
Instructors Manual
Technical Notes
About the Author
Chapter 1 Introduction
1.1 EXCHANGE-TRADED MARKETS
Electronic Markets
1.2 OVER-THE-COUNTER MARKETS
Market Size
1.3 FORWARD CONTRACTS
Payoffs from Forward Contracts
Forward Prices and Spot Prices
1.4 FUTURES CONTRACTS
1.5 OPTIONS
1.6 TYPES OF TRADERS
1.7 HEDGERS
Hedging Using Forward Contracts
Hedging Using Options
A Comparison
1.8 SPECULATORS
Speculation Using Futures
Speculation Using Options
A Comparison
1.9 ARBITRAGEURS
1.10 DANGERS
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 2 Futures Markets and Central Counterparties
2.1 BACKGROUND
Closing Out Positions
2.2 SPECIFICATION OF A FUTURES CONTRACT
The Asset
The Contract Size
Delivery Arrangements
Delivery Months
Price Quotes
Price Limits and Position Limits
2.3 CONVERGENCE OF FUTURES PRICE TO SPOT PRICE
2.4 THE OPERATION OF MARGIN ACCOUNTS
Daily Settlement
Further Details
The Clearing House and Its Members
Credit Risk
2.5 OTC MARKETS
Central Counterparties
Bilateral Clearing
Futures Trades vs. OTC Trades
2.6 MARKET QUOTES
Prices
Settlement Price
Trading Volume and Open Interest
Patterns of Futures
2.7 DELIVERY
Cash Settlement
2.8 TYPES OF TRADERS AND TYPES OF ORDERS
Orders
2.9 REGULATION
Trading Irregularities
2.10 ACCOUNTING AND TAX
Accounting
Tax
2.11 FORWARD vs. FUTURES CONTRACTS
Profits from Forward and Futures Contracts
Foreign Exchange Quotes
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 3 Hedging Strategies Using Futures
3.1 BASIC PRINCIPLES
Short Hedges
Long Hedges
3.2 ARGUMENTS FOR AND AGAINST HEDGING
Hedging and Shareholders
Hedging and Competitors
Hedging Can Lead to a Worse Outcome
3.3 BASIS RISK
The Basis
Choice of Contract
3.4 CROSS HEDGING
Calculating the Minimum Variance Hedge Ratio
Optimal Number of Contracts
Impact of Daily Settlement
3.5 STOCK INDEX FUTURES
Stock Indices
Hedging an Equity Portfolio
Reasons for Hedging an Equity Portfolio
Changing the Beta of a Portfolio
Locking in the Benefits of Stock Picking
3.6 STACK AND ROLL
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
APPENDIX CAPITAL ASSET PRICING MODEL
Chapter 4 Interest Rates
4.1 TYPES OF RATES
Treasury Rates
LIBOR
Overnight Rates
Repo Rates
4.2 SWAP RATES
Overnight Indexed Swaps
4.3 THE RISK-FREE RATE
4.4 MEASURING INTEREST RATES
Continuous Compounding
4.5 ZERO RATES
4.6 BOND PRICING
Bond Yield
Par Yield
4.7 DETERMINING ZERO RATES
Treasury Rates
OIS Rates
4.8 FORWARD RATES
4.9 FORWARD RATE AGREEMENTS
Valuation
4.10 DURATION
Modified Duration
Bond Portfolios
4.11 CONVEXITY
4.12 THEORIES OF THE TERM STRUCTURE OF INTEREST RATES
The Management of Net Interest Income
Liquidity
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
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
A Generalization
What If Short Sales Are Not Possible?
5.5 KNOWN INCOME
A Generalization
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
Index Arbitrage
5.10 FORWARD AND FUTURES CONTRACTS ON CURRENCIES
A Foreign Currency as an Asset Providing a Known Yield
5.11 FUTURES ON COMMODITIES
Income and Storage Costs
Consumption Commodities
Convenience Yields
5.12 THE COST OF CARRY
5.13 DELIVERY OPTIONS
5.14 FUTURES PRICES AND EXPECTED FUTURE SPOT PRICES
Keynes and Hicks
Risk and Return
The Risk in a Futures Position
Normal Backwardation and Contango
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 6 Interest Rate Futures
6.1 DAY COUNT AND QUOTATION CONVENTIONS
Day Counts
Price Quotations of U.S. Treasury Bills
Price Quotations of U.S. Treasury Bonds
6.2 TREASURY BOND FUTURES
Quotes
Conversion Factors
Cheapest-to-Deliver Bond
Determining the Futures Price
6.3 EURODOLLAR FUTURES
Forward vs. Futures Interest Rates
Convexity Adjustment
Using Eurodollar Futures to Extend the LIBOR Zero Curve
6.4 DURATION-BASED HEDGING STRATEGIES USING FUTURES
6.5 HEDGING PORTFOLIOS OF ASSETS AND LIABILITIES
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 7 Swaps
7.1 MECHANICS OF INTEREST RATE SWAPS
LIBOR
Illustration
Using the Swap to Transform a Liability
Using the Swap to Transform an Asset
Organization of Trading
7.2 DAY COUNT ISSUES
7.3 CONFIRMATIONS
7.4 THE COMPARATIVE-ADVANTAGE ARGUMENT
Illustration
Criticism of the Comparative-Advantage Argument
7.5 VALUATION OF INTEREST RATE SWAPS
Bootstrapping LIBOR Forward Rates
7.6 HOW THE VALUE CHANGES THROUGH TIME
7.7 FIXED-FOR-FIXED CURRENCY SWAPS
Illustration
Use of a Currency Swap to Transform Liabilities and Assets
Comparative Advantage
7.8 VALUATION OF FIXED-FOR-FIXED CURRENCY SWAPS
Valuation in Terms of Bond Prices
7.9 OTHER CURRENCY SWAPS
7.10 CREDIT RISK
7.11 CREDIT DEFAULT SWAPS
7.12 OTHER TYPES OF SWAPS
Variations on the Standard Interest Rate Swap
Quantos
Equity Swaps
Options
Commodity, Volatility, and Other Swaps
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 8 Securitization and the Credit Crisis of 2007
8.1 SECURITIZATION
ABSs
ABS CDOs
8.2 THE U.S. HOUSING MARKET
The Relaxation of Lending Standards
Subprime Mortgage Securitization
The Bubble Bursts
The Losses
The Credit Crisis
8.3 WHAT WENT WRONG?
Regulatory Arbitrage
Incentives
8.4 THE AFTERMATH
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 9 XVAs
9.1 CVA AND DVA
Collateral
9.2 FVA AND MVA
9.3 KVA
9.4 CALCULATION ISSUES
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 10 Mechanics of Options Markets
10.1 TYPES OF OPTIONS
Call Options
Put Options
Early Exercise
10.2 OPTION POSITIONS
10.3 UNDERLYING ASSETS
Stock Options
ETP Options
Foreign Currency Options
Index Options
Futures Options
10.4 SPECIFICATION OF STOCK OPTIONS
Expiration Dates
Strike Prices
Terminology
FLEX Options
Other Nonstandard Products
Dividends and Stock Splits
Position Limits and Exercise Limits
10.5 TRADING
Market Makers
Offsetting Orders
10.6 COMMISSIONS
10.7 MARGIN REQUIREMENTS
Writing Naked Options
Other Rules
10.8 THE OPTIONS CLEARING CORPORATION
Exercising an Option
10.9 REGULATION
10.10 TAXATION
Wash Sale Rule
Constructive Sales
10.11 WARRANTS, EMPLOYEE STOCK OPTIONS, AND CONVERTIBLES
10.12 OVER-THE-COUNTER OPTIONS MARKETS
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 11 Properties of Stock Options
11.1 Factors Affecting Option Prices
Stock Price and Strike Price
Time to Expiration
Volatility
Risk-Free Interest Rate
Amount of Future Dividends
11.2 ASSUMPTIONS AND NOTATION
11.3 UPPER AND LOWER BOUNDS FOR OPTION PRICES
Upper Bounds
Lower Bound for Calls on Non-Dividend-Paying Stocks
Lower Bound for European Puts on Non-Dividend-Paying Stocks
11.4 PUT–CALL PARITY
American Options
11.5 CALLS ON A NON-DIVIDEND-PAYING STOCK
Bounds
11.6 PUTS ON A NON-DIVIDEND-PAYING STOCK
Bounds
11.7 EFFECT OF DIVIDENDS
Lower Bound for Calls and Puts
Early Exercise
Put–Call Parity
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
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
Bull Spreads
Bear Spreads
Box Spreads
Butterfly Spreads
Calendar Spreads
Diagonal Spreads
12.4 COMBINATIONS
Straddle
Strips and Straps
Strangles
12.5 OTHER PAYOFFS
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 13 Binomial Trees
13.1 A ONE-STEP BINOMIAL MODEL AND A NO-ARBITRAGE ARGUMENT
A Generalization
Irrelevance of the Stock’s Expected Return
13.2 RISK-NEUTRAL VALUATION
The One-Step Binomial Example Revisited
Real World vs. Risk-Neutral World
13.3 TWO-STEP BINOMIAL TREES
A Generalization
13.4 A PUT EXAMPLE
13.5 AMERICAN OPTIONS
13.6 DELTA
13.7 MATCHING VOLATILITY WITH u AND d
Girsanov’s Theorem
13.8 THE BINOMIAL TREE FORMULAS
13.9 INCREASING THE NUMBER OF STEPS
13.10 USING DerivaGem
13.11 OPTIONS ON OTHER ASSETS
Options on Stocks Paying a Continuous Dividend Yield
Options on Stock Indices
Options on Currencies
Options on Futures
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
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
Wiener Process
Generalized Wiener Process
Itô Process
14.3 THE PROCESS FOR A STOCK PRICE
Discrete-Time Model
Monte Carlo Simulation
14.4 THE PARAMETERS
14.5 CORRELATED PROCESSES
14.6 ITÔ’S LEMMA
Application to Forward Contracts
14.7 THE LOGNORMAL PROPERTY
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
APPENDIX A NONRIGOROUS 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
Estimating Volatility from Historical Data
Trading Days vs. Calendar Days
15.5 THE IDEA UNDERLYING THE BLACK–SCHOLES–MERTON DIFFERENTIAL EQUATION
Assumptions
15.6 DERIVATION OF THE BLACK–SCHOLES–MERTON DIFFERENTIAL EQUATION
A Perpetual Derivative
The Prices of Tradeable Derivatives
15.7 RISK-NEUTRAL VALUATION
Application to Forward Contracts on a Stock
15.8 BLACK–SCHOLES–MERTON PRICING FORMULAS
Understanding N(d1) and N(d2)
Properties of the Black–Scholes–Merton Formulas
15.9 CUMULATIVE NORMAL DISTRIBUTION FUNCTION
15.10 WARRANTS AND EMPLOYEE STOCK OPTIONS
15.11 IMPLIED VOLATILITIES
The VIX Index
15.12 DIVIDENDS
European Options
American Call Options
Black’s Approximation
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
APPENDIX PROOF OF THE BLACK–SCHOLES–MERTON FORMULA USING RISK-NEUTRAL VALUATION
Key Result
Proof of Key Result
The Black–Scholes–Merton Result
Chapter 16 Employee Stock Options
16.1 CONTRACTUAL ARRANGEMENTS
The Early Exercise Decision
16.2 DO OPTIONS ALIGN THE INTERESTS OF SHAREHOLDERS AND MANAGERS?
16.3 ACCOUNTING ISSUES
Alternatives to Stock Options
16.4 VALUATION
The “Quick and Dirty” Approach
Binomial Tree Approach
The Exercise Multiple Approach
A Market-Based Approach
Dilution
16.5 BACKDATING SCANDALS
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 17 Options on Stock Indices and Currencies
17.1 OPTIONS ON STOCK INDICES
Portfolio Insurance
When the Portfolio’s Beta Is Not 1.0
17.2 CURRENCY OPTIONS
Range Forwards
17.3 OPTIONS ON STOCKS PAYING KNOWN DIVIDEND YIELDS
Lower Bounds for Option Prices
Put–Call Parity
Pricing Formulas
Differential Equation and Risk-Neutral Valuation
17.4 VALUATION OF EUROPEAN STOCK INDEX OPTIONS
Forward Prices
Implied Dividend Yields
17.5 VALUATION OF EUROPEAN CURRENCY OPTIONS
Using Forward Exchange Rates
17.6 AMERICAN OPTIONS
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 18 Futures Options and Black’s Model
18.1 NATURE OF FUTURES OPTIONS
Expiration Months
Options on Interest Rate Futures
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 DRIFT OF A FUTURES PRICE IN A RISK-NEUTRAL WORLD
Differential Equation
18.7 BLACK’S MODEL FOR VALUING FUTURES OPTIONS
18.8 USING BLACK’S MODEL INSTEAD OF BLACK–SCHOLES–MERTON
18.9 VALUATION OF FUTURES OPTIONS USING BINOMIAL TREES
A Generalization
Multistep Trees
18.10 AMERICAN FUTURES OPTIONS vs. AMERICAN SPOT OPTIONS
18.11 FUTURES-STYLE OPTIONS
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 19 The Greek Letters
19.1 ILLUSTRATION
19.2 NAKED AND COVERED POSITIONS
A Stop-Loss Strategy
19.3 GREEK LETTER CALCULATION
19.4 DELTA HEDGING
Delta of European Stock Options
Dynamic Aspects of Delta Hedging
Where the Cost Comes From
Delta of a Portfolio
Transaction Costs
19.5 THETA
19.6 GAMMA
Making a Portfolio Gamma Neutral
Calculation of 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
Delta of Forward Contracts
Delta of a Futures Contract
19.13 PORTFOLIO INSURANCE
Use of Index Futures
19.14 STOCK MARKET VOLATILITY
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
APPENDIX TAYLOR SERIES EXPANSIONS AND GREEK LETTERS
The Practitioner Black–Scholes Model
Chapter 20 Volatility Smiles
20.1 WHY THE VOLATILITY SMILE IS THE SAME FOR CALLS AND PUTS
20.2 FOREIGN CURRENCY OPTIONS
Empirical Results
Reasons for the Smile in Foreign Currency Options
20.3 EQUITY OPTIONS
The Reason for the Smile in Equity Options
20.4 ALTERNATIVE WAYS OF CHARACTERIZING THE VOLATILITY SMILE
20.5 THE VOLATILITY TERM STRUCTURE AND VOLATILITY SURFACES
20.6 MINIMUM VARIANCE DELTA
20.7 THE ROLE OF THE MODEL
20.8 WHEN A SINGLE LARGE JUMP IS ANTICIPATED
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
APPENDIX DETERMINING IMPLIED RISK-NEUTRAL DISTRIBUTIONS FROM VOLATILITY SMILES
Chapter 21 Basic Numerical Procedures
21.1 BINOMIAL TREES
Risk-Neutral Valuation
Determination of p, u, and d
Tree of Asset Prices
Working Backward through the Tree
Expressing the Approach Algebraically
Estimating Delta and Other Greek Letters
21.2 USING THE BINOMIAL TREE FOR OPTIONS ON INDICES, CURRENCIES, AND FUTURES CONTRACTS
21.3 BINOMIAL MODEL FOR A DIVIDEND-PAYING STOCK
Known Dividend Yield
Known Dollar Dividend
Control Variate Technique
21.4 ALTERNATIVE PROCEDURES FOR CONSTRUCTING TREES
Trinomial Trees
21.5 TIME-DEPENDENT PARAMETERS
21.6 MONTE CARLO SIMULATION
Derivatives Dependent on More than One Market Variable
Generating the Random Samples from Normal Distributions
Number of Trials
Sampling through a Tree
Calculating the Greek Letters
Applications
21.7 VARIANCE REDUCTION PROCEDURES
Antithetic Variable Technique
Control Variate Technique
Importance Sampling
Stratified Sampling
Moment Matching
Using Quasi-Random Sequences
21.8 FINITE DIFFERENCE METHODS
Implicit Finite Difference Method
Explicit Finite Difference Method
Change of Variable
Relation to Trinomial Tree Approaches
Other Finite Difference Methods
Applications of Finite Difference Methods
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 22 Value at Risk and Expected Shortfall
22.1 THE VaR AND ES MEASURES
The Time Horizon
22.2 HISTORICAL SIMULATION
Illustration: Investment in Four Stock Indices
Expected Shortfall
Stressed VaR and Stressed ES
22.3 MODEL-BUILDING APPROACH
Daily Volatilities
Single-Asset Case
Two-Asset Case
The Benefits of Diversification
ES Calculation
22.4 THE LINEAR MODEL
Correlation and Covariance Matrices
Handling Interest Rates
Applications of the Linear Model
The Linear Model and Options
22.5 THE QUADRATIC MODEL
22.6 MONTE CARLO SIMULATION
22.7 COMPARISON OF APPROACHES
22.8 BACK TESTING
22.9 PRINCIPAL COMPONENTS ANALYSIS
Using Principal Components Analysis to Calculate VaR
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 23 Estimating Volatilities and Correlations
23.1 ESTIMATING VOLATILITY
Weighting Schemes
23.2 THE EXPONENTIALLY WEIGHTED MOVING AVERAGE MODEL
23.3 THE GARCH(1,1) MODEL
The Weights
Mean Reversion
23.4 CHOOSING BETWEEN THE MODELS
23.5 MAXIMUM LIKELIHOOD METHODS
Estimating a Constant Variance
Estimating EWMA or GARCH (1,1) Parameters
How Good Is the Model?
23.6 USING GARCH(1,1) TO FORECAST FUTURE VOLATILITY
Volatility Term Structures
Impact of Volatility Changes
23.7 CORRELATIONS
Consistency Condition for Covariances
23.8 APPLICATION OF EWMA TO FOUR-INDEX EXAMPLE
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 24 Credit Risk
24.1 CREDIT RATINGS
24.2 HISTORICAL DEFAULT PROBABILITIES
Hazard Rates
24.3 RECOVERY RATES
The Dependence of Recovery Rates on Default Rates
24.4 ESTIMATING DEFAULT PROBABILITIES FROM BOND YIELD SPREADS
Matching Bond Prices
The Risk-Free Rate
Asset Swap Spreads
24.5 COMPARISON OF DEFAULT PROBABILITY ESTIMATES
Real-World vs. Risk-Neutral Probabilities
Which Default Probability Estimate Should Be Used?
24.6 USING EQUITY PRICES TO ESTIMATE DEFAULT PROBABILITIES
24.7 CREDIT RISK IN DERIVATIVES TRANSACTIONS
CVA and DVA
Credit Risk Mitigation
Special Cases
24.8 DEFAULT CORRELATION
The Gaussian Copula Model for Time to Default
A Factor-Based Correlation Structure
24.9 CREDIT VAR
CreditMetrics
SUMMARY
Further Reading
Practice Questions (Answers in the Solutions Manual)
Further Questions
Chapter 25 Credit Derivatives
25.1 CREDIT DEFAULT SWAPS
Credit Default Swaps and Bond Yields
The Cheapest-to-Deliver Bond
25.2 VALUATION OF CREDIT DEFAULT SWAPS
Marking to Market a CDS
Estimating Default Probabilities
Binary Credit Default Swaps
How Important Is the Recovery Rate?
25.3 CREDIT INDICES
25.4 THE USE OF FIXED COUPONS
25.5 CDS FORWARDS AND OPTIONS
25.6 BASKET CREDIT DEFAULT SWAPS
25.7 TOTAL RETURN SWAPS
25.8 COLLATERALIZED DEBT OBLIGATIONS
Synthetic CDOs
Standard Portfolios and Single-Tranche Trading
25.9 ROLE OF CORRELATION IN A BASKET CDS AND CDO
25.10 VALUATION OF A SYNTHETIC CDO
Using the Gaussian Copula Model of Time to Default
Valuation of kth-to-Default CDS
Implied Correlation
Valuing Nonstandard Tranches
25.11 ALTERNATIVES TO THE STANDARD MARKET MODEL
Heterogeneous Model
Other Copulas
Random Recovery and Factor Loadings
The Implied Copula Model
Dynamic Models
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 26 Exotic Options
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
Valuation of Variance Swap
Valuation of a Volatility Swap
The VIX Index
26.17 STATIC OPTIONS REPLICATION
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 27 More on Models and Numerical Procedures
27.1 ALTERNATIVES TO BLACK–SCHOLES–MERTON
The Constant Elasticity of Variance Model
Merton’s Mixed Jump–Diffusion Model
Simulating Jumps
The Variance-Gamma Model
27.2 STOCHASTIC VOLATILITY MODELS
The SABR Model
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
Transforming Variables
Using a Nonrectangular Tree
Adjusting the Probabilities
27.8 MONTE CARLO SIMULATION AND AMERICAN OPTIONS
The Least-Squares Approach
The Exercise Boundary Parameterization Approach
Upper Bounds
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 28 Martingales and Measures
28.1 THE MARKET PRICE OF RISK
Alternative Worlds
28.2 SEVERAL STATE VARIABLES
28.3 MARTINGALES
The Equivalent Martingale Measure Result
28.4 ALTERNATIVE CHOICES FOR THE NUMERAIRE
Money Market Account as the Numeraire
Zero-Coupon Bond Price as the Numeraire
Forward Interest Rates
Annuity Factor as 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
A Final Point
Summary
Further Reading
Practice Questions (Answers in the Solutions Manual)
Further Questions
Chapter 29 Interest Rate Derivatives: The Standard Market Models
29.1 BOND OPTIONS
Embedded Bond Options
European Bond Options
Yield Volatilities
29.2 INTEREST RATE CAPS AND FLOORS
The Cap as a Portfolio of Interest Rate Options
A Cap as a Portfolio of Bond Options
Floors and Collars
Valuation of Caps and Floors
Theoretical Justification for the Model
Use of DerivaGem
The Impact of Day Count Conventions
Negative Rates
29.3 EUROPEAN SWAP OPTIONS
Valuation of European Swaptions
Theoretical Justification for the Swaption Model
The Impact of Day Count Conventions
Negative Rates
29.4 HEDGING INTEREST RATE DERIVATIVES
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 30 Convexity, Timing, and Quanto Adjustments
30.1 CONVEXITY ADJUSTMENTS
Application 1: Interest Rates
Application 2: Swap Rates
30.2 TIMING ADJUSTMENTS
Application 1 Revisited
30.3 QUANTOS
Using Traditional Risk-Neutral Measures
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
APPENDIX PROOF OF THE CONVEXITY ADJUSTMENT FORMULA
Chapter 31 Equilibrium Models of the Short Rate
31.1 BACKGROUND
31.2 ONE-FACTOR MODELS
The Rendleman and Bartter Model
The Vasicek Model
The Cox, Ingersoll, and Ross Model
Properties of Vasicek and CIR
The Bond Price Process
31.3 REAL-WORLD VS. RISK-NEUTRAL PROCESSES
31.4 ESTIMATING PARAMETERS
31.5 MORE SOPHISTICATED MODELS
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 32 No-Arbitrage Models of the Short Rate
32.1 EXTENSIONS OF EQUILIBRIUM MODELS
The Ho–Lee Model
The Hull–White One-Factor Model
The Black–Derman–Toy Model
The Black–Karasinski Model
The Hull–White Two-Factor Model
32.2 OPTIONS ON BONDS
Options on Coupon-Bearing Bonds
32.3 VOLATILITY STRUCTURES
32.4 INTEREST RATE TREES
Illustration of Use of Trinomial Trees
Nonstandard Branching
32.5 A GENERAL TREE-BUILDING PROCEDURE
First Stage
Second Stage
Illustration of Second Stage
Formulas for ?’s and Q’s
Extension to Other Models
Negative Rates
OIS Discounting
Using Analytic Results in Conjunction with Trees
Tree for American Bond Options
32.6 CALIBRATION
32.7 HEDGING USING A ONE-FACTOR MODEL
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 33 HJM, LMM, and Multiple Zero Curves
33.1 THE HEATH, JARROW, AND MORTON MODEL
Processes for Zero-Coupon Bond Prices and Forward Rates
Extension to Several Factors
33.2 THE LIBOR MARKET MODEL
The Model
Forward Rate Volatilities
Implementation of the Model
Extension to Several Factors
Ratchet Caps, Sticky Caps, and Flexi Caps
Valuing European Swap Options
Calibrating the Model
Volatility Skews
Bermudan Swap Options
33.3 HANDLING MULTIPLE ZERO CURVES
33.4 AGENCY MORTGAGE-BACKED SECURITIES
Collateralized Mortgage Obligations
Valuing Agency Mortgage-Backed Securities
Option-Adjusted Spread
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 34 Swaps Revisited
34.1 VARIATIONS ON THE VANILLA DEAL
34.2 COMPOUNDING SWAPS
34.3 CURRENCY SWAPS
34.4 MORE COMPLEX SWAPS
LIBOR-in-Arrears Swap
CMS and CMT Swaps
Differential Swaps
34.5 EQUITY SWAPS
34.6 SWAPS WITH EMBEDDED OPTIONS
Accrual Swaps
Cancelable Swap
Cancelable Compounding Swaps
34.7 OTHER SWAPS
Bizarre Deals
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 35 Energy and Commodity Derivatives
35.1 AGRICULTURAL COMMODITIES
35.2 METALS
35.3 ENERGY PRODUCTS
Crude Oil
Natural Gas
Electricity
35.4 MODELING COMMODITY PRICES
A Simple Process
Mean Reversion
Interpolation and Seasonality
Jumps
Other Models
35.5 WEATHER DERIVATIVES
35.6 INSURANCE DERIVATIVES
35.7 PRICING WEATHER AND INSURANCE DERIVATIVES
35.8 HOW AN ENERGY PRODUCER CAN HEDGE RISKS
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 36 Real Options
36.1 CAPITAL INVESTMENT APPRAISAL
36.2 EXTENSION OF THE RISK-NEUTRAL VALUATION FRAMEWORK
36.3 ESTIMATING THE MARKET PRICE OF RISK
36.4 APPLICATION TO THE VALUATION OF A BUSINESS
36.5 EVALUATING OPTIONS IN AN INVESTMENT OPPORTUNITY
Illustration
Evaluation with No Embedded Options
Use of a Tree
Option to Abandon
Option to Expand
Multiple Options
Several Stochastic Variables
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 37 Derivatives Mishaps and What We Can Learn from Them
37.1 LESSONS FOR ALL USERS OF DERIVATIVES
Define Risk Limits
Take the Risk Limits Seriously
Do Not Assume You Can Outguess the Market
Do Not Underestimate the Benefits of Diversification
Carry out Scenario Analyses and Stress Tests
37.2 LESSONS FOR FINANCIAL INSTITUTIONS
Monitor Traders Carefully
Separate the Front, Middle, and Back Office
Do Not Blindly Trust Models
Be Conservative in Recognizing Inception Profits
Do Not Sell Clients Inappropriate Products
Beware of Easy Profits
Do Not Ignore Liquidity Risk
Beware When Everyone Is Following the Same Trading Strategy
Do Not Make Excessive Use of Short-Term Funding for Long-Term Needs
Market Transparency Is Important
Manage Incentives
Never Ignore Risk Management
37.3 LESSONS FOR NONFINANCIAL CORPORATIONS
Make Sure You Fully Understand the Trades You Are Doing
Make Sure a Hedger Does Not Become a Speculator
Be Cautious about Making the Treasury Department a Profit Center
Summary
Further Reading
Glossary of Terms
DerivaGem Software
Major Exchanges Trading Futures and Options
Table for N(x) When x?0.
Table for N(x) When x?0
Author Index
Subject Index
