Test bank for Options Futures and Other Derivatives 9th Edition by John C. Hull
Test bank for Options Futures and Other Derivatives 9th Edition by John C. Hull
For graduate courses in business, economics, financial mathematics, and financial engineering; for advanced undergraduate courses with students who have good quantitative skills; and for practitioners involved in derivatives markets
Practitioners refer to it as “the bible;” in the university and college marketplace it’s the best seller, and now it’s been revised and updated to cover the industry’s hottest topics and the most up-to-date material on new regulations. Options, Futures, and Other Derivatives by John C. Hull bridge the gap between theory and practice by providing a current look at the industry, a careful balance of mathematical sophistication, and an outstanding ancillary package that makes it accessible to a wide audience. Through its coverage of important topics such as the securitization and the credit crisis, the overnight indexed swap, the Black-Scholes-Merton formulas, and the way commodity prices are modeled and commodity derivatives valued, it helps students and practitioners alike keep up with the fast pace of change in today’s derivatives markets.
Table of contents
Options, Futures, and Other Derivatives
Options, Futures, and Other Derivatives
Business Snapshots
Technical Notes
Preface
What’s New in the Ninth Edition?
DerivaGem Software
Slides
Solutions Manual
Instructor’s Manual
Technical Notes
Acknowledgments
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 Mechanics of Futures Markets
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
Example 3.1
Example 3.2
3.4 Cross Hedging
Calculating the Minimum Variance Hedge Ratio
Optimal Number of Contracts
Example 3.3
Tailing the Hedge
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
The Fed Funds Rate
Repo Rates
The “Risk-Free” Rate
4.2 Measuring Interest Rates
Continuous Compounding
Example 4.1
Example 4.2
4.3 Zero Rates
4.4 Bond Pricing
Bond Yield
Par Yield
4.5 Determining Treasury Zero Rates
4.6 Forward Rates
4.7 Forward Rate Agreements
Example 4.3
Valuation
Example 4.4
4.8 Duration
Example 4.5
Modified Duration
Example 4.6
Bond Portfolios
4.9 Convexity
4.10 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
Example 5.1
What If Short Sales Are Not Possible?
5.5 Known Income
A Generalization
Example 5.2
5.6 Known Yield
Example 5.3
5.7 Valuing Forward Contracts
Example 5.4
5.8 Are Forward Prices and Futures Prices Equal?
5.9 Futures Prices of Stock Indices
Example 5.5
Index Arbitrage
5.10 Forward and Futures Contracts on Currencies
Example 5.6
Example 5.7
A Foreign Currency as an Asset Providing a Known Yield
5.11 Futures on Commodities
Income and Storage Costs
Example 5.8
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 US Treasury Bills
Price Quotations of US Treasury Bonds
6.2 Treasury Bond Futures
Quotes
Conversion Factors
Cheapest-to-Deliver Bond
Example 6.1
Determining the Futures Price
Example 6.2
6.3 Eurodollar Futures
Example 6.3
Forward vs. Futures Interest Rates
Convexity Adjustment
Example 6.4
Using Eurodollar Futures to Extend the LIBOR Zero Curve
Example 6.5
6.4 Duration-Based Hedging Strategies Using Futures
Example 6.6
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
Role of Financial Intermediary
Market Makers
7.2 Day Count Issues
7.3 Confirmations
7.4 The Comparative-Advantage Argument
Criticism of the Argument
7.5 The Nature of Swap Rates
7.6 Determining Libor/Swap Zero Rates
Example 7.1
7.7 Valuation of Interest Rate Swaps
Valuation in Terms of Bond Prices
Example 7.2
Valuation in Terms of FRAs
Example 7.3
7.8 Term Structure Effects
7.9 Fixed-for-Fixed Currency Swaps
Illustration
Use of a Currency Swap to Transform Liabilities and Assets
Comparative Advantage
7.10 Valuation of Fixed-for-Fixed Currency Swaps
Valuation in Terms of Bond Prices
Example 7.4
Valuation as Portfolio of Forward Contracts
Example 7.5
7.11 Other Currency Swaps
7.12 Credit Risk
Central Clearing
Credit Default Swaps
7.13 Other Types of Swaps
Variations on the Standard Interest Rate Swap
Diff Swaps
Equity Swaps
Options
Commodity Swaps, Volatility Swaps, and Other Exotic Instruments
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 US 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 OIS Discounting, Credit Issues, and Funding Costs
9.1 The Risk-Free Rate
9.2 The OIS Rate
Example 9.1
Determining the OIS Zero Curve
9.3 Valuing Swaps and Fras with OIS Discounting
Determining Forward LIBOR Rates with OIS Discounting
Example 9.2
Example 9.3
9.4 OIS vs. Libor: Which is Correct?
9.5 Credit Risk: CVA and DVA
Collateral
9.6 Funding Costs
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
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
Example 10.1
Example 10.2
Position Limits and Exercise Limits
10.5 Trading
Market Makers
Offsetting Orders
10.6 Commissions
10.7 Margin Requirements
Writing Naked Options
Example 10.3
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
Example 11.1
Lower Bound for European Puts on Non-Dividend-Paying Stocks
Example 11.2
11.4 Put – Call Parity
American Options
Example 11.3
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
Example 12.1
12.2 Trading an Option and the Underlying Asset
12.3 Spreads
Bull Spreads
Example 12.2
Bear Spreads
Example 12.3
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
Example 13.1
Options on Currencies
Example 13.2
Options on Futures
Example 13.3
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
Example 14.1
Generalized Wiener Process
Example 14.2
Itô Process
14.3 The Process for a Stock Price
Discrete-Time Model
Example 14.3
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
On Efficient Markets and the Markov Property of Stock Prices
On Stochastic Processes
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 15 The Black–Scholes–Merton Model
15.1 Lognormal Property of Stock Prices
Example 15.1
Example 15.2
15.2 The Distribution of the Rate of Return
Example 15.3
15.3 The Expected Return
15.4 Volatility
Estimating Volatility from Historical Data
Example 15.4
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
Example 15.5
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
Example 15.6
15.10 Warrants and Employee Stock Options
Example 15.7
15.11 Implied Volatilities
The VIX Index
Example 15.8
15.12 Dividends
European Options
Example 15.9
American Call Options
Black’s Approximation
Summary
Further Reading
On the Distribution of Stock Price Changes
On the Black–Scholes–Merton Analysis
On Risk-Neutral Valuation
Practice Questions (Answers in Solutions Manual)
Further Questions
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
Example 16.1
Binomial Tree Approach
Example 16.2
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
Example 17.1
Forward Prices
Implied Dividend Yields
17.5 Valuation of European Currency Options
Example 17.2
Using Forward Exchange Rates
17.6 American Options
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 18 Futures Options
18.1 Nature of Futures Options
Example 18.1
Example 18.2
Expiration Months
Options on Interest Rate Futures
Example 18.3
Example 18.4
18.2 Reasons for the Popularity of Futures Options
18.3 European Spot and Futures Options
18.4 Put–Call Parity
Example 18.5
18.5 Bounds for Futures Options
18.6 Valuation of Futures Options Using Binomial Trees
A Generalization
Multistep Trees
18.7 Drift of a Futures Price in a Risk-Neutral World
Differential Equation
18.8 Black’s Model For Valuing Futures Options
Example 18.6
Using Black’s Model Instead of Black–Scholes–Merton
Example 18.7
18.9 American Futures Options Vs. American Spot Options
18.10 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
19.3 A Stop-Loss Strategy
19.4 Delta Hedging
Delta of European Stock Options
Example 19.1
Dynamic Aspects of Delta Hedging
Where the Cost Comes From
Delta of a Portfolio
Transaction Costs
19.5 Theta
Example 19.2
19.6 Gamma
Example 19.3
Making a Portfolio Gamma Neutral
Calculation of Gamma
Example 19.4
19.7 Relationship Between Delta, Theta, and Gamma
19.8 Vega
Example 19.5
Example 19.6
19.9 RHO
Example 19.7
19.10 The Realities of Hedging
19.11 Scenario Analysis
19.12 Extension of Formulas
Delta of Forward Contracts
Delta of a Futures Contract
Example 19.8
19.13 Portfolio Insurance
Example 19.9
Use of Index Futures
Example 19.10
19.14 Stock Market Volatility
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
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
Example 20.1
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 Greek Letters
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
Example 20A.1
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
Example 21.1
Expressing the Approach Algebraically
Estimating Delta and Other Greek Letters
Example 21.2
21.2 Using the Binomial Tree for Options on Indices, Currencies, and Futures Contracts
Example 21.3
Example 21.4
21.3 Binomial Model for a Dividend-Paying Stock
Known Dividend Yield
Known Dollar Dividend
Example 21.5
Control Variate Technique
21.4 Alternative Procedures for Constructing Trees
Example 21.6
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
Example 21.7
Example 21.8
Sampling through a Tree
Example 21.9
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
Example 21.10
Explicit Finite Difference Method
Example 21.11
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
22.1 The VaR Measure
The Time Horizon
22.2 Historical Simulation
Illustration: Investment in Four Stock Indices
22.3 Model-Building Approach
Daily Volatilities
Single-Asset Case
Two-Asset Case
The Benefits of Diversification
22.4 The Linear Model
Correlation and Covariance Matrices
Handling Interest Rates
Applications of the Linear Model
The Linear Model and Options
Example 22.1
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
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
Example 23.1
23.3 The Garch(1, 1) Model
Example 23.2
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
Example 23.3
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
Example 24.1
Matching Bond Prices
Example 24.2
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
Example 24.3
24.7 Credit Risk in Derivatives Transactions
CVA and DVA
Example 24.4
Credit Risk Mitigation
Special Cases
Example 24.5
Example 24.6
24.8 Default Correlation
The Gaussian Copula Model for Time to Default
Example 24.6
A Factor-Based Correlation Structure
24.9 Credit Var
Example 24.7
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
Example 25.1
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
Example 25.2
Valuation of kth-to-Default CDS
Example 25.3
Implied Correlation
Valuing Nonstandard Tranches
25.11 Alternatives to the Standard Market Model
Heterogeneous Model
Other Copulas
Random 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
Example 26.1
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
Example 26.2
26.12 Shout Options
26.13 Asian Options
Example 26.3
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
Example 26.4
Valuation of a Volatility Swap
Example 26.5
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
The Variance-Gamma Model
27.2 Stochastic Volatility Models
27.3 The IVF Model
27.4 Convertible Bonds
Example 27.1
27.5 Path-Dependent Derivatives
Illustration Using Lookback Options
Generalization
27.6 Barrier Options
The Adaptive Mesh Model
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
Example 28.1
Example 28.2
Alternative Worlds
28.2 Several State Variables
Example 28.3
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
Interest Rates When Zero-Coupon Bond Price is the Numeraire
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
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
Example 29.1
Yield Volatilities
Example 29.2
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
Example 29.3
Spot Volatilities vs. Flat Volatilities
Theoretical Justification for the Model
Use of DerivaGem
The Impact of Day Count Conventions
29.3 European Swap Options
Valuation of European Swaptions
Example 29.4
Broker Quotes
Theoretical Justification for the Swaption Model
The Impact of Day Count Conventions
29.4 Ois Discounting
29.5 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
Example 30.1
Application 2: Swap Rates
Example 30.2
30.2 Timing Adjustments
Example 30.3
Application 1 Revisited
30.3 Quantos
Example 30.4
Using Traditional Risk-Neutral Measures
Example 30.5
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter31 Interest Rate Derivatives: Models of the Short Rate
31.1 Background
31.2 Equilibrium Models
The Rendleman and Bartter Model
The Vasicek Model
The Cox, Ingersoll, and Ross Model
Properties of Vasicek and CIR
Example 31.1
Applications of Equilibrium Models
Example 31.2
Example 31.3
31.3 No-Arbitrage 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
31.4 Options on Bonds
Options on Coupon-Bearing Bonds
31.5 Volatility Structures
31.6 Interest Rate Trees
Illustration of Use of Trinomial Trees
Nonstandard Branching
31.7 A General Tree-Building Procedure
First Stage
Second Stage
Illustration of Second Stage
Formulas for α’s and Q’s
Extension to Other Models
Handling Low Interest Rate Environments
Using Analytic Results in Conjunction with Trees
Example 31.1
Tree for American Bond Options
31.8 Calibration
31.9 Hedging Using A One-Factor Model
Summary
Further Reading
Equilibrium Models
No-Arbitrage Models
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 32 HJM, LMM, and Multiple Zero Curves
32.1 The Heath, Jarrow, and Morton Model
Processes for Zero-Coupon Bond Prices and Forward Rates
Extension to Several Factors
32.2 The Libor Market Model
The Model
Forward Rate Volatilities
Example 32.1
Example 32.2
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
32.3 Handling Multiple Zero Curves
32.4 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 33 Swaps Revisited
33.1 Variations on the Vanilla Deal
33.2 Compounding Swaps
Example 33.1
33.3 Currency Swaps
33.4 More Complex Swaps
LIBOR-in-Arrears Swap
Example 33.2
CMS and CMT Swaps
Example 33.3
Differential Swaps
Example 33.4
33.5 Equity Swaps
33.6 Swaps with Embedded Options
Accrual Swaps
Cancelable Swap
Cancelable Compounding Swaps
33.7 Other Swaps
Bizarre Deals
Summary
Further Reading
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 34 Energy and Commodity Derivatives
34.1 Agricultural Commodities
34.2 Metals
34.3 Energy Products
Crude Oil
Natural Gas
Electricity
34.4 Modeling Commodity Prices
A Simple Process
Example 34.1
Example 34.2
Mean Reversion
Example 34.3
Interpolation and Seasonality
Jumps
Other Models
34.5 Weather Derivatives
34.6 Insurance Derivatives
34.7 Pricing Weather and Insurance Derivatives
Example 34.4
34.8 How an Energy Producer Can Hedge Risks
Summary
Further Reading
On commodity derivatives
On weather derivatives
On insurance derivatives
Practice Questions (Answers in Solutions Manual)
Further Questions
Chapter 35 Real Options
35.1 Capital Investment Appraisal
35.2 Extension of the Risk-Neutral Valuation Framework
Example 35.1
35.3 Estimating the Market Price of Risk
Example 35.2
35.4 Application to the Valuation of a Business
35.5 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 36 Derivatives Mishaps and What We Can Learn from Them
36.1 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
36.2 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
36.3 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
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
Free Sample Test bank for Options Futures and Other Derivatives 9th Edition by John C. Hull
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Test bank for Options Futures and Other Derivatives 9th Edition by John C. Hull
