### 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

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