Options, Futures, and Other Derivatives, 11th Edition, By John Hull | [PDF] [eBook]

Options, Futures, and Other Derivatives Technical Notes Preface New to this Edition Solving Teaching and Learning Challenges Employability About the Author Chapter 1 Introduction 1.1 Exchange-Traded Markets Elec ...

Options, Futures, and Other Derivatives Technical Notes Preface New to this Edition Solving Teaching and Learning Challenges Employability About the Author Chapter 1 Introduction 1.1 Exchange-Traded Markets Electronic Markets 1.2 Over-the-Counter Markets Market Size 1.3 Forward Contracts Payoffs from Forward Contracts Forward Prices and Spot Prices 1.4 Futures Contracts 1.5 Options 1.6 Types of Traders 1.7 Hedgers Hedging Using Forward Contracts Hedging Using Options A Comparison 1.8 Speculators Speculation Using Futures Speculation Using Options A Comparison 1.9 Arbitrageurs 1.10 Dangers Summary Further Reading Short Concept Questions Practice Questions Chapter 2 Futures Markets and Central Counterparties 2.1 Background Closing Out Positions 2.2 Specification of a Futures Contract The Asset The Contract Size Delivery Arrangements Delivery Months Price Quotes Price Limits and Position Limits 2.3 Convergence of Futures Price to Spot Price 2.4 The Operation of Margin Accounts Daily Settlement 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 Short Concept Questions Practice Questions Chapter 3 Hedging Strategies Using Futures 3.1 Basic Principles Short Hedges Long Hedges 3.2 Arguments for and Against Hedging Hedging and Shareholders Hedging and Competitors Hedging Can Lead to a Worse Outcome 3.3 Basis Risk The Basis Choice of Contract 3.4 Cross Hedging Calculating the Minimum Variance Hedge Ratio Optimal Number of Contracts Impact of Daily Settlement 3.5 Stock Index Futures Stock Indices Hedging an Equity Portfolio Reasons for Hedging an Equity Portfolio Changing the Beta of a Portfolio Locking in the Benefits of Stock Picking 3.6 Stack and Roll Summary Further Reading Short Concept Questions Practice Questions Appendix Capital Asset Pricing Model Chapter 4 Interest Rates 4.1 Types of Rates Treasury Rates Overnight Rates Repo Rates 4.2 Reference Rates Libor The New Reference Rates Reference Rates and Credit Risk 4.3 The Risk-Free Rate 4.4 Measuring Interest Rates Continuous Compounding 4.5 Zero Rates 4.6 Bond Pricing Bond Yield Par Yield 4.7 Determining Zero Rates 4.8 Forward Rates 4.9 Forward Rate Agreements 4.10 Duration Modified Duration Bond Portfolios 4.11 Convexity 4.12 Theories of the Term Structure of Interest Rates The Management of Net Interest Income Liquidity Summary Further Reading Short Concept Questions Practice Questions Chapter 5 Determination of Forward and Futures Prices 5.1 Investment Assets vs. Consumption Assets 5.2 Short Selling 5.3 Assumptions and Notation 5.4 Forward Price for an Investment Asset A Generalization What If Short Sales are Not Possible? 5.5 Known Income A Generalization 5.6 Known Yield 5.7 Valuing Forward Contracts 5.8 Are Forward Prices and Futures Prices Equal? 5.9 Futures Prices of Stock Indices Index Arbitrage 5.10 Forward and Futures Contracts on Currencies A Foreign Currency as an Asset Providing a Known Yield 5.11 Futures on Commodities Income and Storage Costs Consumption Commodities Convenience Yields 5.12 The Cost of Carry 5.13 Delivery Options 5.14 Futures Prices and Expected Future Spot Prices Keynes and Hicks Risk and Return The Risk in a Futures Position Normal Backwardation and Contango Summary Further Reading Short Concept Questions Practice Questions Chapter 6 Interest Rate Futures 6.1 Day Count and Quotation Conventions Day Counts Price Quotations of U.S. Treasury Bills Price Quotations of U.S. Treasury Bonds 6.2 Treasury Bond Futures Quotes Conversion Factors Cheapest-to-Deliver Bond Determining the Futures Price 6.3 Eurodollar and SOFR Futures Eurodollar Futures SOFR Futures Convexity Adjustments Calculating Zero Curves 6.4 Duration-Based Hedging Strategies Using Futures 6.5 Hedging Portfolios of Assets and Liabilities Summary Further Reading Short Concept Questions Practice Questions Chapter 7 Swaps 7.1 Mechanics of Interest Rate Swaps 7.2 Determining Risk-free Rates 7.3 Reasons for Trading Interest Rate Swaps Using the Swap to Transform a Liability Using the Swap to Transform an Asset 7.4 The Organization of Trading Day Count Issues Confirmations 7.5 The Comparative-Advantage Argument Illustration Criticism of the Comparative-Advantage Argument 7.6 Valuation of Interest Rate Swaps 7.7 How the Value Changes Through Time 7.8 Fixed-for-Fixed Currency Swaps Illustration Use of a Currency Swap to Transform Liabilities and Assets Comparative Advantage 7.9 Valuation of fixed-for-fixed Currency Swaps Valuation in Terms of Bond Prices 7.10 Other Currency Swaps 7.11 Credit Risk 7.12 Credit Default Swaps 7.13 Other Types of Swaps Variations on the Standard Interest Rate Swap Quantos Equity Swaps Options Commodity, Volatility, and Other Swaps Summary Further Reading Short Concept Questions Practice Questions Chapter 8 Securitization and the Financial Crisis of 2007–8 8.1 Securitization ABSs ABS CDOs 8.2 The U.S. Housing Market The Relaxation of Lending Standards Subprime Mortgage Securitization The Bubble Bursts The Losses Credit Spreads 8.3 What Went Wrong? Regulatory Arbitrage Incentives 8.4 The Aftermath Summary Further Reading Short Concept Questions Practice Questions Chapter 9 XVAs 9.1 CVA and DVA Collateral 9.2 FVA and MVA 9.3 KVA 9.4 Calculation Issues Application of Machine Learning Summary Further Reading Short Concept Questions Practice Questions Chapter 10 Mechanics of Options Markets 10.1 Types of Options Call Options Put Options Early Exercise 10.2 Option Positions 10.3 Underlying Assets Stock Options ETP Options Foreign Currency Options Index Options Futures Options 10.4 Specification of Stock Options Expiration Dates Strike Prices Terminology FLEX Options Dividends and Stock Splits Position Limits and Exercise Limits 10.5 Trading Market Makers Offsetting Orders 10.6 Trading Costs 10.7 Margin Requirements Writing Naked Options Other Rules 10.8 The Options Clearing Corporation Exercising an Option 10.9 Regulation 10.10 Taxation Wash Sale Rule Constructive Sales 10.11 Warrants, Employee Stock Options, and Convertibles 10.12 Over-the-Counter Options Markets Summary Further Reading Short Concept Questions Practice Questions Chapter 11 Properties of Stock Options 11.1 Factors Affecting Option Prices Stock Price and Strike Price Time to Expiration Volatility Risk-Free Interest Rate Amount of Future Dividends 11.2 Assumptions and Notation 11.3 Upper and Lower Bounds for Option Prices Upper Bounds Lower Bound for Calls on Non-Dividend-Paying Stocks Lower Bound for European Puts on Non-Dividend-Paying Stocks 11.4 Put–Call Parity American Options 11.5 Calls on a Non-Dividend-Paying Stock Bounds 11.6 Puts on a Non-Dividend-Paying Stock Bounds 11.7 Effect of Dividends Lower Bound for Calls and Puts Early Exercise Put–Call Parity Summary Further Reading Short Concept Questions Practice Questions Chapter 12 Trading Strategies Involving Options 12.1 Principal-Protected Notes 12.2 Trading an Option and the Underlying Asset 12.3 Spreads Bull Spreads Bear Spreads Box Spreads Butterfly Spreads Calendar Spreads Diagonal Spreads 12.4 Combinations Straddle Strips and Straps Strangles 12.5 Other Payoffs Summary Further Reading Short Concept Questions Practice Questions Chapter 13 Binomial Trees 13.1 A One-Step Binomial Model and a No-Arbitrage Argument A Generalization Irrelevance of the Stock’s Expected Return 13.2 Risk-Neutral Valuation The One-Step Binomial Example Revisited Real World vs. Risk-Neutral World 13.3 Two-Step Binomial Trees A Generalization 13.4 A Put Example 13.5 American Options 13.6 Delta 13.7 Matching Volatility with u and d Girsanov’s Theorem 13.8 The Binomial Tree Formulas 13.9 Increasing the Number of Steps 13.10 Using DerivaGem 13.11 Options on Other Assets Options on Stocks Paying a Continuous Dividend Yield Options on Stock Indices Options on Currencies Options on Futures Summary Further Reading Short Concept Questions Practice Questions Appendix Derivation of the Black–Scholes–Merton Option-Pricing Formula from a Binomial Tree Chapter 14 Wiener Processes and Itô’s Lemma 14.1 The Markov Property 14.2 Continuous-Time Stochastic Processes Wiener Process Generalized Wiener Process Itô Process 14.3 The Process for a Stock Price Discrete-Time Model Monte Carlo Simulation 14.4 The Parameters 14.5 Correlated Processes 14.6 Itô’s Lemma Application to Forward Contracts 14.7 The Lognormal Property 14.8 Fractional Brownian Motion Summary Further Reading Short Concept Questions Practice Questions Appendix A Nonrigorous Derivation of Itô’s Lemma Chapter 15 The Black–Scholes–Merton Model 15.1 Lognormal Property of Stock Prices 15.2 The Distribution of the Rate of Return 15.3 The Expected Return 15.4 Volatility Estimating Volatility from Historical Data Trading Days vs. Calendar Days 15.5 The Idea Underlying the Black–Scholes–Merton Differential Equation Assumptions 15.6 Derivation of the Black–Scholes–Merton Differential Equation A Perpetual Derivative The Prices of Tradeable Derivatives 15.7 Risk-Neutral Valuation Application to Forward Contracts on a Stock 15.8 Black–Scholes–Merton Pricing Formulas Understanding N(d1) and N(d2) Properties of the Black–Scholes–Merton Formulas 15.9 Cumulative Normal Distribution Function 15.10 Warrants and Employee Stock Options 15.11 Implied Volatilities The VIX Index 15.12 Dividends European Options American Call Options Black’s Approximation Summary Further Reading Short Concept Questions Practice Questions Appendix Proof of the Black–Scholes–Merton Formula Using Risk-Neutral Valuation Key Result Proof of Key Result The Black–Scholes–Merton Result Chapter 16 Employee Stock Options 16.1 Contractual Arrangements The Early Exercise Decision 16.2 Do Options Align the Interests of Shareholders and Managers? 16.3 Accounting Issues Alternatives to Stock Options 16.4 Valuation Using the Black–Scholes–Merton Model Binomial Tree Approach Exercise Multiple Approach A Market-Based Approach Dilution 16.5 The Backdating Scandal Summary Further Reading Short Concept Questions Practice Questions Chapter 17 Options on Stock Indices and Currencies 17.1 Options on Stock Indices Portfolio Insurance When the Portfolio’s Beta Is Not 1.0 17.2 Currency Options Range Forwards 17.3 Options on Stocks Paying Known Dividend Yields Lower Bounds for Option Prices Put–Call Parity Pricing Formulas Differential Equation and Risk-Neutral Valuation 17.4 Valuation of European Stock Index Options Forward Prices and the Estimation of Dividend Yields 17.5 Valuation of European Currency Options Using Forward Exchange Rates 17.6 American Options Summary Further Reading Short Concept Questions Practice Questions Chapter 18 Futures Options and Black’s Model 18.1 Nature of Futures Options Expiration Months Options on Interest Rate Futures 18.2 Reasons for the Popularity of Futures Options 18.3 European Spot and Futures Options 18.4 Put–Call Parity 18.5 Bounds for Futures Options 18.6 Drift of a Futures Price in a Risk-Neutral World Differential Equation 18.7 Black’s Model for Valuing Futures Options 18.8 Using Black’s Model Instead of Black–Scholes–Merton 18.9 Valuation of Futures Options Using Binomial Trees A Generalization Multistep Trees 18.10 American Futures Options vs. American Spot Options 18.11 Futures-Style Options Summary Further Reading Short Concept Questions Practice Questions Chapter 19 The Greek Letters 19.1 Illustration 19.2 Naked and Covered Positions A Stop-Loss Strategy 19.3 Greek Letter Calculation 19.4 Delta Hedging Delta of European Stock Options Dynamic Aspects of Delta Hedging Where the Cost Comes From Delta of a Portfolio Transaction Costs 19.5 Theta 19.6 Gamma Making a Portfolio Gamma Neutral Calculation of Gamma 19.7 Relationship Between Delta, Theta, and Gamma 19.8 Vega 19.9 Rho 19.10 The Realities of Hedging 19.11 Scenario Analysis 19.12 Extension of Formulas Delta of Forward Contracts Delta of a Futures Contract 19.13 Portfolio Insurance Use of Index Futures Impact on Volatility 19.14 Application of Machine Learning to Hedging Summary Further Reading Short Concept Questions Practice Questions Appendix Taylor Series Expansions and Greek Letters The Practitioner Black–Scholes Model Chapter 20 Volatility Smiles and Volatility Surfaces 20.1 Implied Volatilities of Calls and Puts 20.2 Volatility Smile for Foreign Currency Options Empirical Results Reasons for the Smile in Foreign Currency Options 20.3 Volatility Smile for Equity Options The Reason for the Smile in Equity Options 20.4 Alternative Ways of Characterizing the Volatility Smile 20.5 The Volatility Term Structure and Volatility Surfaces 20.6 Minimum Variance Delta 20.7 The Role of the Model 20.8 When a Single Large Jump is Anticipated Summary Further Reading Short Concept Questions Practice Questions Appendix Determining Implied Risk-Neutral Distributions from Volatility Smiles Chapter 21 Basic Numerical Procedures 21.1 Binomial Trees Risk-Neutral Valuation Determination of p, u, and d Tree of Asset Prices Working Backward through the Tree Expressing the Approach Algebraically Estimating Delta and Other Greek Letters 21.2 Using the Binomial Tree for Options on Indices, Currencies, and Futures Contracts 21.3 Binomial Model for a Dividend-Paying Stock Known Dividend Yield Known Dollar Dividend Control Variate Technique 21.4 Alternative Procedures for Constructing Trees Trinomial Trees 21.5 Time-Dependent Parameters 21.6 Monte Carlo Simulation Derivatives Dependent on More than One Market Variable Generating the Random Samples from Normal Distributions Number of Trials Sampling through a Tree Calculating the Greek Letters Applications 21.7 Variance Reduction Procedures Antithetic Variable Technique Control Variate Technique Importance Sampling Stratified Sampling Moment Matching Using Quasi-Random Sequences 21.8 Finite Difference Methods Implicit Finite Difference Method Explicit Finite Difference Method Change of Variable Relation to Trinomial Tree Approaches Other Finite Difference Methods Applications of Finite Difference Methods Summary Further Reading Practice Questions Chapter 22 Value at Risk and Expected Shortfall 22.1 The VaR and ES Measures The Time Horizon 22.2 Historical Simulation Illustration: Investment in Four Stock Indices Expected Shortfall Weighting Observations Stressed VaR and Stressed ES 22.3 Model-Building Approach Daily Volatilities Single-Asset Case Two-Asset Case The Benefits of Diversification ES Calculation 22.4 The Linear Model Correlation and Covariance Matrices The Four-Index Example Handling Interest Rates Applications of the Linear Model The Linear Model and Options 22.5 The Quadratic Model 22.6 Monte Carlo Simulation 22.7 Comparison of Approaches 22.8 Back Testing 22.9 Principal Components Analysis Using Principal Components Analysis to Calculate VaR Summary Further Reading Practice Questions Chapter 23 Estimating Volatilities and Correlations 23.1 Estimating Volatility Weighting Schemes 23.2 The Exponentially Weighted Moving Average Model 23.3 The Garch(1,1) Model The Weights Mean Reversion 23.4 Choosing Between the Models 23.5 Maximum Likelihood Methods Estimating a Constant Variance Estimating EWMA or GARCH (1,1) Parameters How Good Is the Model? 23.6 Using Garch(1,1) to Forecast Future Volatility Volatility Term Structures Impact of Volatility Changes 23.7 Correlations Consistency Condition for Covariances Summary Further Reading Practice Questions Chapter 24 Credit Risk 24.1 Credit Ratings 24.2 Historical Default Probabilities Hazard Rates 24.3 Recovery Rates The Dependence of Recovery Rates on Default Rates 24.4 Estimating Default Probabilities from Bond Yield Spreads Matching Bond Prices The Risk-Free Rate 24.5 Comparison of Default Probability Estimates Real-World vs. Risk-Neutral Probabilities Which Default Probability Estimate Should Be Used? 24.6 Using Equity Prices to Estimate Default Probabilities 24.7 Credit Risk in Derivatives Transactions CVA and DVA Credit Risk Mitigation Special Cases 24.8 Default Correlation The Gaussian Copula Model for Time to Default A Factor-Based Correlation Structure 24.9 Credit VaR CreditMetrics Summary Further Reading Practice Questions Chapter 25 Credit Derivatives 25.1 Credit Default Swaps Credit Default Swaps and Bond Yields The Cheapest-to-Deliver Bond 25.2 Valuation of Credit Default Swaps Marking to Market a CDS Estimating Default Probabilities Binary Credit Default Swaps How Important Is the Recovery Rate? 25.3 Credit Indices 25.4 The Use of Fixed Coupons 25.5 CDS Forwards and Options 25.6 Basket Credit Default Swaps 25.7 Total Return Swaps 25.8 Collateralized Debt Obligations Synthetic CDOs Standard Portfolios and Single-Tranche Trading 25.9 Role of Correlation in a Basket CDS and CDO 25.10 Valuation of a Synthetic CDO Using the Gaussian Copula Model of Time to Default Valuation of kth-to-Default CDS Implied Correlation Valuing Nonstandard Tranches 25.11 Alternatives to the Standard Market Model Heterogeneous Model Other Copulas Random Recovery and Factor Loadings The Implied Copula Model Dynamic Models Summary Further Reading Practice Questions Chapter 26 Exotic Options 26.1 Packages 26.2 Perpetual American Call and Put Options 26.3 Nonstandard American Options 26.4 Gap Options 26.5 Forward Start Options 26.6 Cliquet Options 26.7 Compound Options 26.8 Chooser Options 26.9 Barrier Options 26.10 Binary Options 26.11 Lookback Options 26.12 Shout Options 26.13 Asian Options 26.14 Options to Exchange One Asset for Another 26.15 Options Involving Several Assets 26.16 Volatility and Variance Swaps Valuation of Variance Swap Valuation of a Volatility Swap The VIX Index 26.17 Static Options Replication Summary Further Reading Practice Questions Chapter 27 More on Models and Numerical Procedures 27.1 Alternatives to Black–Scholes–Merton The Constant Elasticity of Variance Model Merton’s Mixed Jump–Diffusion Model Simulating Jumps The Variance-Gamma Model 27.2 Stochastic Volatility Models The SABR Model Rough Volatility Models 27.3 The IVF Model 27.4 Convertible Bonds 27.5 Path-Dependent Derivatives 27.6 Barrier Options 27.7 Options on Two Correlated Assets 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 Chapter 28 Martingales and Measures 28.1 The Market Price of Risk Alternative Worlds 28.2 Several State Variables 28.3 Martingales The Equivalent Martingale Measure Result 28.4 Alternative Choices for the Numeraire Money Market Account as the Numeraire Zero-Coupon Bond Price as the Numeraire Forward Interest Rates Annuity Factor as the Numeraire 28.5 Extension to Several Factors 28.6 Black’s Model Revisited 28.7 Option to Exchange One Asset for Another 28.8 Change of Numeraire A Final Point Summary Further Reading Practice Questions Chapter 29 Interest Rate Derivatives: The Standard Market Models 29.1 Bond Options Embedded Bond Options European Bond Options Yield Volatilities 29.2 Interest Rate Caps and Floors The Cap as a Portfolio of Interest Rate Options A Cap as a Portfolio of Bond Options Floors and Collars Valuation of Caps and Floors Theoretical Justification for the Model Use of DerivaGem The Impact of Day Count Conventions Negative Rates Backward-Looking Reference Rates 29.3 European Swap Options Valuation of European Swaptions Theoretical Justification for the Swaption Model The Impact of Day Count Conventions Negative Rates 29.4 Hedging Interest Rate Derivatives Summary Further Reading Practice Questions Chapter 30 Convexity, Timing, and Quanto Adjustments 30.1 Convexity Adjustments 30.2 Timing Adjustments 30.3 Quantos Using Traditional Risk-Neutral Measures Summary Further Reading Practice Questions Appendix Proof of the Convexity Adjustment Formula Chapter 31 Equilibrium Models of the Short Rate 31.1 Background 31.2 One-Factor Models The Rendleman and Bartter Model The Vasicek Model The Cox, Ingersoll, and Ross Model Properties of Vasicek and CIR The Bond Price Process 31.3 Real-World vs. Risk-Neutral Processes 31.4 Estimating Parameters 31.5 More Sophisticated Models Summary Further Reading Practice Questions Chapter 32 No-Arbitrage Models of the Short Rate 32.1 Extensions of Equilibrium Models The Ho–Lee Model The Hull–White One-Factor Model The Black–Derman–Toy Model The Black–Karasinski Model The Hull–White Two-Factor Model 32.2 Options on Bonds Options on Coupon-Bearing Bonds 32.3 Volatility Structures 32.4 Interest Rate Trees Illustration of Use of Trinomial Trees Nonstandard Branching 32.5 A General Tree-Building Procedure First Stage Second Stage Illustration of Second Stage Formulas for α’s and Q’s Extension to Other Models Negative Rates Multiple Yield Curves Using Analytic Results in Conjunction with Trees Tree for American Bond Options 32.6 Calibration 32.7 Hedging Using a One-Factor Model Summary Further Reading Practice Questions Chapter 33 Modeling Forward Rates 33.1 The Heath, Jarrow, and Morton Model Processes for Zero-Coupon Bond Prices and Forward Rates Extension to Several Factors 33.2 The BGM Model The Model Forward Rate Volatilities Implementation of the Model Extension to Several Factors Ratchet Caps, Sticky Caps, and Flexi Caps Valuing European Swap Options Calibrating the Model Volatility Skews Bermudan Swap Options 33.3 Agency Mortgage-Backed Securities Collateralized Mortgage Obligations Valuing Agency Mortgage-Backed Securities Option-Adjusted Spread Summary Further Reading Practice Questions Chapter 34 Swaps Revisited 34.1 Variations on the Vanilla Deal 34.2 Compounding Swaps 34.3 Currency and Nonstandard Swaps 34.4 Equity Swaps 34.5 Swaps with Embedded Options Accrual Swaps Cancelable Swap Cancelable Compounding Swaps 34.6 Other Swaps Bizarre Deals Summary Further Reading Practice Questions Chapter 35 Energy and Commodity Derivatives 35.1 Agricultural Commodities 35.2 Metals 35.3 Energy Products Crude Oil Natural Gas Electricity 35.4 Modeling Commodity Prices A Simple Process Mean Reversion Interpolation and Seasonality Jumps Other Models 35.5 Weather Derivatives 35.6 Insurance Derivatives 35.7 Pricing Weather and Insurance Derivatives 35.8 How an Energy Producer can Hedge Risks Summary Further Reading Practice Questions Chapter 36 Real Options 36.1 Capital Investment Appraisal 36.2 Extension of the Risk-Neutral Valuation Framework 36.3 Estimating the Market Price of Risk 36.4 Application to the Valuation of a Business 36.5 Evaluating Options in an Investment Opportunity Illustration Evaluation with No Embedded Options Use of a Tree Option to Abandon Option to Expand Multiple Options Several Stochastic Variables Summary Further Reading Practice Questions Chapter 37 Derivatives Mishaps and What We Can Learn from Them 37.1 Lessons for all Users of Derivatives Define Risk Limits Take the Risk Limits Seriously Do Not Assume You Can Outguess the Market Do Not Underestimate the Benefits of Diversification Carry out Scenario Analyses and Stress Tests 37.2 Lessons for Financial Institutions Monitor Traders Carefully Separate the Front, Middle, and Back Office Do Not Blindly Trust Models Be Conservative in Recognizing Inception Profits Do Not Sell Clients Inappropriate Products Beware of Easy Profits Do Not Ignore Liquidity Risk Beware When Everyone Is Following the Same Trading Strategy Do Not Make Excessive Use of Short-Term Funding for Long-Term Needs Market Transparency Is Important Manage Incentives Never Ignore Risk Management 37.3 Lessons for Nonfinancial Corporations Make Sure You Fully Understand the Trades You Are Doing Make Sure a Hedger Does Not Become a Speculator Be Cautious about Making the Treasury Department a Profit Center Summary Further Reading Glossary of Terms DerivaGem Software Exchanges Trading Futures and Options