Verfügbarkeit: Derivatives markets

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Bibliographische Detailangaben
1. Verfasser:	McDonald, Robert L. 1954- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boston [u.a.] Addison Wesley 2006
Ausgabe:	2. ed.
Schriftenreihe:	Addison-Wesley series in finance
Schlagworte:	Finanzderivat Derivative securities Derivat > Wertpapier Finanzinstrument Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XXIX, 964 S. graph. Darst. 1 CD-ROM (12 cm)
ISBN:	0321311493

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Datensatz im Suchindex

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adam_text	Preface xxi Chapter I Introduction to Derivatives 1 1.1 What Is a Derivative? 1 Uses of Derivatives 2 Perspectives on Derivatives 3 Financial Engineering and Security Design 3 1.2 The Role of Financial Markets 4 Financial Markets and the Averages 4 Risk-Sharing 5 1.3 Derivatives in Practice 6 Growth in Derivatives Trading 7 How Are Derivatives Used? 10 1.4 Buying and Short-Selling Financial Assets 11 Buying an Asset 11 Short-Selling 12 The Lease Rate of an Asset 14 Risk and Scarcity in Short-Selling 15 Chapter Summary 16 Further Reading 16 Problems 17 PART ONE INSURANCE, HEDGING, AND SIMPLE STRATEGIES 19 Chapter 2 An Introduction to Forwards and Options 21 2.1 Forward Contracts 21 The Payoff on a Forward Contract 23 Graphing the Payoff on a Forward Contract 25 Comparing a Forward and Outright Purchase 26 Zero-Coupon Bonds in Payoff and Profit Diagrams 28 Cash Settlement Versus Delivery 30 Credit Risk 30 2.2 Call Options 31 Option Terminology 32 Payoff and Profit for a Purchased Call Option 33 Payoff and Profit for a Written Call Option 37 2.3 Put Options 38 Payoff and Profit for a Purchased Put Option 39 Payoff and Profit for a Written Put Option 40 The Moneyness of an Option 43 2.4 Summary of Forward and Option Positions 43 Long Positions 44 Short Positions 44 2.5 Options Are Insurance 45 Homeowner s Insurance Is a Put Option 45 But I Thought Insurance Is Prudent and Put Options Are Risky ... 47 Call Options Are Also Insurance 47 2.6 Example: Equity-Linked CDs 48 Graphing the Payoff on the CD 49 Economics of the CD 50 Why Equity-Linked CDs? 51 Chapter Summary 52 Further Reading 53 Problems 54 Appendix 2. A: More on Buying a Stock Option 56 Dividends 56 VII viii Contents Exercise 57 Margins for Written Options 57 Taxes 58 Chapter 3 Insurance, Collars, and Other Strategies 59 3.1 Basic Insurance Strategies 59 Insuring a Long Position: Floors 59 Insuring a Short Position: Caps 62 Selling Insurance 63 3.2 Synthetic Forwards 66 Put-Call Parity 68 3.3 Spreads and Collars 70 Bull and Bear Spreads 71 Box Spreads 72 Ratio Spreads 73 Collars 73 3.4 Speculating on Volatility 78 Straddles 78 Butterfly Spreads 81 Asymmetric Butterfly Spreads 82 3.5 Example: Another Equity-Linked Note 83 Chapter Summary 85 Further Reading 86 Problems 87 Chapter 4 Introduction to Risk Management 91 4.1 Basic Risk Management: The Producer s Perspective 91 Hedging with a Forward Contract 92 Insurance: Guaranteeing a Minimum Price with a Put Option 93 Insuring by Selling a Call 95 Adjusting the Amount of Insurance 96 4.2 Basic Risk Management: The Buyer s Perspective 98 Hedging with a Forward Contract 98 Insurance: Guaranteeing a Maximum Price with a Call Option 99 4.3 Why Do Firms Manage Risk? 100 An Example Where Hedging Adds Value 101 Reasons to Hedge 103 Reasons Noi to Hedge 106 Empirical Evidence on Hedging 106 4.4 Golddiggers Revisited 108 Selling the Gain: Collars 108 Other Collar Strategies 112 Paylater Strategies 113 4.5 Selecting the Hedge Ratio 113 Cross-Hedging 114 Quantity Uncertainty 116 Chapter Summary 119 Further Reading 120 Problems 120 PART TWO FORWARDS, FUTURES, AND SWAPS 125 Chapter 5 Financial Forwards and Futures 127 5.1 Alternative Ways to Buy a Stock 127 5.2 Prepaid Forward Contracts on Stock 128 Pricing the Prepaid Forward by Analogy 128 Pricing the Prepaid Forward by Discounted Present Value 129 Pricing the Prepaid Forward by Arbitrage 129 Pricing Prepaid Forwards with Dividends 131 5.3 Forward Contracts on Stock 133 Creating a Synthetic Forward Contract 135 Synthetic Forwards in Market-Making and Arbitrage 136 Contents їх No-Arbitrage Bounds with Transaction Costs 138 Quasi- Ar bitrage 139 Does the Forward Price Predict the Future Price? 140 An Interpretation of the Forward Pricing Formula 141 5.4 Futures Contracts 142 The S&P 500 Futures Contract 143 Margins and Marking to Market 144 Comparing Futures and Forward Prices 146 Arbitrage in Practice: S&P 500 Index Arbitrage 147 Quanto Index Contracts 149 5.5 Uses of Index Futures 150 Asset Allocation 150 Cross-hedging with Index Futures 151 5.6 Currency Contracts 154 Currency Prepaid Forward 155 Currency Forward 156 Covered Interest Arbitrage 156 5.7 Eurodollar Futures 160 Chapter Summary 160 Further Reading 162 Problems 162 Appendix 5. A: Taxes and the Forward Price 166 Appendix 5.B: Equating Forwards and Futures 166 Chapter 6 Commodity Forwards and Futures 169 6.1 Introduction to Commodity Forwards 169 6.2 Equilibrium Pricing of Commodity Forwards 171 6.3 Nonstorability: Electricity 172 6.4 Pricing Commodity Forwards by Arbitrage: An Example 174 An Apparent Arbitrage and Resolution 175 Pencils Have a Positive Lease Rate 176 6.5 The Commodity Lease Rate 178 The Lease Market for a Commodity 178 Forward Prices and the Lease Rate 179 6.6 Carry Markets 181 Storage Costs and Forward Prices 181 Storage Costs and the Lease Rate 182 The Convenience Yield 182 6.7 Gold Futures 184 Gold Investments 187 Evaluation of Gold Production 187 6.8 Seasonality: The Corn Forward Market 188 6.9 Natural Gas 191 6.10 Oil 194 6.11 Commodity Spreads 195 6.12 Hedging Strategies 196 Basis Risk 197 Hedging Jet Fuel with Crude Oil 199 Weather Derivatives 199 Chapter Summary 200 Further Reading 201 Problems 201 Chapter 7 Interest Rate Forwards and Futures 205 7.1 Bond Basics 205 Zero-Coupon Bonds 206 Implied Forward Rates 208 Coupon Bonds 210 Zeros from Coupons 211 Interpreting the Coupon Rate 212 Continuously Compounded Yields 213 7.2 Forward Rate Agreements, Eurodollars, and Hedging 214 Forward Rate Agreements 214 Synthetic FRAs 216 Eurodollar Futures 218 Interest Rate Strips and Stacks 223 Contents 7.3 Duration and Convexity 223 Duration 224 Duration Matching 227 Convexity 228 7.4 Treasury-Bond and Treasury-Note Futures 230 7.5 Repurchase Agreements 233 Chapter Summary 235 Further Reading 237 Problems 237 Appendix 7. A: Interest Rate and Bond Frice Conventions 241 Bonds 242 Bills 244 Chapter 8 Swaps 247 8.1 An Example of a Commodity Swap 247 Physical Versus Financial Settlement 248 Why Is the Swap Price Not $20.50? 250 The Swap Counterparty 250 The Market Value of a Swap 253 8.2 Interest Rate Swaps 254 A Simple Interest Rate Swap 254 Pricing and the Swap Counterparty 255 Computing the Swap Rate in General 257 The Swap Curve 258 The Swap s Implicit Loan Balance 260 Deferred Swaps 261 Why Swap Interest Rates? 262 Amortizing and Accreting Swaps 263 8.3 Currency Swaps 264 Currency Swap Formulas 267 Other Currency Swaps 267 8.4 Commodity Swaps 268 The Commodity Swap Price 268 Swaps with Variable Quantity and Price 269 8.5 Swaptions 271 8.6 Total Return Swaps 272 Chapter Summary 274 Further Reading 275 Problems 275 PART THREE OPTIONS 279 Chapter 9 Parity and Other Option Relationships 281 9.1 Put-Call Parity 281 Options on Stocks 283 Options on Currencies 286 Options on Bonds 286 9.2 Generalized Parity and Exchange Options 287 Options to Exchange Stock 288 What Are Calls and Puts? 289 Currency Options 290 9.3 Comparing Options with Respect to Style, Maturity, and Strike 292 European Versus American Options 293 Maximum and Minimum Option Prices 293 Early Exercise for American Options 294 Time to Expiration 297 Different Strike Prices 299 Exercise and Moneyness 304 Chapter Summary 305 Further Reading 306 Problems 306 Appendix 9. A: Parity Bounds for American Options 310 Appendix 9.B: Algebraic Proofs of Strike-Price Relations 311 Chapter 10 Binomial Option Pricing: I 313 10.1 A One-Period Binomial Tree 313 Computing the Option Price 314 The Binomial Solution 315 Arbitraging a Mispriced Option 318 Contents χι A Graphical Interpretation of the Binomial Formula 319 Risk-Neutral Pricing 320 Constructing a Binomial Tree 321 Another One-Period Example 322 Summary 322 10.2 Two or More Binomial Periods 323 A Two-Period European Call 323 Many Binomial Periods 326 10.3 Put Options 328 10.4 American Options 329 10.5 Options on Other Assets 330 Option on a Stock Index 330 Options on Currencies 332 Options on Futures Contracts 332 Options on Commodities 334 Options on Bonds 335 Summary 336 Chapter Summary 337 Further Reading 337 Problems 338 Appendix 1 0.A: Taxes and Option Prices 341 Chapter 11 Binomial Option Pricing: II 343 11.1 Understanding Early Exercise 343 11.2 Understanding Risk-Neutral Pricing 346 The Risk-Neutral Probability 346 Pricing an Option Using Real Probabilities 347 11.3 The Binomial Tree and Lognormality 351 The Random Walk Model 351 Modeling Stock Prices as a Random Walk 352 Continuously Compounded Returns 353 The Standard Deviation of Returns 354 The Binomial Model 355 Lognormality and the Binomial Model 355 Alternative Binomial Trees 358 Is the Binomial Model Realistic? 359 11.4 Estimating Volatility 360 11.5 Stocks Paying Discrete Dividends 361 Modeling Discrete Dividends 361 Problems with the Discrete Dividend Tree 362 A Binomial Tree Using the Prepaid Forward 363 Chapter Summary 365 Further Reading 366 Problems 366 Appendix 11. A: Pricing Options with True Probabilities 369 Appendix ll.B: Why Does Risk-Neutral Pricing Work? 369 Utility-Based Valuation 369 Standard Discounted Cash Flow 371 Risk-Neutral Pricing 371 Example 372 Why Risk-Neutral Pricing Works 3 73 Chapter 12 The Black-Scholes Formula 375 12.1 Introduction to the Black-Scholes Formula 375 Call Options 375 Put Options 378 When Is the Black-Scholes Formula Valid? 379 12.2 Applying the Formula to Other Assets 379 Options on Stocks with Discrete Dividends 380 Options on Currencies 381 Options on Futures 381 12.3 Option Greeks 382 Definition of the Greeks 382 Greek Measures for Portfolios 388 Option Elasticity 389 xii Contents 12.4 Profit Diagrams Before Maturity 395 Purchased Call Option 396 Calendar Spreads 397 12.5 Implied Volatility 400 Computing Implied Volatility 400 Using Implied Volatility 402 12.6 Perpetual American Options 403 Barrier Present Values 403 Perpetual Calls 404 Perpetual Puts 404 Chapter Summary 405 Further Reading 405 Problems 406 Appendix 12. A: The Standard Normal Distribution 409 Appendix 12. B: Formulas for Option Greeks 410 Delta 410 Gamma 410 Theta 410 Vega 411 Rho 411 Psi 411 Chapter 13 Market-Making and Delta-Hedging 413 13.1 What Do Market-Makers Do? 413 13.2 Market-Maker Risk 414 Option Risk in the Absence of Hedging 414 Delta and Gamma as Measures of Exposure 416 13.3 Delta-Hedging 417 An Example of Delta-Hedging for 2 Days 417 Interpreting the Profit Calculation 418 Delta-Hedging for Several Days 420 A Self-Financing Portfolio: The Stock Moves One σ 422 13.4 The Mathematics of Delta-Hedging 422 Using Gamma to Better Approximate the Change in the Option Price 423 Delta-Gamma Approximations 424 Theta: Accounting for Time 425 Understanding the Market-Maker s Profit 427 13.5 The Black-Scholes Analysis 429 The Black-Scholes Argument 429 Delta-Hedging of American Options 430 What Is the Advantage to Frequent Re-Hedging? 431 Delta-Hedging in Practice 432 Gamma-Neutrality 433 13.6 Market-Making as Insurance 436 Insurance 436 Market-Makers 437 Chapter Summary 438 Further Reading 438 Problems 438 Appendix 13. A: Taylor Series Approximations 441 Appendix 13. B: Greeks in the Binomial Model 441 Chapter 14 Exotic Options: I 443 14.1 Introduction 443 14.2 Asian Options 444 XYZ s Hedging Problem 445 Options on the Average 446 Comparing Asian Options 447 An Asian Solution for XYZ 448 14.3 Barrier Options 449 Types of Barrier Options 450 Currency Hedging 451 14.4 Compound Options 453 Compound Option Parity 454 Options on Dividend-Paying Stocks 455 Currency Hedging with Compound Options 456 14.5 Gap Options 457 14.6 Exchange Options 459 European Exchange Options 459 Chapter Summary 461 Further Reading 462 Contents xiii Problems 462 Appendix 14. A: Pricing Formulas for Exotic Options 466 Asian Options Based on the Geometric Average 466 Compound Options 467 Infinitely Lived Exchange Option 468 PART FOUR FINANCIAL ENGINEERING AND APPLICATIONS 471 Chapter 15 Financial Engineering and Security Design 473 15.1 The Modigliani-Miller Theorem 473 15.2 Pricing and Designing Structured Notes 474 Zero-Coupon Bonds 474 Coupon Bonds 475 Equity-Linked Bonds 476 Commodity-Linked Bonds 478 Currency-Linked Bonds 481 15.3 Bonds with Embedded Options 482 Options in Coupon Bonds 482 Options in Equity-Linked Notes 483 Valuing and Structuring an Equity-Linked CD 483 Alternative Structures 485 15.4 Engineered Solutions for Golddiggers 486 Gold-Linked Notes 486 Notes with Embedded Options 488 15.5 Strategies Motivated by Tax and Regulatory Considerations 490 Capital Gains Deferral 490 Tax-Deductible Equity 495 Chapter Summary 498 Further Reading 498 Problems 498 Chapter 16 Corporate Applications 503 16.1 Equity, Debt, and Warrants 503 Debt and Equity as Options 503 Multiple Debt Issues 511 Warrants 512 Convertible Bonds 513 Callable Bonds 516 Bond Valuation Based on the Stock Price 520 Other Bond Features 520 Put Warrants 522 16.2 Compensation Options 523 Whose Valuation? 525 Valuation Inputs 527 An Alternative Approach to Expensing Option Grants 528 Repricing of Compensation Options 531 Reload Options 532 Level 3 Communications 534 16.3 The Use of Collars in Acquisitions 538 The Northrop Grumman-TRV Merger 538 Chapter Summary 542 Further Reading 542 Problems 543 Chapter 17 Real Options 547 17.1 Investment and the NPV Rule 548 Static NPV 548 The Correct Use of NPV 549 The Project as an Option 550 17.2 Investment under Uncertainty 551 A Simple DCF Problem 551 Valuing Derivatives on the Cash Flow 552 Evaluating a Project with a 2-Year Investment Horizon 554 Evaluating the Project with an Infinite Investment Horizon 558 xiv Contents 17.3 Real Options in Practice 558 Peak-Load Electricity Generation 559 Research and Development 563 17.4 Commodity Extraction as an Option 565 Single-Barrel Extraction under Certainty 565 Single-Barrel Extraction under Uncertainty 569 Valuing an Infinite Oil Reserve 570 17.5 Commodity Extraction with Shut-Down and Restart Options 572 Permanent Shutting Down 574 Investment When Shutdown Is Possible 576 Restarting Production 578 Additional Options 578 Chapter Summary 579 Further Reading 580 Problems 580 Appendix 17. A: Calculation of Optimal Time to Drill an Oil Well 583 Appendix 17. В : The Solution with Shutting Down and Restarting 583 PART FIVE THEORY 585 ADVANCED PRICING Chapter 18 The Lognormal Distribution 587 18.1 The Normal Distribution 587 Converting a Normal Random Variable to Standard Normal 590 Sums of Normal Random Variables 591 18.2 The Lognormal Distribution 593 18.3 A Lognormal Model of Stock Prices 595 18.4 Lognormal Probability Calculations 598 Probabilities 599 Lognormal Confidence Intervals 600 The Conditional Expected Price 602 The Black-Scholes Formula 604 18.5 Estimating the Parameters of a Lognormal Distribution 605 18.6 How Are Asset Prices Distributed? 608 Histograms 608 Normal Probability Plots 609 Chapter Summary 613 Further Reading 613 Problems 614 Appendix 18. A: The Expectation of a Lognormal Variable 615 Appendix 18.B: Constructing a Normal Probability Plot 616 Chapter 19 Monte Carlo Valuation 617 19.1 Computing the Option Price as a Discounted Expected Value 617 Valuation with Risk-Neutral Probabilities 618 Valuation with True Probabilities 619 19.2 Computing Random Numbers 621 Using Sums of Uniformly Distributed Random Variables 622 Using the Inverse Cumulative Normal Distribution 622 19.3 Simulating Lognormal Stock Prices 623 Simulating a Sequence of Stock Prices 623 19.4 Monte Carlo Valuation 624 Monte Carlo Valuation of a European Call 625 Accuracy of Monte Carlo 626 Arithmetic Asian Option 627 19.5 Efficient Monte Carlo Valuation 630 Control Variate Method 630 Other Monte Carlo Methods 632 19.6 Valuation of American Options 633 Contents xv 19.7 The Poisson Distribution 636 19.8 Simulating Jumps with the Poisson Distribution 639 Multiple Jumps 643 19.9 Simulating Correlated Stock Prices 643 Generating η Correlated Lognormal Random Variables 644 Chapter Summary 645 Further Reading 645 Problems 646 Appendix 19. A: Formulas for Geometric Average Options 648 Chapter 20 Brownian Motion and Itô s Lemma 649 20.1 The Black-Scholes Assumption about Stock Prices 649 20.2 Brownian Motion 650 Definition of Brownian Motion 650 Properties of Brownian Motion 652 Arithmetic Brownian Motion 653 The Ornstein-Uhlenbeck Process 654 20.3 Geometric Brownian Motion 655 Lognormality 655 Relative Importance of the Drift and Noise Terms 656 Correlated Ito Processes 657 Multiplication Rules 658 20.4 The Sharpe Ratio 659 20.5 The Risk-Neutral Process 660 20.6 Itô s Lemma 663 Functions of an Ito Process 663 Multivariate Itô s Lemma 665 20.7 Valuing a Claim on S 666 The Process Followed by S 667 Proving the Proposition 668 Specific Examples 669 Valuing a Claim on S Qh 670 20.8 Jumps in the Stock Price 672 Chapter Summary 674 Further Reading 674 Problems 675 Chapter 21 The Black-Scholes Equation 679 21.1 Differential Equations and Valuation under Certainty 679 The Valuation Equation 680 Bonds 680 Dividend-Paying Stocks 681 The General Structure 681 21.2 The Black-Scholes Equation 681 Verifying the Formula for a Derivative 683 The Black-Scholes Equation and Equilibrium Returns 686 What If the Underlying Asset Is Not an Investment Asset? 688 21.3 Risk-Neutral Pricing 690 Interpreting the Black-Scholes Equation 690 The Backward Equation 691 Derivative Prices as Discounted Expected Cash Flows 692 21.4 Changing the Numeraire 693 21.5 Option Pricing When the Stock Price Can Jump 696 Merton s Solution for Diversifiable Jumps 697 Chapter Summary 698 Further Reading 698 Problems 699 Appendix 21. A: Multivariate Black-Scholes Analysis 700 Appendix 21.B: Proof of Proposition 21.1 701 Chapter 22 Exotic Options: II 703 22.1 AU-or-Nothing Options 703 Terminology 703 Cash-or-Nothing Options 704 Asset-or-Nothing Options 706 xvi Contents Ordinary Options and Gap Options 706 Delta-Hedging All-or-Nothing Options 707 22.2 All-or-Nothing Barrier Options 710 Cash-or-Nothing Barrier Options 710 Asset-or-Nothing Barrier Options 715 Rebate Options 716 22.3 Barrier Options 717 22.4 Quantos 718 The Yen Perspective 720 The Dollar Perspective 721 A Binomial Model for the Dollar-Denominated Investor 724 22.5 Currency-Linked Options 727 Foreign Equity Call Struck in Foreign Currency 728 Foreign Equity Call Struck in Domestic Currency 729 Fixed Exchange Rate Foreign Equity Call 730 Equity-Linked Foreign Exchange Call 731 22.6 Other Multivariate Options 732 Exchange Options 732 Options on the Best of Two Assets 733 Basket Options 735 Chapter Summary 736 Further Reading 736 Problems 737 Chapter 23 Volatility 741 23.1 Implied Volatility 741 23.2 Measurement and Behavior of Volatility 744 Historical Volatility 744 Exponentially Weighted Moving Average 746 Time-Varying Volatility: ARCH 747 The GARCH Model 751 Realized Quadratic Variation 755 23.3 Hedging and Pricing Volatility 757 Variance and Volatility Swaps 758 Pricing Volatility 759 23.4 Extending the Black-Scholes Model 763 Jump Risk and Implied Volatility 764 Constant Elasticity of Variance 766 The Heston Model 768 Evidence 771 Chapter Summary 773 Further Reading 773 Problems 774 Appendix 23.A 777 Chapter 24 Interest Rate Models 779 24.1 Market-Making and Bond Pricing 779 The Behavior of Bonds and Interest Rates 780 An Impossible Bond Pricing Model 780 An Equilibrium Equation for Bonds 781 Delta-Gamma Approximations for Bonds 784 24.2 Equilibrium Short-Rate Bond Price Models 785 The Rendelman-Bartter Model 785 The Vasicek Model 786 The Cox-Ingersoll-Ross Model 787 Comparing Vasicek and CIR 788 24.3 Bond Options, Caps, and the Black Model 790 24.4 A Binomial Interest Rate Model 793 Zero-Coupon Bond Prices 794 Yields and Expected Interest Rates 796 Option Pricing 797 24.5 The Black-Derman-Toy Model 798 Verifying Yields 802 Verifying Volatilities 803 Constructing a Black-Derman-Toy Tree 804 Pricing Examples 805 Contents xvii Chapter Summary 808 Further Reading 808 Problems 809 Appendix 24.A: The Heath- ) arrow-Morton Model 811 Chapter 25 Value at Risk 813 25.1 Value at Risk 813 Value at Risk for One Stock 815 VaR for Two or More Stocks 817 VaR for Nonlinear Portfolios 819 VaR for Bonds 826 Estimating Volatility 830 Bootstrapping Return Distributions 831 25.2 Issues with VaR 832 Alternative Risk Measures 832 VaR and the Risk-Neutral Distribution 835 Subadditive Risk Measures 837 Chapter Summary 838 Further Reading 839 Problems 839 Chapter 26 Credit Risk 841 26.1 Default Concepts and Terminology 841 26.2 The Merton Default Model 843 Default at Maturity 843 Related Models 845 26.3 Bond Ratings and Default Experience 847 Using Ratings to Assess Bankruptcy Probability 847 Recovery Rates 850 Reduced Form Bankruptcy Models 852 26.4 Credit Instruments 853 Collateralized Debt Obligations 853 Credit Default Swaps and Related Structures 858 Pricing a Default Swap 862 CDS Indices 864 Chapter Summary 866 Further Reading 867 Problems 867 PART SIX APPENDIXES 871 Appendix A The Greek Alphabet 873 Appendix В Continuous Compounding 875 B.I The Language of Interest Rates 875 B.2 The Logarithmic and Exponential Functions 876 Changing Interest Rates 877 Symmetry for Increases and Decreases 878 Problems 878 Appendix С Jensen s Inequality 881 C.I Example: The Exponential Function 881 C.2 Example: The Price of a Call 882 C.3 Proof of Jensen s Inequality 884 Problems 884 Appendix D An Introduction to Visual Basic for Applications 885 D.I Calculations without VBA 885 D.2 How to Learn VBA 886 D.3 Calculations with VBA 886 Creating a Simple Function 886 A Simple Example of a Subroutine 888 Creating a Button to Invoke a Subroutine QQQ OOO Functions Can Call Functions 889 Illegal Function Names 889 Differences between Functions and Subroutines 890 xviii Contents D.4 Storing and Retrieving Variables in a Worksheet 890 Using a Named Range to Read and Write Numbers from a Spreadsheet 891 Reading and Writing to Cells That Are Not Named 892 Using the Cells Functions to Read and Write to Cells 892 Reading from within a Function 893 D.5 Using Excel Functions from within VBA 893 Using VBA to Compute the Black-Scholes Formula 894 The Object Browser 895 D.6 Checking for Conditions 896 D.7 Arrays 897 Defining Arrays 897 D.8 Iteration 899 A Simple for Loop 899 Creating a Binomial Tree 900 Other Kinds of Loops 901 D.9 Reading and Writing Arrays 901 Arrays as Outputs 901 Arrays as Inputs 903 D.10 Miscellany 904 Getting Excel to Generate Macros for You 904 Using Multiple Modules 905 Recalculation Speed 905 Debugging 906 Creating an Add-In 906 Glossary 907 Bibliography 921 Index 935
adam_txt	Preface xxi Chapter I Introduction to Derivatives 1 1.1 What Is a Derivative? 1 Uses of Derivatives 2 Perspectives on Derivatives 3 Financial Engineering and Security Design 3 1.2 The Role of Financial Markets 4 Financial Markets and the Averages 4 Risk-Sharing 5 1.3 Derivatives in Practice 6 Growth in Derivatives Trading 7 How Are Derivatives Used? 10 1.4 Buying and Short-Selling Financial Assets 11 Buying an Asset 11 Short-Selling 12 The Lease Rate of an Asset 14 Risk and Scarcity in Short-Selling 15 Chapter Summary 16 Further Reading 16 Problems 17 PART ONE INSURANCE, HEDGING, AND SIMPLE STRATEGIES 19 Chapter 2 An Introduction to Forwards and Options 21 2.1 Forward Contracts 21 The Payoff on a Forward Contract 23 Graphing the Payoff on a Forward Contract 25 Comparing a Forward and Outright Purchase 26 Zero-Coupon Bonds in Payoff and Profit Diagrams 28 Cash Settlement Versus Delivery 30 Credit Risk 30 2.2 Call Options 31 Option Terminology 32 Payoff and Profit for a Purchased Call Option 33 Payoff and Profit for a Written Call Option 37 2.3 Put Options 38 Payoff and Profit for a Purchased Put Option 39 Payoff and Profit for a Written Put Option 40 The "Moneyness" of an Option 43 2.4 Summary of Forward and Option Positions 43 Long Positions 44 Short Positions 44 2.5 Options Are Insurance 45 Homeowner's Insurance Is a Put Option 45 But I Thought Insurance Is Prudent and Put Options Are Risky . 47 Call Options Are Also Insurance 47 2.6 Example: Equity-Linked CDs 48 Graphing the Payoff on the CD 49 Economics of the CD 50 Why Equity-Linked CDs? 51 Chapter Summary 52 Further Reading 53 Problems 54 Appendix 2. A: More on Buying a Stock Option 56 Dividends 56 VII viii Contents Exercise 57 Margins for Written Options 57 Taxes 58 Chapter 3 Insurance, Collars, and Other Strategies 59 3.1 Basic Insurance Strategies 59 Insuring a Long Position: Floors 59 Insuring a Short Position: Caps 62 Selling Insurance 63 3.2 Synthetic Forwards 66 Put-Call Parity 68 3.3 Spreads and Collars 70 Bull and Bear Spreads 71 Box Spreads 72 Ratio Spreads 73 Collars 73 3.4 Speculating on Volatility 78 Straddles 78 Butterfly Spreads 81 Asymmetric Butterfly Spreads 82 3.5 Example: Another Equity-Linked Note 83 Chapter Summary 85 Further Reading 86 Problems 87 Chapter 4 Introduction to Risk Management 91 4.1 Basic Risk Management: The Producer's Perspective 91 Hedging with a Forward Contract 92 Insurance: Guaranteeing a Minimum Price with a Put Option 93 Insuring by Selling a Call 95 Adjusting the Amount of Insurance 96 4.2 Basic Risk Management: The Buyer's Perspective 98 Hedging with a Forward Contract 98 Insurance: Guaranteeing a Maximum Price with a Call Option 99 4.3 Why Do Firms Manage Risk? 100 An Example Where Hedging Adds Value 101 Reasons to Hedge 103 Reasons Noi to Hedge 106 Empirical Evidence on Hedging 106 4.4 Golddiggers Revisited 108 Selling the Gain: Collars 108 Other Collar Strategies 112 Paylater Strategies 113 4.5 Selecting the Hedge Ratio 113 Cross-Hedging 114 Quantity Uncertainty 116 Chapter Summary 119 Further Reading 120 Problems 120 PART TWO FORWARDS, FUTURES, AND SWAPS 125 Chapter 5 Financial Forwards and Futures 127 5.1 Alternative Ways to Buy a Stock 127 5.2 Prepaid Forward Contracts on Stock 128 Pricing the Prepaid Forward by Analogy 128 Pricing the Prepaid Forward by Discounted Present Value 129 Pricing the Prepaid Forward by Arbitrage 129 Pricing Prepaid Forwards with Dividends 131 5.3 Forward Contracts on Stock 133 Creating a Synthetic Forward Contract 135 Synthetic Forwards in Market-Making and Arbitrage 136 Contents їх No-Arbitrage Bounds with Transaction Costs 138 Quasi- Ar bitrage 139 Does the Forward Price Predict the Future Price? 140 An Interpretation of the Forward Pricing Formula 141 5.4 Futures Contracts 142 The S&P 500 Futures Contract 143 Margins and Marking to Market 144 Comparing Futures and Forward Prices 146 Arbitrage in Practice: S&P 500 Index Arbitrage 147 Quanto Index Contracts 149 5.5 Uses of Index Futures 150 Asset Allocation 150 Cross-hedging with Index Futures 151 5.6 Currency Contracts 154 Currency Prepaid Forward 155 Currency Forward 156 Covered Interest Arbitrage 156 5.7 Eurodollar Futures 160 Chapter Summary 160 Further Reading 162 Problems 162 Appendix 5. A: Taxes and the Forward Price 166 Appendix 5.B: Equating Forwards and Futures 166 Chapter 6 Commodity Forwards and Futures 169 6.1 Introduction to Commodity Forwards 169 6.2 Equilibrium Pricing of Commodity Forwards 171 6.3 Nonstorability: Electricity 172 6.4 Pricing Commodity Forwards by Arbitrage: An Example 174 An Apparent Arbitrage and Resolution 175 Pencils Have a Positive Lease Rate 176 6.5 The Commodity Lease Rate 178 The Lease Market for a Commodity 178 Forward Prices and the Lease Rate 179 6.6 Carry Markets 181 Storage Costs and Forward Prices 181 Storage Costs and the Lease Rate 182 The Convenience Yield 182 6.7 Gold Futures 184 Gold Investments 187 Evaluation of Gold Production 187 6.8 Seasonality: The Corn Forward Market 188 6.9 Natural Gas 191 6.10 Oil 194 6.11 Commodity Spreads 195 6.12 Hedging Strategies 196 Basis Risk 197 Hedging Jet Fuel with Crude Oil 199 Weather Derivatives 199 Chapter Summary 200 Further Reading 201 Problems 201 Chapter 7 Interest Rate Forwards and Futures 205 7.1 Bond Basics 205 Zero-Coupon Bonds 206 Implied Forward Rates 208 Coupon Bonds 210 Zeros from Coupons 211 Interpreting the Coupon Rate 212 Continuously Compounded Yields 213 7.2 Forward Rate Agreements, Eurodollars, and Hedging 214 Forward Rate Agreements 214 Synthetic FRAs 216 Eurodollar Futures 218 Interest Rate Strips and Stacks 223 Contents 7.3 Duration and Convexity 223 Duration 224 Duration Matching 227 Convexity 228 7.4 Treasury-Bond and Treasury-Note Futures 230 7.5 Repurchase Agreements 233 Chapter Summary 235 Further Reading 237 Problems 237 Appendix 7. A: Interest Rate and Bond Frice Conventions 241 Bonds 242 Bills 244 Chapter 8 Swaps 247 8.1 An Example of a Commodity Swap 247 Physical Versus Financial Settlement 248 Why Is the Swap Price Not $20.50? 250 The Swap Counterparty 250 The Market Value of a Swap 253 8.2 Interest Rate Swaps 254 A Simple Interest Rate Swap 254 Pricing and the Swap Counterparty 255 Computing the Swap Rate in General 257 The Swap Curve 258 The Swap's Implicit Loan Balance 260 Deferred Swaps 261 Why Swap Interest Rates? 262 Amortizing and Accreting Swaps 263 8.3 Currency Swaps 264 Currency Swap Formulas 267 Other Currency Swaps 267 8.4 Commodity Swaps 268 The Commodity Swap Price 268 Swaps with Variable Quantity and Price 269 8.5 Swaptions 271 8.6 Total Return Swaps 272 Chapter Summary 274 Further Reading 275 Problems 275 PART THREE OPTIONS 279 Chapter 9 Parity and Other Option Relationships 281 9.1 Put-Call Parity 281 Options on Stocks 283 Options on Currencies 286 Options on Bonds 286 9.2 Generalized Parity and Exchange Options 287 Options to Exchange Stock 288 What Are Calls and Puts? 289 Currency Options 290 9.3 Comparing Options with Respect to Style, Maturity, and Strike 292 European Versus American Options 293 Maximum and Minimum Option Prices 293 Early Exercise for American Options 294 Time to Expiration 297 Different Strike Prices 299 Exercise and Moneyness 304 Chapter Summary 305 Further Reading 306 Problems 306 Appendix 9. A: Parity Bounds for American Options 310 Appendix 9.B: Algebraic Proofs of Strike-Price Relations 311 Chapter 10 Binomial Option Pricing: I 313 10.1 A One-Period Binomial Tree 313 Computing the Option Price 314 The Binomial Solution 315 Arbitraging a Mispriced Option 318 Contents χι A Graphical Interpretation of the Binomial Formula 319 Risk-Neutral Pricing 320 Constructing a Binomial Tree 321 Another One-Period Example 322 Summary 322 10.2 Two or More Binomial Periods 323 A Two-Period European Call 323 Many Binomial Periods 326 10.3 Put Options 328 10.4 American Options 329 10.5 Options on Other Assets 330 Option on a Stock Index 330 Options on Currencies 332 Options on Futures Contracts 332 Options on Commodities 334 Options on Bonds 335 Summary 336 Chapter Summary 337 Further Reading 337 Problems 338 Appendix 1 0.A: Taxes and Option Prices 341 Chapter 11 Binomial Option Pricing: II 343 11.1 Understanding Early Exercise 343 11.2 Understanding Risk-Neutral Pricing 346 The Risk-Neutral Probability 346 Pricing an Option Using Real Probabilities 347 11.3 The Binomial Tree and Lognormality 351 The Random Walk Model 351 Modeling Stock Prices as a Random Walk 352 Continuously Compounded Returns 353 The Standard Deviation of Returns 354 The Binomial Model 355 Lognormality and the Binomial Model 355 Alternative Binomial Trees 358 Is the Binomial Model Realistic? 359 11.4 Estimating Volatility 360 11.5 Stocks Paying Discrete Dividends 361 Modeling Discrete Dividends 361 Problems with the Discrete Dividend Tree 362 A Binomial Tree Using the Prepaid Forward 363 Chapter Summary 365 Further Reading 366 Problems 366 Appendix 11. A: Pricing Options with True Probabilities 369 Appendix ll.B: Why Does Risk-Neutral Pricing Work? 369 Utility-Based Valuation 369 Standard Discounted Cash Flow 371 Risk-Neutral Pricing 371 Example 372 Why Risk-Neutral Pricing Works 3 73 Chapter 12 The Black-Scholes Formula 375 12.1 Introduction to the Black-Scholes Formula 375 Call Options 375 Put Options 378 When Is the Black-Scholes Formula Valid? 379 12.2 Applying the Formula to Other Assets 379 Options on Stocks with Discrete Dividends 380 Options on Currencies 381 Options on Futures 381 12.3 Option Greeks 382 Definition of the Greeks 382 Greek Measures for Portfolios 388 Option Elasticity 389 xii Contents 12.4 Profit Diagrams Before Maturity 395 Purchased Call Option 396 Calendar Spreads 397 12.5 Implied Volatility 400 Computing Implied Volatility 400 Using Implied Volatility 402 12.6 Perpetual American Options 403 Barrier Present Values 403 Perpetual Calls 404 Perpetual Puts 404 Chapter Summary 405 Further Reading 405 Problems 406 Appendix 12. A: The Standard Normal Distribution 409 Appendix 12. B: Formulas for Option Greeks 410 Delta 410 Gamma 410 Theta 410 Vega 411 Rho 411 Psi 411 Chapter 13 Market-Making and Delta-Hedging 413 13.1 What Do Market-Makers Do? 413 13.2 Market-Maker Risk 414 Option Risk in the Absence of Hedging 414 Delta and Gamma as Measures of Exposure 416 13.3 Delta-Hedging 417 An Example of Delta-Hedging for 2 Days 417 Interpreting the Profit Calculation 418 Delta-Hedging for Several Days 420 A Self-Financing Portfolio: The Stock Moves One σ 422 13.4 The Mathematics of Delta-Hedging 422 Using Gamma to Better Approximate the Change in the Option Price 423 Delta-Gamma Approximations 424 Theta: Accounting for Time 425 Understanding the Market-Maker's Profit 427 13.5 The Black-Scholes Analysis 429 The Black-Scholes Argument 429 Delta-Hedging of American Options 430 What Is the Advantage to Frequent Re-Hedging? 431 Delta-Hedging in Practice 432 Gamma-Neutrality 433 13.6 Market-Making as Insurance 436 Insurance 436 Market-Makers 437 Chapter Summary 438 Further Reading 438 Problems 438 Appendix 13. A: Taylor Series Approximations 441 Appendix 13. B: Greeks in the Binomial Model 441 Chapter 14 Exotic Options: I 443 14.1 Introduction 443 14.2 Asian Options 444 XYZ's Hedging Problem 445 Options on the Average 446 Comparing Asian Options 447 An Asian Solution for XYZ 448 14.3 Barrier Options 449 Types of Barrier Options 450 Currency Hedging 451 14.4 Compound Options 453 Compound Option Parity 454 Options on Dividend-Paying Stocks 455 Currency Hedging with Compound Options 456 14.5 Gap Options 457 14.6 Exchange Options 459 European Exchange Options 459 Chapter Summary 461 Further Reading 462 Contents xiii Problems 462 Appendix 14. A: Pricing Formulas for Exotic Options 466 Asian Options Based on the Geometric Average 466 Compound Options 467 Infinitely Lived Exchange Option 468 PART FOUR FINANCIAL ENGINEERING AND APPLICATIONS 471 Chapter 15 Financial Engineering and Security Design 473 15.1 The Modigliani-Miller Theorem 473 15.2 Pricing and Designing Structured Notes 474 Zero-Coupon Bonds 474 Coupon Bonds 475 Equity-Linked Bonds 476 Commodity-Linked Bonds 478 Currency-Linked Bonds 481 15.3 Bonds with Embedded Options 482 Options in Coupon Bonds 482 Options in Equity-Linked Notes 483 Valuing and Structuring an Equity-Linked CD 483 Alternative Structures 485 15.4 Engineered Solutions for Golddiggers 486 Gold-Linked Notes 486 Notes with Embedded Options 488 15.5 Strategies Motivated by Tax and Regulatory Considerations 490 Capital Gains Deferral 490 Tax-Deductible Equity 495 Chapter Summary 498 Further Reading 498 Problems 498 Chapter 16 Corporate Applications 503 16.1 Equity, Debt, and Warrants 503 Debt and Equity as Options 503 Multiple Debt Issues 511 Warrants 512 Convertible Bonds 513 Callable Bonds 516 Bond Valuation Based on the Stock Price 520 Other Bond Features 520 Put Warrants 522 16.2 Compensation Options 523 Whose Valuation? 525 Valuation Inputs 527 An Alternative Approach to Expensing Option Grants 528 Repricing of Compensation Options 531 Reload Options 532 Level 3 Communications 534 16.3 The Use of Collars in Acquisitions 538 The Northrop Grumman-TRV Merger 538 Chapter Summary 542 Further Reading 542 Problems 543 Chapter 17 Real Options 547 17.1 Investment and the NPV Rule 548 Static NPV 548 The Correct Use of NPV 549 The Project as an Option 550 17.2 Investment under Uncertainty 551 A Simple DCF Problem 551 Valuing Derivatives on the Cash Flow 552 Evaluating a Project with a 2-Year Investment Horizon 554 Evaluating the Project with an Infinite Investment Horizon 558 xiv Contents 17.3 Real Options in Practice 558 Peak-Load Electricity Generation 559 Research and Development 563 17.4 Commodity Extraction as an Option 565 Single-Barrel Extraction under Certainty 565 Single-Barrel Extraction under Uncertainty 569 Valuing an Infinite Oil Reserve 570 17.5 Commodity Extraction with Shut-Down and Restart Options 572 Permanent Shutting Down 574 Investment When Shutdown Is Possible 576 Restarting Production 578 Additional Options 578 Chapter Summary 579 Further Reading 580 Problems 580 Appendix 17. A: Calculation of Optimal Time to Drill an Oil Well 583 Appendix 17. В : The Solution with Shutting Down and Restarting 583 PART FIVE THEORY 585 ADVANCED PRICING Chapter 18 The Lognormal Distribution 587 18.1 The Normal Distribution 587 Converting a Normal Random Variable to Standard Normal 590 Sums of Normal Random Variables 591 18.2 The Lognormal Distribution 593 18.3 A Lognormal Model of Stock Prices 595 18.4 Lognormal Probability Calculations 598 Probabilities 599 Lognormal Confidence Intervals 600 The Conditional Expected Price 602 The Black-Scholes Formula 604 18.5 Estimating the Parameters of a Lognormal Distribution 605 18.6 How Are Asset Prices Distributed? 608 Histograms 608 Normal Probability Plots 609 Chapter Summary 613 Further Reading 613 Problems 614 Appendix 18. A: The Expectation of a Lognormal Variable 615 Appendix 18.B: Constructing a Normal Probability Plot 616 Chapter 19 Monte Carlo Valuation 617 19.1 Computing the Option Price as a Discounted Expected Value 617 Valuation with Risk-Neutral Probabilities 618 Valuation with True Probabilities 619 19.2 Computing Random Numbers 621 Using Sums of Uniformly Distributed Random Variables 622 Using the Inverse Cumulative Normal Distribution 622 19.3 Simulating Lognormal Stock Prices 623 Simulating a Sequence of Stock Prices 623 19.4 Monte Carlo Valuation 624 Monte Carlo Valuation of a European Call 625 Accuracy of Monte Carlo 626 Arithmetic Asian Option 627 19.5 Efficient Monte Carlo Valuation 630 Control Variate Method 630 Other Monte Carlo Methods 632 19.6 Valuation of American Options 633 Contents xv 19.7 The Poisson Distribution 636 19.8 Simulating Jumps with the Poisson Distribution 639 Multiple Jumps 643 19.9 Simulating Correlated Stock Prices 643 Generating η Correlated Lognormal Random Variables 644 Chapter Summary 645 Further Reading 645 Problems 646 Appendix 19. A: Formulas for Geometric Average Options 648 Chapter 20 Brownian Motion and Itô's Lemma 649 20.1 The Black-Scholes Assumption about Stock Prices 649 20.2 Brownian Motion 650 Definition of Brownian Motion 650 Properties of Brownian Motion 652 Arithmetic Brownian Motion 653 The Ornstein-Uhlenbeck Process 654 20.3 Geometric Brownian Motion 655 Lognormality 655 Relative Importance of the Drift and Noise Terms 656 Correlated Ito Processes 657 Multiplication Rules 658 20.4 The Sharpe Ratio 659 20.5 The Risk-Neutral Process 660 20.6 Itô's Lemma 663 Functions of an Ito Process 663 Multivariate Itô's Lemma 665 20.7 Valuing a Claim on S" 666 The Process Followed by S" 667 Proving the Proposition 668 Specific Examples 669 Valuing a Claim on S" Qh 670 20.8 Jumps in the Stock Price 672 Chapter Summary 674 Further Reading 674 Problems 675 Chapter 21 The Black-Scholes Equation 679 21.1 Differential Equations and Valuation under Certainty 679 The Valuation Equation 680 Bonds 680 Dividend-Paying Stocks 681 The General Structure 681 21.2 The Black-Scholes Equation 681 Verifying the Formula for a Derivative 683 The Black-Scholes Equation and Equilibrium Returns 686 What If the Underlying Asset Is Not an Investment Asset? 688 21.3 Risk-Neutral Pricing 690 Interpreting the Black-Scholes Equation 690 The Backward Equation 691 Derivative Prices as Discounted Expected Cash Flows 692 21.4 Changing the Numeraire 693 21.5 Option Pricing When the Stock Price Can Jump 696 Merton's Solution for Diversifiable Jumps 697 Chapter Summary 698 Further Reading 698 Problems 699 Appendix 21. A: Multivariate Black-Scholes Analysis 700 Appendix 21.B: Proof of Proposition 21.1 701 Chapter 22 Exotic Options: II 703 22.1 AU-or-Nothing Options 703 Terminology 703 Cash-or-Nothing Options 704 Asset-or-Nothing Options 706 xvi Contents Ordinary Options and Gap Options 706 Delta-Hedging All-or-Nothing Options 707 22.2 All-or-Nothing Barrier Options 710 Cash-or-Nothing Barrier Options 710 Asset-or-Nothing Barrier Options 715 Rebate Options 716 22.3 Barrier Options 717 22.4 Quantos 718 The Yen Perspective 720 The Dollar Perspective 721 A Binomial Model for the Dollar-Denominated Investor 724 22.5 Currency-Linked Options 727 Foreign Equity Call Struck in Foreign Currency 728 Foreign Equity Call Struck in Domestic Currency 729 Fixed Exchange Rate Foreign Equity Call 730 Equity-Linked Foreign Exchange Call 731 22.6 Other Multivariate Options 732 Exchange Options 732 Options on the Best of Two Assets 733 Basket Options 735 Chapter Summary 736 Further Reading 736 Problems 737 Chapter 23 Volatility 741 23.1 Implied Volatility 741 23.2 Measurement and Behavior of Volatility 744 Historical Volatility 744 Exponentially Weighted Moving Average 746 Time-Varying Volatility: ARCH 747 The GARCH Model 751 Realized Quadratic Variation 755 23.3 Hedging and Pricing Volatility 757 Variance and Volatility Swaps 758 Pricing Volatility 759 23.4 Extending the Black-Scholes Model 763 Jump Risk and Implied Volatility 764 Constant Elasticity of Variance 766 The Heston Model 768 Evidence 771 Chapter Summary 773 Further Reading 773 Problems 774 Appendix 23.A 777 Chapter 24 Interest Rate Models 779 24.1 Market-Making and Bond Pricing 779 The Behavior of Bonds and Interest Rates 780 An Impossible Bond Pricing Model 780 An Equilibrium Equation for Bonds 781 Delta-Gamma Approximations for Bonds 784 24.2 Equilibrium Short-Rate Bond Price Models 785 The Rendelman-Bartter Model 785 The Vasicek Model 786 The Cox-Ingersoll-Ross Model 787 Comparing Vasicek and CIR 788 24.3 Bond Options, Caps, and the Black Model 790 24.4 A Binomial Interest Rate Model 793 Zero-Coupon Bond Prices 794 Yields and Expected Interest Rates 796 Option Pricing 797 24.5 The Black-Derman-Toy Model 798 Verifying Yields 802 Verifying Volatilities 803 Constructing a Black-Derman-Toy Tree 804 Pricing Examples 805 Contents xvii Chapter Summary 808 Further Reading 808 Problems 809 Appendix 24.A: The Heath- ) 'arrow-Morton Model 811 Chapter 25 Value at Risk 813 25.1 Value at Risk 813 Value at Risk for One Stock 815 VaR for Two or More Stocks 817 VaR for Nonlinear Portfolios 819 VaR for Bonds 826 Estimating Volatility 830 Bootstrapping Return Distributions 831 25.2 Issues with VaR 832 Alternative Risk Measures 832 VaR and the Risk-Neutral Distribution 835 Subadditive Risk Measures 837 Chapter Summary 838 Further Reading 839 Problems 839 Chapter 26 Credit Risk 841 26.1 Default Concepts and Terminology 841 26.2 The Merton Default Model 843 Default at Maturity 843 Related Models 845 26.3 Bond Ratings and Default Experience 847 Using Ratings to Assess Bankruptcy Probability 847 Recovery Rates 850 Reduced Form Bankruptcy Models 852 26.4 Credit Instruments 853 Collateralized Debt Obligations 853 Credit Default Swaps and Related Structures 858 Pricing a Default Swap 862 CDS Indices 864 Chapter Summary 866 Further Reading 867 Problems 867 PART SIX APPENDIXES 871 Appendix A The Greek Alphabet 873 Appendix В Continuous Compounding 875 B.I The Language of Interest Rates 875 B.2 The Logarithmic and Exponential Functions 876 Changing Interest Rates 877 Symmetry for Increases and Decreases 878 Problems 878 Appendix С Jensen's Inequality 881 C.I Example: The Exponential Function 881 C.2 Example: The Price of a Call 882 C.3 Proof of Jensen's Inequality 884 Problems 884 Appendix D An Introduction to Visual Basic for Applications 885 D.I Calculations without VBA 885 D.2 How to Learn VBA 886 D.3 Calculations with VBA 886 Creating a Simple Function 886 A Simple Example of a Subroutine 888 Creating a Button to Invoke a Subroutine QQQ OOO Functions Can Call Functions 889 Illegal Function Names 889 Differences between Functions and Subroutines 890 xviii Contents D.4 Storing and Retrieving Variables in a Worksheet 890 Using a Named Range to Read and Write Numbers from a Spreadsheet 891 Reading and Writing to Cells That Are Not Named 892 Using the Cells Functions to Read and Write to Cells 892 Reading from within a Function 893 D.5 Using Excel Functions from within VBA 893 Using VBA to Compute the Black-Scholes Formula 894 The Object Browser 895 D.6 Checking for Conditions 896 D.7 Arrays 897 Defining Arrays 897 D.8 Iteration 899 A Simple for Loop 899 Creating a Binomial Tree 900 Other Kinds of Loops 901 D.9 Reading and Writing Arrays 901 Arrays as Outputs 901 Arrays as Inputs 903 D.10 Miscellany 904 Getting Excel to Generate Macros for You 904 Using Multiple Modules 905 Recalculation Speed 905 Debugging 906 Creating an Add-In 906 Glossary 907 Bibliography 921 Index 935
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spelling	McDonald, Robert L. 1954- Verfasser (DE-588)128943831 aut Derivatives markets Robert L. McDonald 2. ed. Boston [u.a.] Addison Wesley 2006 XXIX, 964 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in finance Finanzderivat Derivative securities Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Finanzinstrument (DE-588)4461672-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Derivat Wertpapier (DE-588)4381572-8 s Finanzinstrument (DE-588)4461672-7 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016669857&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	McDonald, Robert L. 1954- Derivatives markets Finanzderivat Derivative securities Derivat Wertpapier (DE-588)4381572-8 gnd Finanzinstrument (DE-588)4461672-7 gnd
subject_GND	(DE-588)4381572-8 (DE-588)4461672-7 (DE-588)4123623-3
title	Derivatives markets
title_auth	Derivatives markets
title_exact_search	Derivatives markets
title_exact_search_txtP	Derivatives markets
title_full	Derivatives markets Robert L. McDonald
title_fullStr	Derivatives markets Robert L. McDonald
title_full_unstemmed	Derivatives markets Robert L. McDonald
title_short	Derivatives markets
title_sort	derivatives markets
topic	Finanzderivat Derivative securities Derivat Wertpapier (DE-588)4381572-8 gnd Finanzinstrument (DE-588)4461672-7 gnd
topic_facet	Finanzderivat Derivative securities Derivat Wertpapier Finanzinstrument Lehrbuch
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