Derivitives Markets - GBVDerivitives Markets THIRD EDITION Robert L. McDonald Northwestern...

Derivitives MarketsTHIRD EDITION

Robert L. McDonaldNorthwestern University

Kellogg School of Management

PEARSONBoston Columbus Indianapolis New York San Francisco Upper Saddle River

Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto

Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

Contents

3

Preface

Chapter 1Introduction to Derivatives 11.1 What Is a Derivative? 21.2 An Overview of Financial Markets 2

' Trading of Financial Assets 2Measures of Market Size and Activity 4Stock and Bond Markets 5Derivatives Markets 6

1.3 The Role of Financial Markets 9Financial Markets and the Averages 9Risk-Sharing 10

1.4 The Uses of Derivatives 11Uses of Derivatives 11Perspectives on Derivatives 13Financial Engineering and Security

Design 141.5 Buying and Short-Selling Financial

Assets 14Transaction Costs and the Bid-Ask

Spread 14Ways to Buy or Sell 15Short-Selling 16The Lease Rate of an Asset 18Risk and Scarcity in Short-Selling 18

Chapter Summary 20Further Reading 20Problems 20

PART ONE

Insurance, Hedging, and SimpleStrategies 23

Chapter 2An Introduction to Forwards andOptions 252.1 Forward Contracts 25

The Payoff on a Forward Contract 29Graphing the Payoff on a Forward

Contract 30Comparing a Forward and Outright

, Purchase 30Zero-Coupon Bonds in Payoff and Profit

Diagrams 33Cash Settlement Versus Delivery 34Credit Risk 34

2.2 Call Options 35Option Terminology 35Payoff and Profit for a Purchased Call

Option 36Payoff and Profit for a Written Call

Option 382.3 Put Options 41 ,

Payoff and Profit for a Purchased PutOption 41

Payoff and Profit for a Written PutOption 42

The "Moneyness" of an Option 44

IX

Contents

2.4 Summary of Forward and OptionPositions 45

Positions Long with Respect to theIndex 45

Positions Short with Respect to theIndex 46

2.5 Options Are Insurance 47Homeowners Insurance Is a Put

Option 48But I Thought Insurance Is Prudent and-

'•' r Put Options Are Risky . . . 48'_ Call Options Are Also Insurance 49

2.6 Example: Equity-Linked CDs 50Graphing the Payoff on the CD 50Economics of the CD 52Why Equity-Linked CDs? 52


2.A More on Buying a Stock Option 57

Dividends 57Exercise 57Margins for Written Options 58

• Taxes 58

Chapter 3Insurance, Collars, and OtherStrategies 613.1 Basic Insurance Strategies 61

Insuring a Long Position: Floors 61Insuring a Short Position: Caps 64Selling Insurance 66

3.2 Put-Call Parity 68Synthetic Forwards 68The Put-Call Parity Equation 70

3.3 Spreads and Collars 71Bull and Bear Spreads 71Box Spreads 73Ratio Spreads 74Collars 74

3.4 Speculating on Volatility 79Straddles 79Butterfly Spreads 80Asymmetric Butterfly Spreads 82


Chapter 4Introduction to Risk Management 894.1 Basic Risk Management: The Producer's

Perspective 89Hedging with a Forward Contract 90Insurance: Guaranteeing a Minimum Price

with a Put Option 91Insuring by Selling a Call 93Adjusting the Amount of Insurance 95

4.2 Basic Risk Management: The Buyer'sPerspective 96

Hedging with a Forward Contract 97Insurance: Guaranteeing a Maximum Price

with a Call Option 974.3 Why Do Firms Manage Risk? 99

An Example Where Hedging AddsValue 100

Reasons to Hedge 102Reasons Not to Hedge 104Empirical Evidence on Hedging 104

4.4 Golddiggers Revisited 107Selling the Gain: Collars 107Other Collar Strategies 111Paylater Strategies 111

4.5, Selecting the Hedge Ratio 112Cross-Hedging 112Quantity Uncertainty '114


PART T W O

Forwards, Futures, andSwaps 123

Chapter 5Financial Forwards and Futures 1255.1 Alternative Ways to Buy a Stock 1255.2 Prepaid Forward Contracts on Stock 126

Pricing the Prepaid Forward byAnalogy 127

Pricing the Prepaid Forward by DiscountedPresent Value 127

Contents XI

Pricing the Prepaid Forward byArbitrage 127

Pricing Prepaid Forwards withDividends 129

5.3 Forward Contracts on Stock 131Does the Forward Price Predict the Future

Spot Price? 132Creating a Synthetic Forward

Contract 133Synthetic Forwards in Market-Making and

Arbitrage 135No.i-'Arbitrage Bounds with Transaction

Costs 136Quasi-Arbitrage 137An Interpretation of the Forward Pricing

Formula 1385.4 Futures Contracts 138

The S&P 500 Futures Contract 139Margins and Marking to Market 140Comparing Futures and Forward

Prices 143Arbitrage in Practice: S&P 500 Index

Arbitrage 143Quanto Index Contracts 145

5.5 Uses of Index Futures 146Asset Allocation 146Cross-hedging with Index Futures 147

5.6 Currency Contracts 150Currency Prepaid Forward 150Currency Forward 152Covered Interest Arbitrage 152

5.7 Eurodollar Futures 153Chapter Summary 157\Further Reading 158Problems 158

5.A Taxes and the Forward Rate 1615.B Equating Forwards and Futures 1625.C Forward and Futures Prices 162

Chapter 6Commodity Forwards andFutures 1636.1 Introduction to Commodity

Forwards 164Examples of Commodity Futures

Prices 164 °

Differences Between Commodities andFinancial Assets 166

Commodity Terminology 1666.2 Equilibrium Pricing of Commodity

Forwards 1676.3 Pricing Commodity Forwards by

Arbitrage 168An Apparent Arbitrage 168Short-selling and the Lease Rate 170No-Arbitrage Pricing Incorporating

Storage Costs 172Convenience Yields 174Summary 175

6.4 Gold 175Gold Leasing 176Evaluation of Gold Production 177

6.5 Corn 1786.6 Energy Markets 179

Electricity 180Natural Gas 180Oil 182Oil Distillate Spreads 1.84

6.7 Hedging Strategies 185Basis Risk 186Hedging Jet Fuel with Crude Oil 187Weather Derivatives 188

6.8 Synthetic Commodities 189Chapter Summary 191Further Reading 192Problems 192

Chapter 7Interest Rate Forwards andFutures 1957.1 Bond Basics 195

Zero-Coupon Bonds 196Implied Forward Rates 197Coupon Bonds 199Zeros from Coupons 200Interpreting the Coupon Rate 201Continuously Compounded Yields 202

7.2 Forward Rate Agreements, EurodollarFutures, and Hedging 202

Forward Rate Agreements 203Synthetic FRAs 204Eurodollar Futures 206

Xll Contents

7.3 Duration and Convexity 211Price Value of a Basis Point and DV01 211Duration 213Duration Matching 214Convexity 215

7.4 Treasury-Bond and Treasury-NoteFutures 217

7.5 Repurchase Agreements 220Chapter Summary 222

; Further Reading 224'^Problems 225

7.A - Interest Rate and Bond PriceConventions 228

Bonds 228Bills 230

Chapter 8Swaps 2338.1 An Example of a Commodity Swap 233

Physical Versus Financial Settlement 234Why Is the Swap Price Not $110.50? 236The Swap Counterparty 237The Market Value of a Swap 238

8.2 Computing the Swap Rate in General 240Fixed Quantity Swaps 240Swaps with Variable Quantity and

Price 2418.3^ Interest Rate Swaps 243

A Simple Interest Rate Swap 243Pricing and the Swap Counterparty 244Swap Rate and Bond Calculations 246The Swap Curve 247The Swap's Implicit Loan Balance 248Deferred Swaps 249Related Swaps 250Why Swap Interest Rates? 251Amortizing and Accreting Swaps 252

8.4 Currency Swaps 252Currency Swap Formulas 255Other Currency Swaps 256

8.5 Swaptions 2568.6 Total Return Swaps 257


PART THREE

Options 263

Chapter 9Parity and Other OptionRelationships 2659.1 Put-Call Parity 265

Options on Stocks 266Options on Currencies 269Options on Bonds 269Dividend Forward Contracts 269

9.2 Generalized Parity and ExchangeOptions 270

Options to Exchange Stock 272What Are Calls and Puts? 272Currency Options 273

9.3 Comparing Options with Respect to Style,Maturity, and Strike 275

European Versus American Options 276Maximum and Minimum Option '

Prices 276Early Exercise for American Options 277Time to Expiration 280Different Strike Prices 281Exercise and Moneyness 286


9.A Parity Bounds for American Options 2919.B Algebraic Proofs of Strike-Price

Relations 292

Chapter 10Binomial Option Pricing: BasicConcepts 29310.1 A One-Period Binomial Tree 293

Computing the Option Price 294The Binomial Solution 295Arbitraging a Mispriced Option 297A Graphical Interpretation of the Binomial

Formula 298Risk-Neutral Pricing 299

10.2 Constructing a Binomial Tree 300 -

Contents xui

Continuously Compounded Returns 301Volatility 302Constructing u and d 303Estimating Historical Volatility 303One-Period Example with a Forward

Tree 30510.3 Two or More Binomial Periods 306

A Two-Period European Call 306Many Binomial Periods 308

10.4 Put Options 30910.5 American Options 31010.6 Options on Other Assets 312

Option on a Stock Index 312Options on Currencies 312Options on Futures Contracts 314Options on Commodities 315Options on Bonds 316Summary 317


10.A Taxes and Option Prices 322

Chapter 11Binomial Option Pricing: SelectedTopics 32311.1 Understanding Early Exercise 32311.2 Understanding Risk-Neutral Pricing 326

The Risk-Neutral Probability 326 .Pricing an Option Using Real

Probabilities 32711.3 The Binomial Tree and Lognormality 330

The Random Walk Model 330Modeling Stock Prices as a Random

Walk 331The Binomial Model 332Lognormality and the Binomial Model 333Alternative Binomial Trees 335Is the Binomial Model Realistic? 336

11.4 Stocks Paying Discrete Dividends 336Modeling Discrete Dividends 337Problems with the Discrete Dividend

Tree 337A Binomial Tree Using the Prepaid

Forward 339


11.A Pricing Options with TrueProbabilities 343

ll .B Why Does Risk-Neutral PricingWork? 344

Utility-Based Valuation 344Standard Discounted Cash Flow 345Risk-Neutral Pricing 345Physical vs. Risk-Neutral Probabilities 346Example 347

Chapter 12The Black-Scholes Formula 34912.1 Introduction to the Black-Scholes

Formula 349Call Options 349Put Options 352When Is the Black-Scholes Formula

Valid? 35212.2 Applying the Formula to Other

Assets 353Options on Stocks with Discrete

Dividends 354Options on Currencies 354Options on Futures 355

12.3 Option Greeks 356Definition of the Greeks 356Greek Measures for Portfolios 361Option Elasticity 362

12.4 Profit Diagrams Before Maturity 366Purchased Call Option 366Calendar Spreads 367

12.5 Implied Volatility 369 .Computing Implied Volatility 369Using Implied Volatility 370

12.6 Perpetual American Options 372Valuing Perpetual Options 373Barrier Present Values 374


12.A The Standard Normal Distribution 378

XIV Contents

12.B Formulas for Option Greeks 379Delta (A) 379Gamma (r) 379Theta(0) 379Vega 380Rho (p) 380Psi(VO 380

Chapter 13 .Market-Making and Delta-Hedging 38113.1 What Do Market-Makers Do? 38113.2 Market-Maker Risk 382

Option Risk in the Absence ofHedging 382

Delta and Gamma as Measures ofExposure 383

13.3 Delta-Hedging 384An Example of Delta-Hedging for 2

Days 385Interpreting the Profit Calculation 385Delta-Hedging for Several Days 387A Self-Financing Portfolio: The Stock

Moves One a 38913.4 The Mathematics of Delta-Hedging 389

Using Gamma to Better Approximate theChange in the Option Price 390

Delta-Gamma Approximations 391Theta: Accounting for Time 392Understanding the Market-Maker's

Profit 394 i13.5 The Black-Scholes Analysis 395

The Black-Scholes Argument 396Delta-Hedging of American Options 396What Is the Advantage to Frequent

Re-Hedging? 397Delta-Hedging in Practice 398Gamma-Neutrality 399

13.6 Market-Making as Insurance 402Insurance 402Market-Makers 403


13.A Taylor Series Approximations 40613.B Greeks in the Binomial Model 407

Chapter 14Exotic Options: I 40914.1 Introduction 40914.2 Asian Options 410

XYZ's Hedging Problem 411Options on the Average 411Comparing Asian Options 412An Asian Solution for XYZ 413

14.3 Barrier Options 414Types of Barrier Options 415Currency Hedging 416

14.4 Compound Options 418Compound Option Parity 419Options on Dividend-Paying Stocks 419Currency Hedging with Compound

Options 42114.5 Gap Options 42114.6 Exchange Options 424

European Exchange Options 424Chapter Summary 425Further Reading \ 426Problems 426

14.A Pricing Formulas for Exotic Options 430Asian Options Based on the Geometric

Average 430Compound Options 431Infinitely Lived Exchange Option 432

PART FOUR

Financial Engineering andApplications 435

Chapter 15Financial Engineering and SecurityDesign 43715.1 The Modigliani-Miller Theorem 43715.2 Structured Notes without Options 438

Single Payment Bonds 438Multiple Payment Bonds 441

15.3 Structured Notes with Options 445Convertible Bonds 446Reverse Convertible Bonds 449Tranched Payoffs 451

Contents xv

Variable Prepaid Forwards 45215.4 Strategies Motivated by Tax and

Regulatory Considerations 453Capital Gains Deferral 454Marshall & Ilsley SPACES 458

15.5 Engineered Solutions forGolddiggers 460

Gold-Linked Notes 460Notes with Embedded Options 462

Chapter Summary 463Furt&ef Reading 464Problems 464

Chapter 16Corporate Applications 46916.1 Equity, Debt, and Warrants 469

Debt and Equity as Options 469Leverage and the Expected Return on Debt

and Equity 472Multiple Debt Issues 477Warrants 478Convertible Bonds 479Callable Bonds 482Bond Valuation Based on the Stock

Price 485Other Bond Features 485Put Warrants 486

16.2 Compensation Options 487The Use of Compensation Options 487Valuation of Compensation Options 489Repricing of Compensation Options 492Reload Options 493 ';Level 3 Communications 495

16.3 The Use of Collars in Acquisitions 499The Northrop Grumman—TRW

merger 499 'Chapter Summary 502Further Reading 503Problems 503

16.A An Alternative Approach to ExpensingOption Grants 507

Chapter 17Real Options 50917.1 Investment and the NPV Rule 509

Static NPV 510

The Correct Use of NPV 511The Project as an Option 511

17.2 Investment under Uncertainty 513A Simple DCF Problem 513Valuing Derivatives on the Cash Flow 514Evaluating a Project with a 2-Year

Investment Horizon 515Evaluating the Project with an Infinite

Investment Horizon 51917.3 Real Options in Practice 519

Peak-Load Electricity Generation 519Research and Development 523

17.4 Commodity Extraction as an Option 525Single-Barrel Extraction under

Certainty 525Single-Barrel Extraction under

Uncertainty 528Valuing an Infinite Oil Reserve 530

17.5 Commodity Extraction with Shutdownand Restart Options 531

Permanent Shutting Down 533Investing When Shutdown Is Possible 535Restarting Production 536Additional Options 537


17.A Calculation of Optimal Time to Drill anOil Well 541

17.B The Solution with Shutting Down andRestarting 541

PART FIVE ra__^

Advanced Pricing Theory andApplications 543

Chapter 18The Lognormal Distribution 54518.1 The Normal Distribution 545

Converting a Normal Random Variable toStandard Normal 548

Sums of Normal Random Variables 54918.2 The Lognormal Distribution 55018.3 A Lognormal Model of Stock Prices 552

XVI Contents

18.4 Lognormal Probability Calculations 556Probabilities 556Lognormal Prediction Intervals 557The Conditional Expected Price 559The Black-Scholes Formula 561

18.5 Estimating the Parameters of a LognormalDistribution 562

18.6 How Are Asset Prices Distributed? 564Histograms 564

; Normal Probability Plots 566' Chapter Summary 569.Further Reading 569Problems 570

18.A The Expectation of a LognormalVariable 571

18.B Constructing a Normal ProbabilityPlot 572

Chapter 19Monte Carlo Valuation 57319.1 Computing the Option Price as a

Discounted Expected Value 573Valuation with Risk-Neutral

Probabilities 574Valuation with True Probabilities 575

19.2 Computing Random Numbers 57719.3 Simulating Lognormal Stock Prices 578

Simulating a Sequence of Stock Prices 57819.4 Monte Carlo Valuation 580

Monte Carlo Valuation of a EuropeanCall 580

Accuracy of Monte Carlo 581Arithmetic Asian Option 582

19.5 Efficient Monte Carlo Valuation 584Control Variate Method 584Other Monte Carlo Methods 587

19.6 Valuation of American Options 58819.7 The Poisson Distribution 59119.8 Simulating Jumps with the Poisson

Distribution 593Simulating the Stock Price withJumps 593

Multiple Jumps 59619.9 Simulating Correlated Stock Prices 597

Generating n Correlated LognormalRandom Variables 597


19.A Formulas for Geometric AverageOptions 602

Chapter 20Brownian Motion and Ito'sLemma 60320.1 The Black-Scholes Assumption about

Stock Prices 60320.2 Brownian Motion 604

Definition of Brownian Motion 604Properties of Brownian Motion 606Arithmetic Brownian Motion 607The Ornstein-Uhlenbeck Process 608

20.3 Geometric Brownian Motion 609Lognormality 609Relative Importance of the Drift and Noise

Terms 610 \Multiplication Rules 610Modeling Correlated Asset Prices 612

20.4 Ito's Lemma 613Functions of an Ito Process 614Multivariate Ito's Lemma 616

20.5 The Sharpe Ratio 61720.6 Risk-Neutral Valuation 618

A Claim That Pays S(T)a 619Specific Examples 620Valuing a Claim on Sa Qb 621

20.7 Jumps in the Stock Price 623Chapter Summary 624Further Reading 624Problems 624

20.A Valuation Using Discounted CashFlow 626

Chapter 21The Black-Scholes-MertonEquation 62721.1 Differential Equations and Valuation

under Certainty 627The Valuation Equation 628Bonds 628Dividend-Paying Stocks 629

Contents xvii

The General Structure 62921.2 The Black-Scholes Equation 629,

Verifying the Formula for a Derivative 631The Black-Scholes Equation and

Equilibrium Returns 634What If the Underlying Asset Is Not an

Investment Asset? 63521.3 Risk-Neutral Pricing 637

Interpreting the Black-ScholesEquation 637

The. Backward Equation 637Derivative Prices as Discounted Expected

Cash Flows 63821.4 Changing the Numeraire 63921.5 Option Pricing When the Stock Price Can

Jump 642Mertons Solution for DiversifiableJumps 643


21.A Multivariate Black-Scholes Analysis 64621.B Proof of Proposition 21.1 64621.C Solutions for Prices and Probabilities 647

Asset-or-Nothing Call 665The Black-Scholes Formula 666European Outperformance Option 667Option on a Zero-Coupon Bond 667

22.6 Example: Long-Maturity Put Options 667The Black-Scholes Put Price

Calculation 668Is the Put Price Reasonable? 669Discussion 671


22.A The Portfolio Selection Problem 676The One-Period Portfolio Selection

Problem 676The Risk Premium of an Asset 678Multiple Consumption and Investment

Periods 67922.B Girsanov's Theorem 679

The Theorem 679Constructing Multi^Asset Processes from

Independent Brownian Motions 68022.C Risk-Neutral Pricing and. Marginal Utility

in the Binomial Model 681

Chapter 22Risk-Neutral and MartingalePricing 64922.1 Risk Aversion and Marginal Utility 65022.2 The First-Order Condition for Portfolio

Selection 652 *22.3 Change of Measure and Change of

Numeraire 654Change of Measure 655The Martingale Property 655Girsanov's Theorem 657

22.4 Examples of Numeraire and MeasureChange 658

The Money-Market Account as Numeraire(Risk-Neutral Measure) 659

Risky Asset as Numeraire 662Zero Coupon Bond as Numeraire (Forward

Measure) 66222.5 Examples of Martingale Pricing 663

Cash-or-Nothing Call 663

Chapter 23Exotic Options: II 68323.1 All-or-Nothing Options 683

Terminology 683Cash-or-Nothing Options 684Asset-or-Nothing Options 685Ordinary Options and Gap Options 686Delta-Hedging All-or-Nothing

Options 68723.2 All-or-Nothing Barrier Options 688

Cash-or-Nothing Barrier Options 690Asset-or-Nothing Barrier Options 694Rebate Options 694Perpetual American Options 695

23.3 Barrier Options 69623.4 Quantos 697

The Yen Perspective 698The Dollar Perspective 699A Binomial Model for the Dollar-

Denominated Investor 701

xvm Contents

23.5 Currency-Linked Options 704Foreign Equity Call Struck in Foreign

Currency 705Foreign Equity Call Struck in Domestic

Currency 706Fixed Exchange Rate Foreign Equity

Call 707Equity-Linked Foreign Exchange Call 707

23.6 Other Multivariate Options 708Options on the Best of Two Assets • 709 _ -

/ Basket Options 710*_ Chapter Summary 711

Further Reading 711Problems 712

23.A The Reflection Principle 715

Chapter 24Volatility 71724.1 Implied Volatility 71824.2 Measurement and Behavior of

Volatility 720Historical Volatility 720Exponentially Weighted Moving

Average 721Time-Varying Volatility: ARCH 723The GARCH Model 727Realized Quadratic Variation 729

24.3 Hedging and Pricing Volatility 731Variance and Volatility Swaps 731Pricing Volatility 733

24.4 Extending the Black-Scholes Model 736Jump Risk and Implied Volatility 737Constant Elasticity of Variance 737The Heston Model 740Evidence 742


Chapter 25Interest Rate and BondDerivatives 75125.1 An Introduction to Interest Rate

Derivatives 752Bond and Interest Rate Forwards 752

Options on Bonds and Rates 753Equivalence of a Bond Put and an Interest

Rate Call 754Taxonomy of Interest Rate Models 754

25.2 Interest Rate Derivatives and theBlack-Scholes-Merton Approach 756

An Equilibrium Equation for Bonds 75725.3 Continuous-Time Short-Rate Models 760

The Rendelman-Bartter Model 760The Vasicek Model 761The Cox-Ingersoll-Ross Model 762Comparing Vasicek and CIR 763Duration and Convexity Revisited 764

25.4 Short-Rate Models and Interest RateTrees 765

An Illustrative Tree 765The Black-Derman-Toy Model 769Hull-White Model 773

25.5 Market Models 780The Black Model 780LIBOR Market Model 781


25.A Constructing the BDT Tree 787

Chapter 26Value at Risk 78926.1 Value at Risk 789

Value at Risk for One Stock 793VaR for Two or More Stocks 795VaR for Nonlinear Portfolios 796VaR for Bonds 801Estimating Volatility 805Bootstrapping Return Distributions 806

26.2 Issues with VaR 807Alternative Risk Measures 807VaR and the Risk-Neutral Distribution 810Subadditive Risk Measures 811


Chapter 27Credit Risk 81527.1 Default Concepts and Terminology 815

Contents xix

27.2 The Merton Default Model 817Default at Maturity 817Related Models 819

27.3 Bond Ratings and DefaultExperience 821

Rating Transitions 822Recovery Rates 824Reduced Form Bankruptcy Models 824

27.4 Credit Default Swaps 826Single-Name Credit Default Swaps 826'Pricing a Default Swap 828 »CDS Indices 832Other Credit-Linked Structures 834

27.5 Tranched Structures 834Collateralized Debt Obligations 836CDO-Squareds 840Nth to default baskets 842


Appendix AThe Greek Alphabet 851

Appendix BContinuous Compounding 853B.I The Language of Interest Rates 853B.2 The Logarithmic and Exponential

Functions 854Changing Interest Rates 855Symmetry for Increases and Decreases 855

Problems 856

Appendix CJensen's Inequality 859C.I Example: The Exponential Function 859C.2 Example: The Price of a Call 860C.3 Proof of Jensen's Inequality 861

Problems 862

Appendix DAn Introduction to Visual Basic forApplications 863D.I Calculations without VBA 863

D.2 How to Learn VBA 864D.3 Calculations with VBA 864

Creating a Simple Function 864A Simple Example of a Subroutine 865Creating a Button to Invoke a

Subroutine 866Functions Can Call Functions 867Illegal Function Names 867Differences between Functions and

Subroutines 867D.4 Storing and Retrieving Variables in a

Worksheet 868Using a Named Range to Read and Write

Numbers from the Spreadsheet 868Reading and Writing to Cells That Are Not

Named 869Using the Cells Function to Read and

Write to Cells 870Reading from within a Function 870

D.5 Using Excel Functions from withinVBA 871

Using VBA to Compute the Black-ScholesFormula 871

The Object Browser 872D.6 Checking for Conditions 873D.7 Arrays 874

Defining Arrays 874D.8 Iteration 875

A Simple for Loop 876Creating a Binomial Tree 876Other Kinds of Loops 877

D.9 Reading and Writing Arrays 878Arrays as Output 878Arrays as Inputs 879

D.10 Miscellany 880

Getting Excel to Generate Macros forYou 880

Using Multiple Modules 881Recalculation Speed 881Debugging 882Creating an Add-In 882

Glossary 883

References 897

Index 915

Derivitives Markets - GBVDerivitives Markets THIRD EDITION Robert L. McDonald Northwestern...

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Transcript of Derivitives Markets - GBVDerivitives Markets THIRD EDITION Robert L. McDonald Northwestern...