Foundations of the pricing of financial derivatives: theory and analysis
"This book in manuscript form has been class-tested three times. This course was a doctoral seminar that was open to finance masters and doctoral students and also STEM students across the university. All of these students contributed a great deal to catching errors, forcing us to re-think how...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, New Jersey
Wiley
[2024]
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| Schriftenreihe: | The Frank J. Fabozzi series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This book in manuscript form has been class-tested three times. This course was a doctoral seminar that was open to finance masters and doctoral students and also STEM students across the university. All of these students contributed a great deal to catching errors, forcing us to re-think how we said something, and in some cases contributing end-of-chapter problems. This book would be nowhere near ready for prime time were it not for them."-- |
| Beschreibung: | xvi, 602 Seiten Illustrationen, Diagramme 27 cm |
| ISBN: | 9781394179657 |
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Contents Preface xv CHAPTER 1 Introduction and Overview 1 1.1 Motivation for This Book 1.2 What Is a Derivative? 1.3 Options Versus Forwards, Futures, and Swaps 1.4 Size and Scope of the Financial Derivatives Markets 1.5 Outline and Features of the Book 1.6 Final Thoughts and Preview Questions and Problems Notes 2 6 8 9 12 14 15 15 PARTI Basic Foundations for Derivative Pricing CHAPTER? Boundaries, Limits, and Conditions on Option Prices Setup, Definitions, and Arbitrage Absolute Minimum and Maximum Values The Value of an American Option Relative to the Value of a European Option 2.4 The Value of an Option at Expiration 2.5 The Lower Bounds of European and American Options and the Optimality of Early Exercise 2.6 Differences in Option Values by Exercise Price 2.7 The Effect of Differences in Time to Expiration 2.8 The Convexity Rule 2.9 Put-Call Parity 2.10 The Effect of Interest Rates on Option Prices 2.11 The Effect of Volatility on Option Prices 2.12 The Building Blocks of European Options 2.13 Recap and Preview Questions and Problems Notes 10 2.1 2.2 2.3 20 21 22 22 23 31 37 38 40 47 47 48 49 50 51 V
H!_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ CONTENTS CHAPTERS Elementary Review of Mathematics for Finance 53 3.1 Summation Notation 3.2 Product Notation 3.3 Logarithms and Exponentials 3.4 Series Formulas 3.5 Calculus Derivatives 3.6 Integration 3.7 Differential Equations 3.8 Recap and Preview Questions and Problems Notes 53 55 56 58 59 68 70 71 71 73 CHAPTER 4 Elementary Review of Probability for Finance 75 Marginal, Conditional, and Joint Probabilities Expectations, Variances, and Covariances of Discrete Random Variables 4.3 Continuous Random Variables 4.4 Some General Results in Probability Theory 4.5 Technical Introduction to Common Probability Distributions Used in Finance 95 4.6 Recap and Preview Questions and Problems Notes 4.1 4.2 CHAPTERS Financial Applications of Probability Distributions The Univariate Normal Probability Distribution Contrasting the Normal with the Lognormal Probability Distribution 5.3 Bivariate Normal Probability Distribution 5.4 The Bivariate Lognormal Probability Distribution 5.5 Recap and Preview Appendix 5A An Excel Routine for the Bivariate Normal Probability Questions and Problems Notes 6.1 Valuing Risky Assets 6.2 Risk-Neutral Pricing in Discrete Time 6.3 Identical Assets and the Law of One Price 6.4 Derivative Contracts 6.5 A First Look at Valuing Options 6.6 A World of Risk-Averse and Risk-Neutral Investors 6.7 Pricing Options Under Risk Aversion 6.8 Recap and Preview Questions and Problems Notes 80 86 93 109 109 110 113 5.1 5.2 CHAPTER 6 Basic Concepts in Valuing
Risky Assets and Derivatives 75 113 119 123 125 126 126 128 128 129 129 130 133 134 136 137 138 138 139 139
Contents vii PART II Discrete Time Derivatives Pricing Theory CHAPTER? The Binomial Model 7.1 The One-Period Binomial Model for Calls 7.2 The One-Period Binomial Model for Puts 7.3 Arbitraging Price Discrepancies 7.4 The Multiperiod Model 7.5 American Options and Early Exercise in the Binomial Framework 7.6 Dividends and Recombination 7.7 Path Independence and Path Dependence 7.8 Recap and Preview Appendix 7A Derivation of Equation(7.9) Appendix 7B Pascal’s Triangle and theBinomial Model Questions and Problems Notes CHAPTERS Calculating the Greeks in the Binomial Model 8.1 Standard Approach 8.2 An Enhanced Method for Estimating Delta and Gamma 8.3 Numerical Examples 8.4 Dividends 8.5 Recap and Preview Questions and Problems Notes CHAPTERS Convergence of the Binomial Model to the Black-Scholes-Merton Model 9.1 Setting Up the Problem 9.2 The Hsia Proof 9.3 Put Options 9.4 Dividends 9.5 Recap and Preview Questions and Problems Notes 143 143 146 149 151 154 155 159 159 159 161 163 163 165 165 170 172 174 175 175 176 177 177 181 187 188 188 189 190 PART III Continuous Time Derivatives Pricing Theory CHAPTER 10 The Basics of Brownian Motion and Wiener Processes 10.1 10.2 10.3 Brownian Motion The Wiener Process Properties of a Model of Asset Price Fluctuations 163 195 196
10.4 Building a Model of Asset Price Fluctuations 10.5 Simulating Brownian Motion and Wiener Processes 10.6 Formal Statement of Wiener Process Properties 10.7 Recap and Preview Appendix 10A Simulation of the Wiener Process and the Square of the Wiener Process for Successively Smaller Time Intervals Questions and Problems Notes CHAPTER 11 Stochastic Calculus and Itô's Lemma 11.1 A Result from Basic Calculus 11.2 Introducing Stochastic Calculus and Itô’s Lemma 11.3 Itô’s Integral 11.4 The Integral Form of Itô’s Lemma 11.5 Some Additional Cases of Itô’s Lemma 11.6 Recap and Preview Appendix 11A Technical Stochastic Integral Results 11A.1 Selected Stochastic Integral Results 11A.2 A General Linear Theorem Questions and Problems Notes CHAPTER 12 Properties of the Lognormal and Normal Diffusion Processes for Modeling Assets 12.1 A Stochastic Process for the Asset Relative Return 12.2 A Stochastic Process for the Asset Price Change 12.3 Solving the Stochastic Differential Equation 12.4 Solutions to Stochastic Differential Equations Are Not Always the Same as Solutions to Corresponding Ordinary Differential Equations 12.5 Finding the Expected Future Asset Price 12.6 Geometric Brownian Motion or Arithmetic Brownian Motion? 12.7 Recap and Preview Questions and Problems Notes CHAPTER 13 Deriving the Black-Scholes-Merton Model 13.1 Derivation of the European Call Option Pricing Formula 13.2 The European Put Option Pricing Formula 13.3 Deriving the Black-Scholes-Merton Model as an Expected Value 13.4 Deriving the Black-Scholes-Merton Model as the Solution of a Partial Differential
Equation 13.5 Decomposing the Black-Scholes-Merton Model into Binary Options 13.6 Black-Scholes-Merton Option Pricing When There Are Dividends 13.7 Selected Black-Scholes-Merton Model Limiting Results 13.8 Computing the Black-Scholes-Merton Option Pricing Model Values 199 202 205 207 207 208 209 211 211 212 215 216 217 219 220 220 224 229 230 231 232 235 236 237 238 240 241 242 242 245 245 249 250 254 258 259 259 262
îx Contents 13.9 Recap and Preview Appendix 13.A Deriving the Arithmetic Brownian Motion Option Pricing Model Questions and Problems Notes 265 265 269 270 CHAPTER 14 The Greeks in the Black-Scholes-Merton Model 271 Delta: The First Derivative with Respect to the Underlying Price Gamma: The Second Derivative with Respect to the Underlying Price 274 14.3 Theta: The First Derivative with Respect to Time 14.4 Verifying the Solution of the Partial Differential Equation 14.5 Selected Other Partial Derivatives of the Black-Scholes-Merton Model 14.6 Partial Derivatives of the Black-Scholes-Merton European Put Option Pricing Model 14.7 Incorporating Dividends 14.8 Greek Sensitivities 14.9 Elasticities 14.10 Extended Greeks of the Black-Scholes-Merton Option Pricing Model 14.11 Recap and Preview Questions and Problems Notes 14.1 14.2 CHAPTER 15 Girsanov’s Theorem in Option Pricing 275 275 277 278 279 280 283 284 284 285 286 287 The Martingale Representation Theorem Introducing the Radon-Nikodym Derivative by Changing the Drift for a Single Random Variable 289 15.3 A Complete Probability Space 15.4 Formal Statement of Girsanov’s Theorem 15.5 Changing the Drift in a Continuous Time Stochastic Process 15.6 Changing the Drift of an Asset Price Process 15.7 Recap and Preview Questions and Problems Notes 15.1 15.2 CHAPTER 10 Connecting Discrete and Continuous Brownian Motions Brownian Motion in a Discrete World Moving from a Discrete to a Continuous World Changing the Probability Measure with the Radon-Nikodym Derivative in Discrete Time 16.4 The Kolmogorov Equations 16.5 Recap and Preview
Questions and Problems Notes 274 287 291 292 293 297 300 301 302 303 16.1 16.2 16.3 303 306 310 313 321 322 322
CONTENTS X PART IV Extensions and Generalizations of Derivative Pricing CHAPTER 17 Applying Linear Homogeneity to Option Pricing Introduction to ExchangeOptions Homogeneous Functions Euler’s Rule Using Linear Homogeneityand Euler’s Rule to Derive the Black-Scholes-Merton Model 17.5 Exchange Option Pricing 17.6 Spread Options 17.7 Forward Start Options 17.8 Recap and Preview Appendix 17A Linear Homogeneity and the Arithmetic Brownian Motion Model Appendix 17B Multivariate Itô’s Lemma Appendix 17C Greeks of the ExchangeOption Model Questions and Problems Notes 327 17.1 17.2 17.3 17.4 CHAPTER 18 Compound Option Pricing 18.1 Equity as an Option 18.2 Valuing an Option on the Equity as a CompoundOption 18.3 Compound Option Boundary Conditions and Parities 18.4 Geske’s Approach to Valuing a Call on a Call 18.5 Characteristics of Geske’s Call on Call Option 18.6 Geske’s Call on Call Option Model and LinearHomogeneity 18.7 Generalized Compound Option Pricing Model 18.8 Installment Options 18.9 Recap and Preview Appendix 18 A Selected Greeks of the Compound Option Questions and Problems Notes CHAPTER 19 American Call Option Pricing 19.1 Closed-Form American Call Pricing: Roll-Geske-Whaley 19.2 The Two-Payment Case 19.3 Recap and Preview Appendix 19A Numerical Example of the One-Dividend Model Questions and Problems Notes 327 328 330 330 333 337 339 341 342 344 345 347 347 349 350 351 353 356 358 359 360 361 362 362 363 363 396 366 370 372 373 374 374
Contents xi CHAPTER 20 American Put Option Pricing 20.1 The Nature of the Problem of Pricing an American Put 20.2 The American Put as a Series of Compound Options 20.3 Recap and Preview Questions and Problems Notes CHAPTER 21 Min-Max Option Pricing 21.1 Characteristics of Stulz’s Min-Max Option 21.2 Pricing the Call on the Min 21.3 Other Related Options 21.4 Recap and Preview Appendix 21A Multivariate Feynman-Kac Theorem Appendix 21B An Alternative Derivation of the Min-Max Option Model Questions and Problems Notes CHAPTER 22 Pricing Forwards, Futures, and Options on Forwards and Futures 22.1 Forward Contracts 22.2 Pricing Futures Contracts 22.3 Options on Forwards and Futures 22.4 Recap and Preview Questions and Problems Notes 377 377 378 380 380 381 383 383 388 393 395 395 396 397 397 399 399 404 409 412 413 414 PARTV Numerical Methods CHAPTER 23 Monte Carlo Simulation 23.1 Standard Monte Carlo Simulation of the Lognormal Diffusion 23.2 Reducing the Standard Error 23.3 Simulation with More Than One Random Variable 23.4 Recap and Preview Questions and Problems Notes CHAPTER 24 Finite Difference Methods 24.1 24.2 24.3 24.4 24.5 Setting Up the Finite Difference Problem The Explicit Finite Difference Method The Implicit Finite Difference Method Finite Difference Put Option Pricing Dividends and Early Exercise 417 417 421 424 424 425 426 429 429 431 434 435 435
xii CONTENTS 24.6 Recap and Preview Questions and Problems Notes 436 436 436 PART VI Interest Rate Derivatives CHAPTER 25 The Term Structure of Interest Rates 25.1 The Unbiased Expectations Hypothesis 25.2 The Local Expectations Hypothesis 25.3 The Difference Between the Local and Unbiased Expectations Hypotheses 25.4 Other Term Structure of Interest Rate Hypotheses 25.5 Recap and Preview Questions and Problems Notes 439 440 442 446 447 450 450 450 CHAPTER 26 Interest Rate Contracts: Forward Rate Agreements, Swaps, and Options 26.1 Interest Rate Forwards 26.2 Interest Rate Swaps 26.3 Interest Rate Options 26.4 Recap and Preview Questions and Problems Notes 453 454 459 469 471 471 472 CHAPTER 27 Fitting an Arbitrage-Free Term Structure Model 27.1 Basic Structure of the HJM Model 27.2 Discretizing the HJM Model 27.3 Fitting a Binomial Tree to the HJM Model 27.4 Filling in the Remainder of the HJM Binomial Tree 27.5 Recap and Preview Questions and Problems Notes 475 476 479 481 485 489 490 491 CHAPTER 28 Pricing Fixed-Income Securities and Derivatives Using an Arbitrage-Free Binomial Tree 28.1 Zero-Coupon Bonds 28.2 Coupon Bonds 28.3 Options on Zero-Coupon Bonds 28.4 Options on Coupon Bonds 28.5 Callable Bonds 28.6 Forward Rate Agreements (FRAs) 28.7 Interest Rate Swaps 493 493 496 497 498 499 501 503
Contents 28.8 Interest Rate Options 28.9 Interest Rate Swaptions 28.10 Interest Rate Futures 28.11 Recap and Preview Questions and Problems Notes xiii 505 506 508 510 510 510 PART VII Miscellaneous Topics CHAPTER 29 Option Prices and the Prices of State-Contingent Claims 29.1 Pure Assets in the Market 29.2 Pricing Pure and Complex Assets 29.3 Numerical Example 29.4 State Pricing and Options in a Binomial Framework 29.5 State Pricing and Options in Continuous Time 29.6 Recap and Preview Questions and Problems Notes CHAPTER 30 Option Prices and Expected Returns 30.1 The Basic Framework 30.2 Expected Returns on Options 30.3 Volatilities of Options 30.4 Options and the Capital Asset Pricing Model 30.5 Options and the Sharpe Ratio 30.6 The Stochastic Process Followed by the Option 30.7 Recap and Preview Questions and Problems Notes CHAPTER 31 Implied Volatility and the Volatility Smile 31.1 Historical Volatility and the VIX 31.2 An Example of Implied Volatility 31.3 The Volatility Surface 31.4 The Perfect Substitutability of Options 31.5 Other Attempts to Explain the Implied Volatility Smile 31.6 How Practitioners Use the Implied Volatility Surface 31.7 Recap and Preview Questions and Problems Notes 513 514 514 518 519 522 525 525 526 527 527 529 531 531 532 533 535 535 536 537 538 539 546 547 549 550 551 551 553
xiv CONTENTS CHAPTER 32 Pricing Foreign Currency Options 32.1 Definition of Terms 32.2 Option Payoffs 32.3 Valuation of the Options 32.4 Probability of Exercise 32.5 Some Terminology Confusion 32.6 Recap Questions and Problems Notes 555 556 556 557 561 563 563 564 565 References 567 Symbols Used Symbols Time-Related Notation Instrument-Related Notation 573 573 573 574 About the Website 581 Index 583 |
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| spelling | Brooks, Robert 1960- Verfasser (DE-588)1015877990 aut Foundations of the pricing of financial derivatives theory and analysis Robert E. Brooks, Don M. Chance Hoboken, New Jersey Wiley [2024] © 2024 xvi, 602 Seiten Illustrationen, Diagramme 27 cm txt rdacontent n rdamedia nc rdacarrier The Frank J. Fabozzi series "This book in manuscript form has been class-tested three times. This course was a doctoral seminar that was open to finance masters and doctoral students and also STEM students across the university. All of these students contributed a great deal to catching errors, forcing us to re-think how we said something, and in some cases contributing end-of-chapter problems. This book would be nowhere near ready for prime time were it not for them."-- Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Preisbildung (DE-588)4047103-2 gnd rswk-swf Kapitalanlage (DE-588)4073213-7 gnd rswk-swf Derivative securities / Prices Instruments dérivés (Finances) / Prix Derivat Wertpapier (DE-588)4381572-8 s Kapitalanlage (DE-588)4073213-7 s Preisbildung (DE-588)4047103-2 s DE-604 Chance, Don M. 1951- Sonstige (DE-588)170013944 oth Erscheint auch als Online-Ausgabe, EPUB 978-1-394-17966-4 Erscheint auch als Online-Ausgabe, PDF 978-1-394-17967-1 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034972955&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brooks, Robert 1960- Foundations of the pricing of financial derivatives theory and analysis Derivat Wertpapier (DE-588)4381572-8 gnd Preisbildung (DE-588)4047103-2 gnd Kapitalanlage (DE-588)4073213-7 gnd |
| subject_GND | (DE-588)4381572-8 (DE-588)4047103-2 (DE-588)4073213-7 |
| title | Foundations of the pricing of financial derivatives theory and analysis |
| title_auth | Foundations of the pricing of financial derivatives theory and analysis |
| title_exact_search | Foundations of the pricing of financial derivatives theory and analysis |
| title_exact_search_txtP | Foundations of the pricing of financial derivatives theory and analysis |
| title_full | Foundations of the pricing of financial derivatives theory and analysis Robert E. Brooks, Don M. Chance |
| title_fullStr | Foundations of the pricing of financial derivatives theory and analysis Robert E. Brooks, Don M. Chance |
| title_full_unstemmed | Foundations of the pricing of financial derivatives theory and analysis Robert E. Brooks, Don M. Chance |
| title_short | Foundations of the pricing of financial derivatives |
| title_sort | foundations of the pricing of financial derivatives theory and analysis |
| title_sub | theory and analysis |
| topic | Derivat Wertpapier (DE-588)4381572-8 gnd Preisbildung (DE-588)4047103-2 gnd Kapitalanlage (DE-588)4073213-7 gnd |
| topic_facet | Derivat Wertpapier Preisbildung Kapitalanlage |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034972955&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT brooksrobert foundationsofthepricingoffinancialderivativestheoryandanalysis AT chancedonm foundationsofthepricingoffinancialderivativestheoryandanalysis |