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Arbitrage theory in continuous time:

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Bibliographische Detailangaben
Beteilige Person:	Björk, Tomas (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Oxford [u.a.] Oxford Univ. Press 2004
Ausgabe:	2. ed., 1. publ.
Schlagwörter:	Arbitrage pricing theory Arbitrage Arbitrageverksamhet - matematiska modeller Mathematisches Modell Arbitrage > Problems, exercises, etc Arbitrage > Mathematical models Arbitrage > Mathematical models > Problems, exercises, etc Derivat > Wertpapier Ökonometrie Arbitrage-Pricing-Theorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012045701&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012045701&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVIII, 466 S.
ISBN:	0199271267 9780199271269

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adam_text	CONTENTS Introduction 1 1.1 Problem Formulation 1 The Binomial Model 5 2.1 The One Period Model 5 2.1.1 Model Description 5 2.1.2 Portfolios and Arbitrage 6 2.1.3 Contingent Claims 9 2.1.4 Risk Neutral Valuation 11 2.2 The Multiperiod Model 15 2.2.1 Portfolios and Arbitrage 15 2.2.2 Contingent Claims 17 2.3 Exercises 25 2.4 Notes 25 A More General One Period Model 26 3.1 The Model 26 3.2 Absence of Arbitrage 27 3.3 Martingale Pricing 30 3.4 Completeness 31 3.5 Stochastic Discount Factors 34 3.6 Exercises 35 Stochastic Integrals 36 4.1 Introduction 36 4.2 Information 38 4.3 Stochastic Integrals 40 4.4 Martingales 42 4.5 Stochastic Calculus and the Ito Formula 45 4.6 Examples 50 4.7 The Multidimensional Ito Formula 53 4.8 Correlated Wiener Processes 55 4.9 Exercises 5Í) 4.10 Notes 61 Differential Equations 62 5.1 Stochastic Differential Equations 62 5.2 Geometric Brownian Motion 63 5.3 The Linear SDE 66 5.4 The Infinitesimal Operator 67 CONTENTS xiii 5.5 Partial Differential Equations 68 5.6 The Kolmogorov Equations 72 5.7 Exercises 75 5.8 Notes 79 6 Portfolio Dynamics 80 6.1 Introduction 80 6.2 Self-financing Portfolios 83 6.3 Dividends 85 6.4 Exercise 87 7 Arbitrage Pricing 88 7.1 Introduction 88 7.2 Contingent Claims and Arbitrage 89 7.3 The Black-Scholes Equation 94 7.4 Risk Neutral Valuation 98 7.5 The Black-Scholes Formula 100 7.6 Options on Futures 102 7.6.1 Forward Contracts 102 7.6.2 Futures Contracts and the Black Formula 103 7.7 Volatility 104 7.7.1 Historic Volatility 105 7.7.2 Implied Volatility 106 7.8 American options 106 7.9 Exercises 108 7.10 Notes П0 8 Completeness and Hedging HI 8.1 Introduction HI 8.2 Completeness in the Black-Scholes Model 112 8.3 Completeness — Absence of Arbitrage 117 8.4 Exercises Π 8 8.5 Notes 12° 9 Parity Relations and Delta Hedging 121 9.1 Parity Relations 121 9.2 The Greeks 123 9.3 Delta and Gamma Hedging 126 9.4 Exercises 130 10 The Martingale Approach to Arbitrage Theory* 133 10.1 The Case with Zero Interest Rate 133 10.2 Absence of Arbitrage 136 10.2.1 A Rough Sketch of the Proof 137 10.2.2 Precise Results 14° CONTENTS 10.3 The General Case 142 10.4 Completeness 145 10.5 Martingale Pricing 147 10.6 Stochastic Discount Factors 149 10.7 Summary for the Working Economist 150 10.8 Notes 153 11 The Mathematics of the Martingale Approach* 154 11.1 Stochastic Integral Representations 154 11.2 The Girsanov Theorem: Heuristics 158 11.3 The Girsanov Theorem 160 11.4 The Converse of the Girsanov Theorem 164 11.5 Girsanov Transformations and Stochastic Differentials 164 11.6 Maximum Likelihood Estimation 165 11.7 Exercises 167 11.8 Notes 168 12 Black-Scholes from a Martingale Point of View* 169 12.1 Absence of Arbitrage 169 12.2 Pricing 171 12.3 Completeness 172 13 Multidimensional Models: Classical Approach 175 13.1 Introduction 175 13.2 Pricing 177 13.3 Risk Neutral Valuation 183 13.4 Reducing the State Space 184 13.5 Hedging 188 13.6 Exercises 191 14 Multidimensional Models: Martingale Approach* 192 14.1 Absence of Arbitrage 193 14.2 Completeness 195 14.3 Hedging 196 14.4 Pricing 198 14.5 Markovian Models and PDEs 199 14.6 Market Prices of Risk 200 14.7 Stochastic Discount Factors 201 14.8 Tbc Hansen- -Jagarmatnan Bounds 201 14.9 Exercises 204 14.10 Notes 204 15 Incomplete Markets 205 15.1 Introduction 205 15.2 A Scalar Nonpriccd Underlying Asset 205 15.3 The Multidimensional Case 214 CONTENTS 15.4 A Stochastic Short Rate 15.5 The Martingale Approach* 15.6 Summing Up 15.7 Exercises 15.8 Notes 218 219 220 223 224 16 Dividends 22Г) 16.1 Discrete Dividends 225 16.1.1 Price Dynamics and Dividend Structure 225 16.1.2 Pricing Contingent Claims 226 16.2 Continuous Dividends 231 16.2.1 Continuous Dividend Yield 232 16.2.2 The General Case 235 16.3 Exercises 237 17 Currency Derivatives 239 17.1 Pure Currency Contracts 239 17.2 Domestic and Foreign Equity Markets 242 17.3 Domestic and Foreign Market Prices of Risk 248 17.4 Exercises 252 17.5 Notes 253 18 Barrier Options 254 18.1 Mathematical Background 254 18.2 Out Contracts 256 18.2.1 Down-and-Out Contracts 256 18.2.2 Up-and-Out Contracts 260 18.2.3 Examples 261 18.3 In Contracts 265 18.4 Ladders 267 18.5 Lookbacks 268 18.6 Exercises 270 18.7 Notes 2 ° 19 Stochastic Optimal Control 271 19.1 An Example 271 19.2 The Formal Problem 272 19.3 The Hamilton-Jacobi-Bellman Equation 275 19.4 Handling the HJB Equation 23 19.5 The Linear Regulator ^4 19.6 Optimal Consumption and Investment 2x6 19.6.1 A Generalization 26 19.6.2 Optimal Consumption 2^ 19.7 The Mutual Fund Theorems 2·^ 19.7.1 The Case with No Risk Free Asset 291 19.7.2 The Case with a Risk Free Asset 295 CONTENTS 19.8 Exercises 297 19.9 Notes 301 20 Bonds and Interest Rates 302 20.1 Zero Coupon Bonds 302 20.2 Interest Rates 303 20.2.1 Definitions 303 20.2.2 Relations between åf (t, T), dp(t, T), and dr {t) 305 20.2.3 An Alternative View of the Money Account 308 20.3 Coupon Bonds, Swaps, and Yields 309 20.3.1 Fixed Coupon Bonds 310 20.3.2 Floating Rate Bonds 310 20.3.3 Interest Rate Swaps 312 20.3.4 Yield and Duration 313 20.4 Exercises 314 20.5 Notes 315 21 Short Rate Models 316 21.1 Generalities 316 21.2 The Term Structure Equation 319 21.3 Exercises 324 21.4 Notes 325 22 Martingale Models for the Short Rate 326 22.1 Ç-dynamics 326 22.2 Inversion of the Yield Curve 327 22.3 Affine Term Structures 329 22.3.1 Definition and Existence 329 22.3.2 A Probabilistic Discussion 331 22.4 Some Standard Models 333 22.4.1 The Vasiček Model 333 22.4.2 The Но -Lee Model 334 22.4.3 The CIR Model 335 22.4.4 The Hull-White Model 335 22.5 Exercises 338 22.6 Notes 339 23 Forward Rate Models 340 23.1 The Heath-Jarrow--Morton Framework 340 23.2 Martingale Modeling 342 23.3 The Musióla Parameterization 344 23.4 Exercises 345 23.5 Notes 347 24 Change of Numeraire* 348 24.1 Introduction 348 CONTENTS 24.2 Generalities 349 24.3 Changing the Numeraire 353 24.4 Forward Measures 355 24.4.1 Using the Т -bond as Numeraire 355 24.4.2 An Expectation Hypothesis 357 24.5 A General Option Pricing Formula 358 24.6 The Hull-White Model 361 24.7 The General Gaussian Model 363 24.8 Caps and Floors 365 24.9 Exercises 366 24.10 Notes 366 25 LIBOR and Swap Market Models 368 25.1 Caps: Definition and Market Practice 369 25.2 The LIBOR Market Model 371 25.3 Pricing Caps in the LIBOR Model 372 25.4 Terminal Measure Dynamics and Existence 373 25.5 Calibration and Simulation 376 25.6 The Discrete Savings Account 378 25.7 Swaps 379 25.8 Swaptions: Definition and Market Practice 381 25.9 The Swap Market Models 382 25.10 Pricing Swaptions in the Swap Market Model 383 25.11 Drift Conditions for the Regular Swap Market Model 384 25.12 Concluding Comment 387 25.13 Exercises 388 25.14 Notes 388 26 Forwards and Futures 389 26.1 Forward Contracts 389 26.2 Futures Contracts 391 26.3 Exercises 394 26.4 Notes 394 A Measure and Integration* 395 A.I Sets and Mappings 395 A.2 Measures and Sigma Algebras 397 A.3 Integration 399 A.4 Sigma-Algebras and Partitions 404 A.5 Sets of Measure Zero 405 A.6 The Lp Spaces 406 A.7 Hubert Spaces 407 A.8 Sigma-Algebras and Generators 410 A.9 Product measures 414 A.10 The Lebesgue Integral 415 xviii CONTENTS Α. 11 The Radon-Nikodym Theorem 416 A.12 Exercises 419 A.13 Notes 421 В Probability Theory* 422 B.I Random Variables and Processes 422 B.2 Partitions and Information 425 B.3 Sigma-algebras and Information 427 B.4 Independence 430 B.5 Conditional Expectations 432 B.6 Equivalent Probability Measures 438 B.7 Exercises 441 B.8 Notes 442 С Martingales and Stopping Times* 443 C.I Martingales 443 C.2 Discrete Stochastic Integrals 446 C.3 Likelihood Processes 447 C.4 Stopping Times 448 C.5 Exercises 451 References 453 Index 461 Tomas Björk is Professor of Mathematical Finance at the Stockholm School of Economics. He is co-editor oí Mathematical Finance and is on the editorial board of Finance and Stochastics . He has published numerous journal articles on probability theory, mathematical finance in general, and in particular on interest rate theory. The second edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merlon s fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests farther reading in each chapter. In this substantially extended new edition Tomas Björk has added completely new chapters on measure theory and probability theory, including the Radon-Nikodym Theorem, Girsanov transformations, and stochastic integral martingale representa¬ tions. There is also an extensive new chapter on the abstract martingale approach to arbitrage theory, including a guided tour through the Delbaen-Schachermayer proof of the irsi fundamental theorem, as well as a new chapter on the LIBOR aad swap market models. Providing two full treatments of arbitrage theory — the classical delta hedging approach and the modern martingale approach — the book is written in such a way that these approaches can be studied independently of each other, thus providing the less mathematically oriented reader with a self contained introduction to arbitrage theory, while at the same time allowing the more advanced student to see the full theory in action. This is the textbook of choice for graduate students and advanced undergraduates studying finance and an invaluable introduction to mathematical finance for mathematicians and professionals in financial markets.
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spellingShingle	Björk, Tomas Arbitrage theory in continuous time Arbitrage pricing theory shbe Arbitrage shbe Arbitrageverksamhet - matematiska modeller sao Mathematisches Modell Arbitrage Arbitrage Problems, exercises, etc Arbitrage Mathematical models Arbitrage Mathematical models Problems, exercises, etc Derivat Wertpapier (DE-588)4381572-8 gnd Ökonometrie (DE-588)4132280-0 gnd Arbitrage (DE-588)4002820-3 gnd Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd
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title	Arbitrage theory in continuous time
title_auth	Arbitrage theory in continuous time
title_exact_search	Arbitrage theory in continuous time
title_full	Arbitrage theory in continuous time Tomas Bjørk
title_fullStr	Arbitrage theory in continuous time Tomas Bjørk
title_full_unstemmed	Arbitrage theory in continuous time Tomas Bjørk
title_short	Arbitrage theory in continuous time
title_sort	arbitrage theory in continuous time
topic	Arbitrage pricing theory shbe Arbitrage shbe Arbitrageverksamhet - matematiska modeller sao Mathematisches Modell Arbitrage Arbitrage Problems, exercises, etc Arbitrage Mathematical models Arbitrage Mathematical models Problems, exercises, etc Derivat Wertpapier (DE-588)4381572-8 gnd Ökonometrie (DE-588)4132280-0 gnd Arbitrage (DE-588)4002820-3 gnd Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd
topic_facet	Arbitrage pricing theory Arbitrage Arbitrageverksamhet - matematiska modeller Mathematisches Modell Arbitrage Problems, exercises, etc Arbitrage Mathematical models Arbitrage Mathematical models Problems, exercises, etc Derivat Wertpapier Ökonometrie Arbitrage-Pricing-Theorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012045701&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012045701&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT bjorktomas arbitragetheoryincontinuoustime

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Teilbibliothek Mathematik & Informatik

Bestandsangaben von Teilbibliothek Mathematik & Informatik
Signatur:	0104 MAT 624f 2001 A 682 Lageplan
Exemplar 1	Nicht ausleihbar Bestellt

Teilbibliothek Weihenstephan

Bestandsangaben von Teilbibliothek Weihenstephan
Signatur:	1002 WIR 170 2009 A 557(2) Lageplan
Exemplar 1	Ausleihbar Am Standort