Options, Futures, and Other Derivatives, Ninth Edition

Book Description

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 bridges 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.

 

This program provides a better teaching and learning experience—for you and your students. Here's how:

  • NEW! Available with a new version of DerivaGem software—including two Excel applications, the Options Calculator and the Applications Builder
  • Bridges the gap between theory and practice—a best-selling college text, and considered “the bible” by practitioners, it provides the latest information in the industry
  • Provides the right balance of mathematical sophistication—careful attention to mathematics and notation
  • Offers outstanding ancillaries toround out the high quality of the teaching and learning package

Table of Contents

  1. Options, Futures, and Other Derivatives
  2. Options, Futures, and Other Derivatives
  3. Business Snapshots
  4. Technical Notes
  5. Preface
    1. What’s New in the Ninth Edition?
    2. DerivaGem Software
    3. Slides
    4. Solutions Manual
    5. Instructor’s Manual
    6. Technical Notes
    7. Acknowledgments
  6. Chapter 1 Introduction
    1. 1.1 Exchange-Traded Markets
      1. Electronic Markets
    2. 1.2 Over-The-Counter Markets
      1. Market Size
    3. 1.3 Forward Contracts
      1. Payoffs from Forward Contracts
      2. Forward Prices and Spot Prices
    4. 1.4 Futures Contracts
    5. 1.5 Options
    6. 1.6 Types of Traders
    7. 1.7 Hedgers
      1. Hedging Using Forward Contracts
      2. Hedging Using Options
      3. A Comparison
    8. 1.8 Speculators
      1. Speculation Using Futures
      2. Speculation Using Options
      3. A Comparison
    9. 1.9 Arbitrageurs
    10. 1.10 Dangers
    11. Summary
    12. Further Reading
    13. Practice Questions (Answers in Solutions Manual)
    14. Further Questions
  7. Chapter 2 Mechanics of Futures Markets
    1. 2.1 Background
      1. Closing Out Positions
    2. 2.2 Specification of a Futures Contract
      1. The Asset
      2. The Contract Size
      3. Delivery Arrangements
      4. Delivery Months
      5. Price Quotes
      6. Price Limits and Position Limits
    3. 2.3 Convergence of Futures Price to Spot Price
    4. 2.4 The Operation of Margin Accounts
      1. Daily Settlement
      2. Further Details
      3. The Clearing House and Its Members
      4. Credit Risk
    5. 2.5 OTC Markets
      1. Central Counterparties
      2. Bilateral Clearing
      3. Futures Trades vs. OTC Trades
    6. 2.6 Market Quotes
      1. Prices
      2. Settlement Price
      3. Trading Volume and Open Interest
      4. Patterns of Futures
    7. 2.7 Delivery
      1. Cash Settlement
    8. 2.8 Types of Traders and Types of Orders
      1. Orders
    9. 2.9 Regulation
      1. Trading Irregularities
    10. 2.10 Accounting and Tax
      1. Accounting
      2. Tax
    11. 2.11 Forward vs. Futures Contracts
      1. Profits from Forward and Futures Contracts
      2. Foreign Exchange Quotes
    12. Summary
    13. Further Reading
    14. Practice Questions (Answers in Solutions Manual)
    15. Further Questions
  8. Chapter 3 Hedging Strategies Using Futures
    1. 3.1 Basic Principles
      1. Short Hedges
      2. Long Hedges
    2. 3.2 Arguments for and Against Hedging
      1. Hedging and Shareholders
      2. Hedging and Competitors
      3. Hedging Can Lead to a Worse Outcome
    3. 3.3 Basis Risk
      1. The Basis
      2. Choice of Contract
        1. Example 3.1
        2. Example 3.2
    4. 3.4 Cross Hedging
      1. Calculating the Minimum Variance Hedge Ratio
      2. Optimal Number of Contracts
        1. Example 3.3
      3. Tailing the Hedge
    5. 3.5 Stock Index Futures
      1. Stock Indices
      2. Hedging an Equity Portfolio
      3. Reasons for Hedging an Equity Portfolio
      4. Changing the Beta of a Portfolio
      5. Locking in the Benefits of Stock Picking
    6. 3.6 Stack and Roll
    7. Summary
    8. Further Reading
    9. Practice Questions (Answers in Solutions Manual)
    10. Further Questions
    11. Appendix Capital Asset Pricing Model
  9. Chapter 4 Interest Rates
    1. 4.1 Types of Rates
      1. Treasury Rates
      2. Libor
      3. The Fed Funds Rate
      4. Repo Rates
      5. The “Risk-Free” Rate
    2. 4.2 Measuring Interest Rates
      1. Continuous Compounding
        1. Example 4.1
        2. Example 4.2
    3. 4.3 Zero Rates
    4. 4.4 Bond Pricing
      1. Bond Yield
      2. Par Yield
    5. 4.5 Determining Treasury Zero Rates
    6. 4.6 Forward Rates
    7. 4.7 Forward Rate Agreements
      1. Example 4.3
      2. Valuation
        1. Example 4.4
    8. 4.8 Duration
      1. Example 4.5
      2. Modified Duration
        1. Example 4.6
      3. Bond Portfolios
    9. 4.9 Convexity
    10. 4.10 Theories of the Term Structure of Interest Rates
      1. The Management of Net Interest Income
      2. Liquidity
    11. Summary
    12. Further Reading
    13. Practice Questions (Answers in Solutions Manual)
    14. Further Questions
  10. Chapter 5 Determination of Forward and Futures Prices
    1. 5.1 Investment Assets vs. Consumption Assets
    2. 5.2 Short Selling
    3. 5.3 Assumptions and Notation
    4. 5.4 Forward Price for an Investment Asset
      1. A Generalization
        1. Example 5.1
      2. What If Short Sales Are Not Possible?
    5. 5.5 Known Income
      1. A Generalization
        1. Example 5.2
    6. 5.6 Known Yield
      1. Example 5.3
    7. 5.7 Valuing Forward Contracts
      1. Example 5.4
    8. 5.8 Are Forward Prices and Futures Prices Equal?
    9. 5.9 Futures Prices of Stock Indices
      1. Example 5.5
      2. Index Arbitrage
    10. 5.10 Forward and Futures Contracts on Currencies
      1. Example 5.6
      2. Example 5.7
      3. A Foreign Currency as an Asset Providing a Known Yield
    11. 5.11 Futures on Commodities
      1. Income and Storage Costs
        1. Example 5.8
      2. Consumption Commodities
      3. Convenience Yields
    12. 5.12 The Cost of Carry
    13. 5.13 Delivery Options
    14. 5.14 Futures Prices and Expected Future Spot Prices
      1. Keynes and Hicks
      2. Risk and Return
      3. The Risk in a Futures Position
      4. Normal Backwardation and Contango
    15. Summary
    16. Further Reading
    17. Practice Questions (Answers in Solutions Manual)
    18. Further Questions
  11. Chapter 6 Interest Rate Futures
    1. 6.1 Day Count and Quotation Conventions
      1. Day Counts
      2. Price Quotations of US Treasury Bills
      3. Price Quotations of US Treasury Bonds
    2. 6.2 Treasury Bond Futures
      1. Quotes
      2. Conversion Factors
      3. Cheapest-to-Deliver Bond
        1. Example 6.1
      4. Determining the Futures Price
        1. Example 6.2
    3. 6.3 Eurodollar Futures
      1. Example 6.3
      2. Forward vs. Futures Interest Rates
      3. Convexity Adjustment
        1. Example 6.4
      4. Using Eurodollar Futures to Extend the LIBOR Zero Curve
        1. Example 6.5
    4. 6.4 Duration-Based Hedging Strategies Using Futures
      1. Example 6.6
    5. 6.5 Hedging Portfolios of Assets and Liabilities
    6. Summary
    7. Further Reading
    8. Practice Questions (Answers in Solutions Manual)
    9. Further Questions
  12. Chapter 7 Swaps
    1. 7.1 Mechanics of Interest Rate Swaps
      1. Libor
      2. Illustration
      3. Using the Swap to Transform a Liability
      4. Using the Swap to Transform an Asset
      5. Role of Financial Intermediary
      6. Market Makers
    2. 7.2 Day Count Issues
    3. 7.3 Confirmations
    4. 7.4 The Comparative-Advantage Argument
      1. Criticism of the Argument
    5. 7.5 The Nature of Swap Rates
    6. 7.6 Determining Libor/Swap Zero Rates
      1. Example 7.1
    7. 7.7 Valuation of Interest Rate Swaps
      1. Valuation in Terms of Bond Prices
        1. Example 7.2
      2. Valuation in Terms of FRAs
        1. Example 7.3
    8. 7.8 Term Structure Effects
    9. 7.9 Fixed-for-Fixed Currency Swaps
      1. Illustration
      2. Use of a Currency Swap to Transform Liabilities and Assets
      3. Comparative Advantage
    10. 7.10 Valuation of Fixed-for-Fixed Currency Swaps
      1. Valuation in Terms of Bond Prices
        1. Example 7.4
      2. Valuation as Portfolio of Forward Contracts
        1. Example 7.5
    11. 7.11 Other Currency Swaps
    12. 7.12 Credit Risk
      1. Central Clearing
      2. Credit Default Swaps
    13. 7.13 Other Types of Swaps
      1. Variations on the Standard Interest Rate Swap
      2. Diff Swaps
      3. Equity Swaps
      4. Options
      5. Commodity Swaps, Volatility Swaps, and Other Exotic Instruments
    14. Summary
    15. Further Reading
    16. Practice Questions (Answers in Solutions Manual)
    17. Further Questions
  13. Chapter 8 Securitization and the Credit Crisis of 2007
    1. 8.1 Securitization
      1. ABSs
      2. ABS CDOs
    2. 8.2 The US Housing Market
      1. The Relaxation of Lending Standards
      2. Subprime Mortgage Securitization
      3. The Bubble Bursts
      4. The Losses
      5. The Credit Crisis
    3. 8.3 What Went Wrong?
      1. Regulatory Arbitrage
      2. Incentives
    4. 8.4 The Aftermath
    5. Summary
    6. Further Reading
    7. Practice Questions (Answers in Solutions Manual)
    8. Further Questions
  14. Chapter 9 OIS Discounting, Credit Issues, and Funding Costs
    1. 9.1 The Risk-Free Rate
    2. 9.2 The OIS Rate
      1. Example 9.1
      2. Determining the OIS Zero Curve
    3. 9.3 Valuing Swaps and Fras with OIS Discounting
      1. Determining Forward LIBOR Rates with OIS Discounting
        1. Example 9.2
        2. Example 9.3
    4. 9.4 OIS vs. Libor: Which is Correct?
    5. 9.5 Credit Risk: CVA and DVA
      1. Collateral
    6. 9.6 Funding Costs
    7. Summary
    8. Further Reading
    9. Practice Questions (Answers in Solutions Manual)
    10. Further Questions
  15. Chapter 10 Mechanics of Options Markets
    1. 10.1 Types of Options
      1. Call Options
      2. Put Options
      3. Early Exercise
    2. 10.2 Option Positions
    3. 10.3 Underlying Assets
      1. Stock Options
      2. Foreign Currency Options
      3. Index Options
      4. Futures Options
    4. 10.4 Specification of Stock Options
      1. Expiration Dates
      2. Strike Prices
      3. Terminology
      4. FLEX Options
      5. Other Nonstandard Products
      6. Dividends and Stock Splits
        1. Example 10.1
        2. Example 10.2
      7. Position Limits and Exercise Limits
    5. 10.5 Trading
      1. Market Makers
      2. Offsetting Orders
    6. 10.6 Commissions
    7. 10.7 Margin Requirements
      1. Writing Naked Options
        1. Example 10.3
      2. Other Rules
    8. 10.8 The Options Clearing Corporation
      1. Exercising an Option
    9. 10.9 Regulation
    10. 10.10 Taxation
      1. Wash Sale Rule
      2. Constructive Sales
    11. 10.11 Warrants, Employee Stock Options, and Convertibles
    12. 10.12 Over-the-Counter Options Markets
    13. Summary
    14. Further Reading
    15. Practice Questions (Answers in Solutions Manual)
    16. Further Questions
  16. Chapter 11 Properties of Stock Options
    1. 11.1 Factors Affecting Option Prices
      1. Stock Price and Strike Price
      2. Time to Expiration
      3. Volatility
      4. Risk-Free Interest Rate
      5. Amount of Future Dividends
    2. 11.2 Assumptions and Notation
    3. 11.3 Upper and Lower Bounds for Option Prices
      1. Upper Bounds
      2. Lower Bound for Calls on Non-Dividend-Paying Stocks
        1. Example 11.1
      3. Lower Bound for European Puts on Non-Dividend-Paying Stocks
        1. Example 11.2
    4. 11.4 Put – Call Parity Put – Call Parity
      1. American Options
        1. Example 11.3
    5. 11.5 Calls on a Non-Dividend-Paying Stock
      1. Bounds
    6. 11.6 Puts on a Non-Dividend-Paying Stock
      1. Bounds
    7. 11.7 Effect of Dividends
      1. Lower Bound for Calls and Puts
      2. Early Exercise
      3. Put–Call Parity
    8. Summary
    9. Further Reading
    10. Practice Questions (Answers in Solutions Manual)
    11. Further Questions
  17. CHAPTER 12 Trading Strategies Involving Options
    1. 12.1 Principal-Protected Notes
      1. Example 12.1
    2. 12.2 Trading an Option and the Underlying Asset
    3. 12.3 Spreads
      1. Bull Spreads
        1. Example 12.2
      2. Bear Spreads
        1. Example 12.3
      3. Box Spreads
      4. Butterfly Spreads
      5. Calendar Spreads
      6. Diagonal Spreads
    4. 12.4 Combinations
      1. Straddle
      2. Strips and Straps
      3. Strangles
    5. 12.5 Other Payoffs
    6. Summary
    7. Further Reading
    8. Practice Questions (Answers in Solutions Manual)
    9. Further Questions
  18. CHAPTER 13 Binomial Trees
    1. 13.1 A One-Step Binomial Model and a No-Arbitrage Argument
      1. A Generalization
      2. Irrelevance of the Stock’s Expected Return
    2. 13.2 Risk-Neutral Valuation
      1. The One-Step Binomial Example Revisited
      2. Real World vs. Risk-Neutral World
    3. 13.3 Two-Step Binomial Trees
      1. A Generalization
    4. 13.4 A Put Example
    5. 13.5 American Options
    6. 13.6 Delta
    7. 13.7 Matching Volatility with u and d
      1. Girsanov’s Theorem
    8. 13.8 The Binomial Tree Formulas
    9. 13.9 Increasing the Number of Steps
    10. 13.10 USING DerivaGem
    11. 13.11 Options on Other Assets
      1. Options on Stocks Paying a Continuous Dividend Yield
      2. Options on Stock Indices
        1. Example 13.1
      3. Options on Currencies
        1. Example 13.2
      4. Options on Futures
        1. Example 13.3
    12. Summary
    13. Further Reading
    14. Practice Questions (Answers in Solutions Manual)
    15. Further Questions
    16. Appendix Derivation of the Black–Scholes–Merton Option-Pricing Formula from a Binomial Tree
  19. Chapter 14 Wiener Processes and Itô’s Lemma Wiener Processes and Itô’s Lemma
    1. 14.1 The Markov Property
    2. 14.2 Continuous-Time Stochastic Processes
      1. Wiener Process
        1. Example 14.1
      2. Generalized Wiener Process
        1. Example 14.2
      3. Itô Process
    3. 14.3 The Process for a Stock Price
      1. Discrete-Time Model
        1. Example 14.3
      2. Monte Carlo Simulation
    4. 14.4 The Parameters
    5. 14.5 Correlated Processes
    6. 14.6 Itô’s Lemma Itô’s Lemma
      1. Application to Forward Contracts
    7. 14.7 The Lognormal Property
    8. Summary
    9. Further Reading
      1. On Efficient Markets and the Markov Property of Stock Prices
      2. On Stochastic Processes
      3. Practice Questions (Answers in Solutions Manual)
      4. Further Questions
  20. Chapter 15 The Black–Scholes–Merton Model The Black–Scholes–Merton Model
    1. 15.1 Lognormal Property of Stock Prices
      1. Example 15.1
      2. Example 15.2
    2. 15.2 The Distribution of the Rate of Return
      1. Example 15.3
    3. 15.3 The Expected Return
    4. 15.4 Volatility
      1. Estimating Volatility from Historical Data
        1. Example 15.4
      2. Trading Days vs. Calendar Days
    5. 15.5 The Idea Underlying the Black–Scholes–Merton Differential Equation The Idea Underlying the Black–Scholes–Merton Differential Equation
      1. Assumptions
    6. 15.6 Derivation of the Black–Scholes–Merton Differential Equation Derivation of the Black–Scholes–Merton Differential Equation
      1. Example 15.5
      2. A Perpetual Derivative
      3. The Prices of Tradeable Derivatives
    7. 15.7 Risk-Neutral Valuation
      1. Application to Forward Contracts on a Stock
    8. 15.8 Black–Scholes–Merton Pricing Formulas Black–Scholes–Merton Pricing Formulas
      1. Understanding N(d1) and N(d2)
      2. Properties of the Black–Scholes–Merton Formulas
    9. 15.9 Cumulative Normal Distribution Function
      1. Example 15.6
    10. 15.10 Warrants and Employee Stock Options
      1. Example 15.7
    11. 15.11 Implied Volatilities
      1. The VIX Index
        1. Example 15.8
    12. 15.12 Dividends
      1. European Options
        1. Example 15.9
      2. American Call Options
      3. Black’s Approximation
    13. Summary
    14. Further Reading
      1. On the Distribution of Stock Price Changes
      2. On the Black–Scholes–Merton Analysis
      3. On Risk-Neutral Valuation
      4. Practice Questions (Answers in Solutions Manual)
      5. Further Questions
    15. Key Result
    16. Proof of Key Result
    17. The Black–Scholes–Merton Result
  21. Chapter 16 Employee Stock Options
    1. 16.1 Contractual Arrangements
      1. The Early Exercise Decision
    2. 16.2 Do Options Align The Interests of Shareholders and Managers?
    3. 16.3 Accounting Issues
      1. Alternatives to Stock Options
    4. 16.4 Valuation
      1. The “Quick and Dirty” Approach
        1. Example 16.1
      2. Binomial Tree Approach
        1. Example 16.2
      3. The Exercise Multiple Approach
      4. A Market-Based Approach
      5. Dilution
    5. 16.5 Backdating Scandals
    6. Summary
    7. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  22. Chapter 17 Options on Stock Indices and Currencies
    1. 17.1 Options on Stock Indices
      1. Portfolio Insurance
      2. When the Portfolio’s Beta Is Not 1.0
    2. 17.2 Currency Options
      1. Range Forwards
    3. 17.3 Options on Stocks Paying Known Dividend Yields
      1. Lower Bounds for Option Prices
      2. Put–Call Parity
      3. Pricing Formulas
      4. Differential Equation and Risk-Neutral Valuation
    4. 17.4 Valuation of European Stock Index Options
      1. Example 17.1
      2. Forward Prices
      3. Implied Dividend Yields
    5. 17.5 Valuation of European Currency Options
      1. Example 17.2
      2. Using Forward Exchange Rates
    6. 17.6 American Options
    7. Summary
    8. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  23. Chapter 18 Futures Options
    1. 18.1 Nature of Futures Options
      1. Example 18.1
      2. Example 18.2
      3. Expiration Months
      4. Options on Interest Rate Futures
        1. Example 18.3
        2. Example 18.4
    2. 18.2 Reasons for the Popularity of Futures Options
    3. 18.3 European Spot and Futures Options
    4. 18.4 Put–Call Parity Put–Call Parity
      1. Example 18.5
    5. 18.5 Bounds for Futures Options
    6. 18.6 Valuation of Futures Options Using Binomial Trees
      1. A Generalization
      2. Multistep Trees
    7. 18.7 Drift of a Futures Price in a Risk-Neutral World
      1. Differential Equation
    8. 18.8 Black’s Model For Valuing Futures Options Black’s Model For Valuing Futures Options
      1. Example 18.6
      2. Using Black’s Model Instead of Black–Scholes–Merton
        1. Example 18.7
    9. 18.9 American Futures Options Vs. American Spot Options
    10. 18.10 Futures-Style Options
    11. Summary
    12. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  24. Chapter 19 The Greek Letters
    1. 19.1 Illustration
    2. 19.2 Naked and Covered Positions
    3. 19.3 A Stop-Loss Strategy
    4. 19.4 Delta Hedging
      1. Delta of European Stock Options
        1. Example 19.1
      2. Dynamic Aspects of Delta Hedging
      3. Where the Cost Comes From
      4. Delta of a Portfolio
      5. Transaction Costs
    5. 19.5 Theta
      1. Example 19.2
    6. 19.6 Gamma
      1. Example 19.3
      2. Making a Portfolio Gamma Neutral
      3. Calculation of Gamma
        1. Example 19.4
    7. 19.7 Relationship Between Delta, Theta, and Gamma
    8. 19.8 Vega
      1. Example 19.5
      2. Example 19.6
      3. 19.9 RHO
        1. Example 19.7
    9. 19.10 The Realities of Hedging
    10. 19.11 Scenario Analysis
    11. 19.12 Extension of Formulas
      1. Delta of Forward Contracts
      2. Delta of a Futures Contract
        1. Example 19.8
    12. 19.13 Portfolio Insurance
      1. Example 19.9
      2. Use of Index Futures
        1. Example 19.10
    13. 19.14 Stock Market Volatility
    14. Summary
    15. Further Reading
    16. Practice Questions (Answers in Solutions Manual)
    17. Further Questions
    18. Appendix Taylor Series Expansions and Hedge Parameters
  25. Chapter 20 Volatility Smiles
    1. 20.1 Why the Volatility Smile is the Same for Calls and Puts
      1. Example 20.1
    2. 20.2 Foreign Currency Options
      1. Empirical Results
      2. Reasons for the Smile in Foreign Currency Options
    3. 20.3 Equity Options
      1. The Reason for the Smile in Equity Options
    4. 20.4 Alternative Ways of Characterizing the Volatility Smile
    5. 20.5 The Volatility Term Structure and Volatility Surfaces
    6. 20.6 Greek Letters
    7. 20.7 The Role of the Model
    8. 20.8 When a Single Large Jump is Anticipated
    9. Summary
    10. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
    11. Example 20A.1
  26. Chapter 21 Basic Numerical Procedures
    1. 21.1 Binomial Trees
      1. Risk-Neutral Valuation
      2. Determination of p, u, and d
      3. Tree of Asset Prices
      4. Working Backward through the Tree
        1. Example 21.1
      5. Expressing the Approach Algebraically
      6. Estimating Delta and Other Greek Letters
        1. Example 21.2
    2. 21.2 Using the Binomial Tree for Options on Indices, Currencies, and Futures Contracts
      1. Example 21.3
      2. Example 21.4
    3. 21.3 Binomial Model for a Dividend-Paying Stock
      1. Known Dividend Yield
      2. Known Dollar Dividend
        1. Example 21.5
      3. Control Variate Technique
    4. 21.4 Alternative Procedures for Constructing Trees
      1. Example 21.6
      2. Trinomial Trees
    5. 21.5 Time-Dependent Parameters
    6. 21.6 Monte Carlo Simulation
      1. Derivatives Dependent on More than One Market Variable
      2. Generating the Random Samples from Normal Distributions
      3. Number of Trials
        1. Example 21.7
        2. Example 21.8
      4. Sampling through a Tree
        1. Example 21.9
      5. Calculating the Greek Letters
      6. Applications
    7. 21.7 Variance Reduction Procedures
      1. Antithetic Variable Technique
      2. Control Variate Technique
      3. Importance Sampling
      4. Stratified Sampling
      5. Moment Matching
      6. Using Quasi-Random Sequences
    8. 21.8 Finite Difference Methods
      1. Implicit Finite Difference Method
        1. Example 21.10
      2. Explicit Finite Difference Method
        1. Example 21.11
      3. Change of Variable
      4. Relation to Trinomial Tree Approaches
      5. Other Finite Difference Methods
      6. Applications of Finite Difference Methods
    9. Summary
    10. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  27. Chapter 22 Value at Risk
    1. 22.1 The VaR Measure
      1. The Time Horizon
    2. 22.2 Historical Simulation
      1. Illustration: Investment in Four Stock Indices
    3. 22.3 Model-Building Approach
      1. Daily Volatilities
      2. Single-Asset Case
      3. Two-Asset Case
      4. The Benefits of Diversification
    4. 22.4 The Linear Model
      1. Correlation and Covariance Matrices
      2. Handling Interest Rates
      3. Applications of the Linear Model
      4. The Linear Model and Options
        1. Example 22.1
    5. 22.5 The Quadratic Model
    6. 22.6 Monte Carlo Simulation
    7. 22.7 Comparison of Approaches
    8. 22.8 Stress Testing and Back Testing
    9. 22.9 Principal Components Analysis
      1. Using Principal Components Analysis to Calculate VaR
    10. Summary
    11. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  28. Chapter 23 Estimating Volatilities and Correlations
    1. 23.1 Estimating Volatility
      1. Weighting Schemes
    2. 23.2 The Exponentially Weighted Moving Average Model
      1. Example 23.1
    3. 23.3 The Garch(1, 1) Model
      1. Example 23.2
      2. The Weights
      3. Mean Reversion
    4. 23.4 Choosing Between the Models
      1. 23.5 Maximum Likelihood Methods
      2. Estimating a Constant Variance
      3. Estimating EWMA or GARCH (1,1) Parameters
      4. How Good Is the Model?
    5. 23.6 Using Garch(1,1) to Forecast Future Volatility
      1. Volatility Term Structures
      2. Impact of Volatility Changes
    6. 23.7 Correlations
      1. Example 23.3
      2. Consistency Condition for Covariances
    7. 23.8 Application of Ewma to Four-Index Example
    8. Summary
    9. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  29. Chapter 24 Credit Risk
    1. 24.1 Credit Ratings
    2. 24.2 Historical Default Probabilities
      1. Hazard Rates
    3. 24.3 Recovery Rates
      1. The Dependence of Recovery Rates on Default Rates
    4. 24.4 Estimating Default Probabilities from Bond Yield Spreads
      1. Example 24.1
      2. Matching Bond Prices
        1. Example 24.2
      3. The Risk-Free Rate
      4. Asset Swap Spreads
    5. 24.5 Comparison of Default Probability Estimates
      1. Real-World vs. Risk-Neutral Probabilities
      2. Which Default Probability Estimate Should Be Used?
    6. 24.6 Using Equity Prices to Estimate Default Probabilities
      1. Example 24.3
    7. 24.7 Credit Risk in Derivatives Transactions
      1. CVA and DVA
        1. Example 24.4
      2. Credit Risk Mitigation
      3. Special Cases
        1. Example 24.5
        2. Example 24.6
    8. 24.8 Default Correlation
      1. The Gaussian Copula Model for Time to Default
        1. Example 24.6
      2. A Factor-Based Correlation Structure
    9. 24.9 Credit Var
      1. Example 24.7
      2. CreditMetrics
    10. Summary
    11. Further Reading
      1. Practice Questions (Answers in the Solutions Manual)
      2. Further Questions
  30. Chapter 25 Credit Derivatives
    1. 25.1 Credit Default Swaps
      1. Credit Default Swaps and Bond Yields
      2. The Cheapest-to-Deliver Bond
    2. 25.2 Valuation of Credit Default Swaps
      1. Marking to Market a CDS
      2. Estimating Default Probabilities
      3. Binary Credit Default Swaps
      4. How Important Is the Recovery Rate?
    3. 25.3 Credit Indices
    4. 25.4 The Use of Fixed Coupons
      1. Example 25.1
    5. 25.5 CDS Forwards and Options
    6. 25.6 Basket Credit Default Swaps
    7. 25.7 Total Return Swaps
    8. 25.8 Collateralized Debt Obligations
      1. Synthetic CDOs
      2. Standard Portfolios and Single-Tranche Trading
    9. 25.9 Role of Correlation in a Basket CDS and CDO
    10. 25.10 Valuation of a Synthetic CDO
      1. Using the Gaussian Copula Model of Time to Default
        1. Example 25.2
      2. Valuation of kth-to-Default CDS
        1. Example 25.3
      3. Implied Correlation
      4. Valuing Nonstandard Tranches
    11. 25.11 Alternatives to the Standard Market Model
      1. Heterogeneous Model
      2. Other Copulas
      3. Random Factor Loadings
      4. The Implied Copula Model
      5. Dynamic Models
    12. Summary
    13. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  31. Chapter 26 Exotic Options
    1. 26.1 Packages
    2. 26.2 Perpetual American Call and Put Options
    3. 26.3 Nonstandard American Options
    4. 26.4 Gap Options
      1. Example 26.1
    5. 26.5 Forward Start Options
    6. 26.6 Cliquet Options
    7. 26.7 Compound Options
    8. 26.8 Chooser Options
    9. 26.9 Barrier Options
    10. 26.10 Binary Options
    11. 26.11 Lookback Options
      1. Example 26.2
    12. 26.12 Shout Options
    13. 26.13 Asian Options
      1. Example 26.3
    14. 26.14 Options to Exchange One Asset for Another
    15. 26.15 Options Involving Several Assets
    16. 26.16 Volatility and Variance Swaps
      1. Valuation of Variance Swap
        1. Example 26.4
      2. Valuation of a Volatility Swap
        1. Example 26.5
      3. The VIX Index
    17. 26.17 Static Options Replication
    18. Summary
    19. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  32. Chapter 27 More on Models and Numerical Procedures
    1. 27.1 Alternatives to Black–Scholes–Merton Alternatives to Black–Scholes–Merton
      1. The Constant Elasticity of Variance Model
      2. Merton’s Mixed Jump–Diffusion Model
      3. The Variance-Gamma Model
    2. 27.2 Stochastic Volatility Models
    3. 27.3 The IVF Model
    4. 27.4 Convertible Bonds
      1. Example 27.1
    5. 27.5 Path-Dependent Derivatives
      1. Illustration Using Lookback Options
      2. Generalization
    6. 27.6 Barrier Options
      1. The Adaptive Mesh Model
    7. 27.7 Options on Two Correlated Assets
      1. Transforming Variables
      2. Using a Nonrectangular Tree
      3. Adjusting the Probabilities
    8. 27.8 Monte Carlo Simulation and American Options
      1. The Least-Squares Approach
      2. The Exercise Boundary Parameterization Approach
      3. Upper Bounds
    9. Summary
    10. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  33. Chapter 28 Martingales and Measures
    1. 28.1 The Market Price of Risk
      1. Example 28.1
      2. Example 28.2
      3. Alternative Worlds
    2. 28.2 Several State Variables
      1. Example 28.3
    3. 28.3 Martingales
      1. The Equivalent Martingale Measure Result
    4. 28.4 Alternative Choices for the Numeraire
      1. Money Market Account as the Numeraire
      2. Zero-Coupon Bond Price as the Numeraire
      3. Interest Rates When Zero-Coupon Bond Price is the Numeraire
      4. Annuity Factor as the Numeraire
    5. 28.5 Extension to Several Factors
    6. 28.6 Black’s Model Revisited Black’s Model Revisited
    7. 28.7 Option to Exchange One Asset for Another
    8. 28.8 Change of Numeraire
    9. Summary
    10. Further Reading
      1. Practice Questions (Answers in the Solutions Manual)
      2. Further Questions
  34. Chapter 29 Interest Rate Derivatives: The Standard Market Models
    1. 29.1 Bond Options
      1. Embedded Bond Options
      2. European Bond Options
        1. Example 29.1
      3. Yield Volatilities
        1. Example 29.2
    2. 29.2 Interest Rate Caps and Floors
      1. The Cap as a Portfolio of Interest Rate Options
      2. A Cap as a Portfolio of Bond Options
      3. Floors and Collars
      4. Valuation of Caps and Floors
        1. Example 29.3
      5. Spot Volatilities vs. Flat Volatilities
      6. Theoretical Justification for the Model
      7. Use of DerivaGem
      8. The Impact of Day Count Conventions
    3. 29.3 European Swap Options
      1. Valuation of European Swaptions
        1. Example 29.4
      2. Broker Quotes
      3. Theoretical Justification for the Swaption Model
      4. The Impact of Day Count Conventions
    4. 29.4 Ois Discounting
    5. 29.5 Hedging Interest Rate Derivatives
    6. Summary
    7. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  35. Chapter 30 Convexity, Timing, and Quanto Adjustments
    1. 30.1 Convexity Adjustments
      1. Application 1: Interest Rates
        1. Example 30.1
      2. Application 2: Swap Rates
        1. Example 30.2
    2. 30.2 Timing Adjustments
      1. Example 30.3
      2. Application 1 Revisited
    3. 30.3 Quantos
      1. Example 30.4
      2. Using Traditional Risk-Neutral Measures
        1. Example 30.5
    4. Summary
    5. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  36. Chapter31 Interest Rate Derivatives: Models of the Short Rate
    1. 31.1 Background
    2. 31.2 Equilibrium Models
      1. The Rendleman and Bartter Model
      2. The Vasicek Model
      3. The Cox, Ingersoll, and Ross Model
      4. Properties of Vasicek and CIR
        1. Example 31.1
      5. Applications of Equilibrium Models
        1. Example 31.2
          1. Example 31.3
      6. 31.3 No-Arbitrage Models
        1. The Ho–Lee Model
        2. The Hull–White (One-Factor) Model
        3. The Black–Derman–Toy Model
        4. The Black–Karasinski Model
        5. The Hull–White Two-Factor Model
      7. 31.4 Options on Bonds
        1. Options on Coupon-Bearing Bonds
      8. 31.5 Volatility Structures
      9. 31.6 Interest Rate Trees
        1. Illustration of Use of Trinomial Trees
        2. Nonstandard Branching
      10. 31.7 A General Tree-Building Procedure
        1. First Stage
        2. Second Stage
        3. Illustration of Second Stage
        4. Formulas for α’s and ’s and Q’s ’s
        5. Extension to Other Models
        6. Handling Low Interest Rate Environments
        7. Using Analytic Results in Conjunction with Trees
          1. Example 31.1
        8. Tree for American Bond Options
      11. 31.8 Calibration
      12. 31.9 Hedging Using A One-Factor Model
    3. Summary
    4. Further Reading
      1. Equilibrium Models
      2. No-Arbitrage Models
      3. Practice Questions (Answers in Solutions Manual)
      4. Further Questions
  37. Chapter 32 HJM, LMM, and Multiple Zero Curves
    1. 32.1 The Heath, Jarrow, and Morton Model
      1. Processes for Zero-Coupon Bond Prices and Forward Rates
      2. Extension to Several Factors
    2. 32.2 The Libor Market Model
      1. The Model
      2. Forward Rate Volatilities
        1. Example 32.1
        2. Example 32.2
      3. Implementation of the Model
      4. Extension to Several Factors
      5. Ratchet Caps, Sticky Caps, and Flexi Caps
      6. Valuing European Swap Options
      7. Calibrating the Model
      8. Volatility Skews
      9. Bermudan Swap Options
    3. 32.3 Handling Multiple Zero Curves
    4. 32.4 Agency Mortgage-Backed Securities
      1. Collateralized Mortgage Obligations
      2. Valuing Agency Mortgage-Backed Securities
      3. Option-Adjusted Spread
    5. Summary
    6. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  38. Chapter 33 Swaps Revisited
    1. 33.1 Variations on the Vanilla Deal
    2. 33.2 Compounding Swaps
      1. Example 33.1
    3. 33.3 Currency Swaps
    4. 33.4 More Complex Swaps
      1. LIBOR-in-Arrears Swap
        1. Example 33.2
      2. CMS and CMT Swaps
        1. Example 33.3
      3. Differential Swaps
        1. Example 33.4
    5. 33.5 Equity Swaps
    6. 33.6 Swaps with Embedded Options
      1. Accrual Swaps
      2. Cancelable Swap
      3. Cancelable Compounding Swaps
    7. 33.7 Other Swaps
      1. Bizarre Deals
    8. Summary
    9. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  39. Chapter 34 Energy and Commodity Derivatives
    1. 34.1 Agricultural Commodities
    2. 34.2 Metals
    3. 34.3 Energy Products
      1. Crude Oil
      2. Natural Gas
      3. Electricity
    4. 34.4 Modeling Commodity Prices
      1. A Simple Process
        1. Example 34.1
        2. Example 34.2
      2. Mean Reversion
        1. Example 34.3
      3. Interpolation and Seasonality
      4. Jumps
      5. Other Models
    5. 34.5 Weather Derivatives
    6. 34.6 Insurance Derivatives
    7. 34.7 Pricing Weather and Insurance Derivatives
      1. Example 34.4
    8. 34.8 How an Energy Producer Can Hedge Risks
    9. Summary
    10. Further Reading
      1. On commodity derivatives
      2. On weather derivatives
      3. On insurance derivatives
      4. Practice Questions (Answers in Solutions Manual)
      5. Further Questions
  40. Chapter 35 Real Options
    1. 35.1 Capital Investment Appraisal
    2. 35.2 Extension of the Risk-Neutral Valuation Framework
      1. Example 35.1
    3. 35.3 Estimating the Market Price of Risk
      1. Example 35.2
    4. 35.4 Application to the Valuation of a Business
    5. 35.5 Evaluating Options in an Investment Opportunity
      1. Illustration
      2. Evaluation with No Embedded Options
      3. Use of a Tree
      4. Option to Abandon
      5. Option to Expand
      6. Multiple Options
      7. Several Stochastic Variables
    6. Summary
    7. Further Reading
      1. Practice Questions (Answers in Solutions Manual)
      2. Further Questions
  41. Chapter 36 Derivatives Mishaps and What We Can Learn from Them
    1. 36.1 Lessons for All Users of Derivatives
      1. Define Risk Limits
      2. Take the Risk Limits Seriously
      3. Do Not Assume You Can Outguess the Market
      4. Do Not Underestimate the Benefits of Diversification
        1. Carry out Scenario Analyses and Stress Tests
      5. 36.2 Lessons for Financial Institutions
        1. Monitor Traders Carefully
        2. Separate the Front, Middle, and Back Office
        3. Do Not Blindly Trust Models
        4. Be Conservative in Recognizing Inception Profits
        5. Do Not Sell Clients Inappropriate Products
        6. Beware of Easy Profits
        7. Do Not Ignore Liquidity Risk
        8. Beware When Everyone Is Following the Same Trading Strategy
        9. Do Not Make Excessive Use of Short-Term Funding for Long-Term Needs
        10. Market Transparency Is Important
        11. Manage Incentives
        12. Never Ignore Risk Management
      6. 36.3 Lessons for Nonfinancial Corporations
        1. Make Sure You Fully Understand the Trades You Are Doing
        2. Make Sure a Hedger Does Not Become a Speculator
        3. Be Cautious about Making the Treasury Department a Profit Center
    2. Summary
      1. Further Reading
  42. Glossary of Terms
  43. DerivaGem Software
  44. Major Exchanges Trading Futures and Options
  45. Table for N(x) When x ≤ 0
    1. Table for N(x) When x ≥ 0
  46. Author Index
  47. Subject Index
    1. A
    2. B
    3. C
    4. D
    5. E
    6. F
    7. G
    8. H
    9. I
    10. J
    11. K
    12. L
    13. M
    14. N
    15. O
    16. P
    17. Q
    18. R
    19. S
    20. T
    21. U
    22. V
    23. W
    24. Y
    25. Z

Product Information

  • Title: Options, Futures, and Other Derivatives, Ninth Edition
  • Author(s): John C. Hull
  • Release date: January 2014
  • Publisher(s): Pearson
  • ISBN: 9780133456318