Pricing Derivative Securities

An Interactive Dynamic Environment with Maple V and MATLAB

Prisman

760 pages, parution le 01/04/2000

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Résumé

Pricing derivatives theory comes alive in this self-contained interactive experience in financial pricing. The no-arbitrage perspective in a one-period state-preference model drives the book, and the Maple and Matlab programs help readers visualize payoffs and respond to various constraints and conditions. With clear explanations and lavish illustrations, Pricing Derivative Securities teaches the core theoretical concepts so often disguised behind difficult terms and institutional details. Readers can experiment with the electronic packages forever, using the book and its solutions manual as a tutorial that can help solve problems of increasing complexity.

Enclosed CD-ROM provides an interactive, dynamic and friendly environment allowing students to learn through hands on experience
Enhances learning by altering the commands in the on-line files, varying them at will, in order to experiment with applications of the concepts and different (reader-generated) examples, in addition to the ones already in the prepared file
Provides both the framework and the tools, based on the no free lunch concept, by which readers can analyze and appreciate different scenarios, including those that are not covered in the book, related to derivative securities
Basic concepts of stochastic calculus are enriched with demonstrations using animation, simulation and three-dimensional graphs thereby overcoming mathematical complexity
The MATLAB Graphic User Interface provides the ability to bring to life on the screen the theoretical material of the chapters

Contents

Preface xv
Software xxii
1 Theory of Arbitrage 1
1.1 A Basic One-Period Model 1
1.2 Defining the No-Arbitrage Condition 5
1.2.1 Identifying an Arbitrage Portfolio 8
1.2.2 Law of One Price 11
1.3 Pricing by Replication 13
1.3.1 Three Special Contingent Cash Flows 14
1.4 Stochastic Discount Factors (SDFs) 18
1.4.1 SDFs and Risk-Neutral Probability 22
1.5 Concluding Remarks 28
1.6 Questions and Problems 29
1.7 Appendix 32
1.7.1 Complete Market 32
1.7.2 Incomplete Market 34
1.7.3 Incomplete Market and Arbitrage Bounds 35
1.7.4 The No-Arbitrage Condition and Its Geometric Exposition 42
2 Arbitrage Pricing: Equity Markets 47
2.1 Market Structure and the Risk-Free Rate 47
2.2 One-Period Binomial Model 50
2.3 Valuing Two Propositions 57
2.4 Forwards: A First Look 61
2.4.1 Forward Contract on a Security 62
2.4.2 Forward Contract on the Exchange Rate 67
2.5 Swaps: A First Look 72
2.5.1 Currency Swaps 72
2.5.2 Equity (Asset) Swap 74
2.6 General Valuation 77
2.6.1 The Risk-Free Rate of Interest Implicit in the Market 78
2.6.2 The Two Propositions 78
2.6.3 Forwards 79
2.6.4 Swaps 83
2.7 Concluding Remarks 86
2.8 Questions and Problems 87
3 Pricing by Arbitrage: Debt Markets 91
3.1 Setting the Framework 91
3.2 Arbitrage in the Debt Market 94
3.2.1 Distinct Features of the Debt Market 99
3.2.2 Defining the No-Arbitrage Condition 101
3.3 Discount Factors 104
3.4 Discount Factors and Continuous Compounding 108
3.4.1 Continuous Compounding 108
3.5 Concluding Remarks 110
3.6 Questions and Problems 111
3.7 Appendix 113
3.7.1 No-Arbitrage Condition in the Bond Market 113
4 Fundamentals of Options 115
4.1 Extending the Simple Model 115
4.2 Two Types of Options 116
4.3 Trading Strategies 125
4.3.1 Portfolios of Calls and Puts with the Same Maturity Date 127
4.4 Payoff Diagrams and Relative Pricing 141
4.4.1 Pricing Bounds Obtained by Relative Pricing Results 143
4.4.2 Put-Call Parity 148
4.5 From Payoffs to Portfolios 154
4.6 Concluding Remarks 164
4.7 Questions and Problems 165
4.8 Appendix 168
4.8.1 Explanation of Stripay 168
4.8.2 Procedural Issues 169
5 Risk-Neutral Probability and the SDF 183
5.1 Infinite vs. Finite States of Nature 184
5.2 SDF for an Infinite [Omega] 187
5.3 Risk-Neutral Probability and the SDF 191
5.4 A First Look at Stock Prices 193
5.5 The Distribution of the Rate of Return 196
5.6 Paths of the Price Process 204
5.7 Specifying a Risk-Neutral Probability 208
5.8 Lognormal Distributions and the SDF 213
5.9 The Stochastic Discount Factor Function 215
5.10 Concluding Remarks 220
5.11 Questions and Problems 221
6 Valuation of European Options 223
6.1 Valuing a Call Option 224
6.2 Valuing a Put Option 230
6.3 Combinations across Time 234
6.4 Dividends and Option Pricing 255
6.5 Volatility and Implied Volatility 259
6.5.1 Estimating Volatility from Historical Data 259
6.5.2 Implied Volatility 261
6.6 Concluding Remarks 265
6.7 Questions and Problems 266
6.8 Appendix 268
6.8.1 Estimating Implied Volatility Using Trial and Error 268
7 Sensitivity Measures 271
7.1 The Theta Measure 272
7.2 The Delta Measure 281
7.3 The Gamma Measure 288
7.4 The Vega Measure 293
7.5 The Rho Measure 298
7.6 Concluding Remarks 302
7.7 Questions and Problems 304
7.8 Appendix 307
7.8.1 Derivation of Sensitivity Measures 307
7.8.2 Sensitivities of Other Options 312
7.8.3 Signs of the Sensitivities 317
8 Hedging with the Greeks 323
8.1 Hedging: The General Philosophy 323
8.2 Delta Hedging 326
8.2.1 Solving for a Delta Neutral Portfolio 326
8.3 Delta Neutral Portfolios 341
8.4 General Hedging 347
8.5 Optimizing Hedged Portfolios 364
8.6 Concluding Remarks 370
8.7 Questions and Problems 371
9 The Term Structure and Its Estimation 373
9.1 The Term Structure of Interest Rates 374
9.1.1 Zero-Coupon, Spot, and Yield Curves 377
9.2 Smoothing of the Term Structure 383
9.2.1 Smoothing and Continuous Compounding 389
9.3 Forward Rate 393
9.3.1 Forward Rate: A Classical Approach 393
9.3.2 Forward Rate: A Practical Approach 396
9.4 A Variable Rate Bond 399
9.5 Concluding Remarks 402
9.6 Questions and Problems 404
9.7 Appendix 408
9.7.1 Theories of the Shape of the Term Structure 408
9.7.2 Approximating Functions 411
10 Forwards, Eurodollars, and Futures 413
10.1 Forward Contracts: A Second Look 414
10.2 Valuation of Forward Contracts 415
10.3 Forward Price of Assets 423
10.3.1 Forward Contracts, Prior to Maturity, of Assets That Pay Known Cash Flows 427
10.3.2 Forward Price of a Dividend-Paying Stock 430
10.4 Eurodollar Contracts 432
10.4.1 Forward Rate Agreements (FRAs) 432
10.5 Futures Contracts: A Second Look 435
10.6 Deterministic Term Structure (DTS) 439
10.7 Futures Contracts in a DTS Environment 441
10.8 Concluding Remarks 448
10.9 Questions and Problems 449
11 Swaps: A Second Look 453
11.1 A Fixed-for-Float Swap 453
11.1.1 Valuing an Existing Swap 458
11.2 Currency Swaps 461
11.3 Commodity and Equity Swaps 472
11.3.1 Equity Swaps 475
11.4 Forwards and Swaps: A Visualization 478
11.5 Concluding Remarks 479
11.6 Questions and Problems 481
12 American Options 485
12.1 American Call Option 486
12.1.1 Arbitrage Bounds 486
12.1.2 Early Exercise Decision 487
12.2 American Put Options 488
12.2.1 Arbitrage Bounds 488
12.2.2 Early Exercise Decision 490
12.3 Put--Call Parity 492
12.4 The Effect of Dividends 495
12.4.1 A Call Option 495
12.4.2 A Put Option 501
12.5 Concluding Remarks 502
12.6 Questions and Problems 502
13 Binomial Models I 505
13.1 Setting the Premises 505
13.2 No-Arbitrage and SDFs 511
13.2.1 No-Arbitrage 511
13.2.2 SDF 512
13.3 Valuation 521
13.3.1 Valuation with SDFs 521
13.3.2 Valuation by Replication 522
13.4 Numerical Valuation 529
13.4.1 Price Evolution 529
13.4.2 European Call 530
13.4.3 European Put 539
13.4.4 American Options 546
13.5 Concluding Remarks 554
13.6 Questions and Problems 555
14 Binomial Models II 557
14.1 Binomial Model and Black-Scholes Formula 558
14.1.1 Binomial vs. Lognormal 558
14.1.2 Numerical Implementations 562
14.1.3 The Effect of Dividends 568
14.2 Risk-Neutral Probabilities 571
14.3 Futures and Forwards: A Symbolic Example 579
14.4 Brownian Motion 585
14.5 Concluding Remarks 590
14.6 Questions and Problems 592
14.7 Appendix 593
14.7.1 The Black-Scholes Formula as a Limit of the Binomial Formula 593
15 The Black-Scholes Formula 599
15.1 An Overview 599
15.2 The Price Process: A Second Look 602
15.2.1 Stochastic Evolution: The Discrete Case 605
15.3 Simulation of Stochastic Evolution 608
15.4 Stochastic Evolution 615
15.5 Ito's Lemma 621
15.5.1 Heuristic Proofs of Ito's Lemma 623
15.5.2 Examples Utilizing Ito's Lemma 628
15.6 The Black-Scholes Differential Equation 632
15.6.1 A Second Derivation 640
15.7 Reconciliation with Risk-Neutral Valuation 642
15.8 American vs. European 644
15.9 Concluding Remarks 649
15.10 Questions and Problems 651
15.11 Appendix 652
15.11.1 A Change over an Instant 652
15.11.2 The Limit of a Random Variable 656
15.11.3 A More Rigorous Insight into Ito's Lemma 666
16 Other Types of Options 673
16.1 Early Exercise, Dividends and Binomial Models 674
16.2 Indexes, Foreign Currency, and Futures 677
16.2.1 Stock Index Options 677
16.2.2 Currency Options 679
16.2.3 Options on Futures Contracts 682
16.3 Examples of Exotic Options 688
16.3.1 Binary (Digital) Options 689
16.3.2 Combinations of Binary and Plain Vanilla Options 694
16.3.3 Gap Options 695
16.3.4 Paylater (Cash on Delivery) Options 700
16.4 Interest Rate Derivatives 704
16.4.1 Black's Model 705
16.4.2 The Black, Derman, and Toy Model 714
16.5 Concluding Remarks 729
16.6 Questions and Problems 731
17 The End or the Beginning? 735
Index 743

Caractéristiques techniques

	PAPIER
Éditeur(s)	Academic Press
Auteur(s)	Prisman
Parution	01/04/2000
Nb. de pages	760
Couverture	Broché
Intérieur	Noir et Blanc
EAN13	9780125649155
ISBN13	978-0-12-564915-5