Discrete time asset pricing models in applied stochastic finance:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
London
ISTE Ltd [u.a.]
2010
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Ausgabe: | 1. publ. |
Schriftenreihe: | Applied stochastic methods series
|
Schlagworte: | |
Online-Zugang: | kostenfrei Inhaltsverzeichnis |
Beschreibung: | Includes bibliographical references and index |
Beschreibung: | XIII, 401 S. |
ISBN: | 9781848211582 |
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245 | 1 | 0 | |a Discrete time asset pricing models in applied stochastic finance |c P. C. G. Vassiliou |
250 | |a 1. publ. | ||
264 | 1 | |a London |b ISTE Ltd [u.a.] |c 2010 | |
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490 | 0 | |a Applied stochastic methods series | |
500 | |a Includes bibliographical references and index | ||
650 | 0 | |a Securities / Prices / Mathematical models | |
650 | 0 | |a Capital assets pricing model | |
650 | 0 | |a Stochastic analysis | |
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650 | 4 | |a Mathematisches Modell | |
650 | 4 | |a Capital assets pricing model | |
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Datensatz im Suchindex
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adam_text |
DISCRETE-TIME ASSET PRICING MODELS IN APPLIED STOCHASTIC FINANCE P.C.G.
VASSILIOU ) WILEY TABLE OF CONTENTS PREFACE XI CHAPTER ^PROBABILITY AND
RANDOM VARIABLES 1 1.1. INTRODUCTORY NOTES 1 1.2. PROBABILITY SPACE 2
1.3. CONDITIONAL PROBABILITY AND INDEPENDENCE 8 1.4. RANDOM VARIABLES 12
1.4.1. DISCRETE RANDOM VARIABLES 14 1.4.2. BERNOULLI RANDOM VARIABLES 15
1.4.3. BINOMIAL RANDOM VARIABLES 15 1.4.4. GEOMETRIC RANDOM VARIABLES 16
1.4.5. POISSON RANDOM VARIABLES 17 1.4.6. CONTINUOUS RANDOM VARIABLES 18
. 1.4.7. EXPONENTIAL RANDOM VARIABLES 20 1.4.8. UNIFORM RANDOM VARIABLES
21 1.4.9. GAMMA RANDOM VARIABLES 21 1.4.10. NORMAL RANDOM VARIABLES 22
1.4.LL.LOGNORMAL RANDOM VARIABLES 23 1.4.12. WEIBULL RANDOM VARIABLES 23
1.5. EXPECTATION AND VARIANCE OF A RANDOM VARIABLE 24 1.6. JOINTLY
DISTRIBUTED RANDOM VARIABLES 28 1.6.1. JOINT PROBABILITY DISTRIBUTION OF
FUNCTIONS OF RANDOM VARIABLES . . 30 1.7. MOMENT GENERATING FUNCTIONS 32
1.8. PROBABILITY INEQUALITIES AND LIMIT THEOREMS 37 1.9. MULTIVARIATE
NORMAL DISTRIBUTION 44 CHAPTER 2. AN INTRODUCTION TO FINANCIAL
INSTRUMENTS AND DERIVATIVES . 49 2.1. INTRODUCTION 49 2.2. BONDS AND
BASIC INTEREST RATES 50 VI APPLIED STOCHASTIC FINANCE 2.2.1. SIMPLE
INTEREST RATES 51 2.2.2. DISCRETELY COMPOUNDED INTEREST RATES 51 2.2.3.
CONTINUOUSLY COMPOUNDED INTEREST RATE 52 2.2.4. MONEY-MARKET ACCOUNT 53
2.2.5. BASIC INTEREST RATES 55 2.2.5.1. TREASURY RATE 55 2.2.5.2. LIBOR
RATES 55 2.2.6. TIME VALUE OF MONEY 55 2.2.7. COUPON-BEARING BONDS AND
YIELD-TO-MATURITY 56 2.3. FORWARD CONTRACTS 58 2.3.1. ARBITRAGE 59 2.4.
FUTURES CONTRACTS 60 2.5. SWAPS 60 2.6. OPTIONS 62 2.6.1. EUROPEAN CALL
OPTION * 62 2.6.2. EUROPEAN PUT OPTION 63 2.6.3. AMERICAN CALL OPTION 63
2.6.4. AMERICAN PUT OPTION 64 2.6.5. BASIC PROBLEMS AND ASSUMPTIONS 65
2.7. TYPES OF MARKET PARTICIPANTS 67 2.7.1. HEDGERS 67 2.7.2.
SPECULATORS 67 2.7.3. ARBITRAGEURS 67 2.8. ARBITRAGE RELATIONSHIPS
BETWEEN CALL AND PUT OPTIONS 67 2.9. EXERCISES 69 CHAPTER 3. CONDITIONAL
EXPECTATION AND MARKOV CHAINS 71 3.1. INTRODUCTION 71 3.2. CONDITIONAL
EXPECTATION: THE DISCRETE CASE 72 3.3. APPLICATIONS OF CONDITIONAL
EXPECTATIONS 75 3.3.1. EXPECTATION OF THE SUM OF A RANDOM NUMBER OF
RANDOM VARIABLES 76 3.3.2. EXPECTED VALUE OF A RANDOM NUMBER OF
BERNOULLI TRIALS WITH PROBABILITY OF SUCCESS BEING A RANDOM VARIABLE 77
3.3.3. NUMBER OF BERNOULLI TRIALS UNTIL THERE ARE K CONSECUTIVE
SUCCESSES 78 3.3.4. CONDITIONAL VARIANCE RELATIONSHIP 79 3.3.5. VARIANCE
OF THE SUM OF A RANDOM NUMBER OF RANDOM VARIABLES . . 80 3.4. PROPERTIES
OF THE CONDITIONAL EXPECTATION 81 3.5. MARKOV CHAINS 85 3.5.1.
PROBABILITY DISTRIBUTION IN THE STATES OF A MARKOV CHAIN 90 3.5.2.
STATISTICAL INFERENCE IN MARKOV CHAINS 94 3.5.3. THE STRONG MARKOV
PROPERTY 97 3.5.4. CLASSIFICATION OF STATES OF A MARKOV CHAIN 100 3.5.5.
PERIODIC MARKOV CHAINS 104 TABLE OF CONTENTS VII 3.5.5.1. CYCLIC
SUBCLASSES 106 3.5.5.2. ALGORITHM FOR THE CYCLIC SUBCLASSES 109 3.5.6.
CLASSIFICATION OF STATES 112 3.5.7. ASYMPTOTIC BEHAVIOR OF IRREDUCIBLE
HOMOGENOUS MARKOV CHAINS . 115 3.5.8. THE MEAN TIME OF FIRST ENTRANCE IN
A STATE OF MARKOV CHAIN . . . . 126 3.5.9. THE VARIANCE OF THE TIME OF
FIRST VISIT INTO A STATE OF A MARKOV CHAIN 129 3.6. EXERCISES 131
CHAPTER 4. THE NO-ARBITRAGE BINOMIAL PRICING MODEL 137 4.1. INTRODUCTORY
NOTES 137 4.2. BINOMIAL MODEL 138 4.3. STOCHASTIC EVOLUTION OF THE ASSET
PRICES 141 4.4. BINOMIAL APPROXIMATION TO THE LOGNORMAL DISTRIBUTION . .
143 4.5. ONE-PERIOD EUROPEAN CALL OPTION 145 4.6. TWO-PERIOD EUROPEAN
CALL OPTION 150 4.7. MULTIPERIOD BINOMIAL MODEL 153 4.8. THE EVOLUTION
OF THE ASSET PRICES AS A MARKOV CHAIN 154 4.9. EXERCISES 158 CHAPTER 5.
MARTINGALES 163 5.1. INTRODUCTORY NOTES 163 5.2. MARTINGALES 164 5.3.
OPTIONAL SAMPLING THEOREM 169 5.4. SUBMARTINGALES, SUPERMARTINGALES AND
MARTINGALES CONVERGENCE THEOREM 178 5.5. MARTINGALE TRANSFORMS 182 5.6.
UNIFORM INTEGRABILITY AND DOOB'S DECOMPOSITION 184 5.6.1. DOOB
DECOMPOSITION 186 5.7. THE SNELL ENVELOPE 187 5.8. EXERCISES 190 CHAPTER
6. EQUIVALENT MARTINGALE MEASURES, NO-ARBITRAGE AND COMPLETE MARKETS 195
6.1. INTRODUCTORY NOTES 195 6.2. EQUIVALENT MARTINGALE MEASURE AND THE
RANDON-NIKODYM DERIVATIVE PROCESS 196 6.3. FINITE GENERAL MARKETS 204
6.3.1. UNIQUENESS OF ARBITRAGE PRICE 210 6.3.2. EQUIVALENT MARTINGALE
MEASURES 213 6.4. FUNDAMENTAL THEOREM OF ASSET PRICING 215 6.5. COMPLETE
MARKETS AND MARTINGALE REPRESENTATION 222 VIII APPLIED STOCHASTIC
FINANCE 6.6. FINDING THE EQUIVALENT MARTINGALE MEASURE 228 6.6.1.
EXPLORING THE VITAL EQUATIONS AND CONDITIONS 234 6.6.2. EQUIVALENT
MARTINGALE MEASURES FOR GENERAL FINITE MARKETS . . . . 237 6.7.
EXERCISES 238 CHAPTER 7. AMERICAN DERIVATIVE SECURITIES 241 7.1.
INTRODUCTORY NOTES 241 7.2. A THREE-PERIOD AMERICAN PUT OPTION . . 242
7.3. HEDGING STRATEGY FOR AN AMERICAN PUT OPTION 249 7.4. THE ALGORITHM
OF THE AMERICAN PUT OPTION 254 7.4.1. ALGORITHM OF THE AMERICAN PUT
OPTION 254 7.4.1.1. PRICING OF THE AMERICAN PUT OPTION 254 7.4.1.2.
TRADING STRATEGY FOR HEDGING 254 7.5. OPTIMAL TIME FOR THE HOLDER TO
EXERCISE 255 7.6. AMERICAN DERIVATIVES IN GENERAL MARKETS 262 7.7.
EXTENDING THE CONCEPT OF SELF-FINANCING STRATEGIES 266 7.8. EXERCISES
269 CHAPTER 8. FIXED-INCOME MARKETS AND INTEREST RATES 273 8.1.
INTRODUCTORY NOTES 273 8.2. THE ZERO COUPON BONDS OF ALL MATURITIES 274
8.3. ARBITRAGE-FREE FAMILY OF BOND PRICES 278 8.4. INTEREST RATE PROCESS
AND THE TERM STRUCTURE OF BOND PRICES 282 8.5. THE EVOLUTION OF THE
INTEREST RATE PROCESS 290 8.6. BINOMIAL MODEL WITH NORMALLY DISTRIBUTED
SPREAD OF INTEREST RATES . . . 293 8.7. BINOMIAL MODEL WITH LOGNORMALLY
DISTRIBUTED SPREAD OF INTEREST RATES . . 296 8.8. OPTION ARBITRAGE
PRICING ON ZERO COUPON BONDS 298 8.8.1. VALUATION OF THE EUROPEAN PUT
CALL 298 8.8.2. HEDGING THE EUROPEAN PUT OPTION 300 8.9. FIXED INCOME
DERIVATIVES 302 8.9.1. INTEREST RATE SWAPS 304 8.9.2. INTEREST RATE CAPS
AND FLOORS 307 8.10. T-PERIOD EQUIVALENT FORWARD MEASURE 308 8.11.
FUTURES CONTRACTS 317 8.12. EXERCISES 319 CHAPTER 9. CREDIT RISK 323
9.1. INTRODUCTORY NOTES 323 9.2. CREDIT RATINGS AND CORPORATE BONDS 324
9.3. CREDIT RISK METHODOLOGIES 326 9.3.1. STRUCTURAL METHODOLOGIES 326
9.3.2. REDUCED-FORM METHODOLOGIES 327 TABLE OF CONTENTS IX 9.4.
ARBITRAGE PRICING OF DEFAULTABLE BONDS 327 9.5. MIGRATION PROCESS AS A
MARKOV CHAIN 330 9.5.1. CHANGE OF REAL-WORLD PROBABILITY MEASURE TO
EQUIVALENT T* -FORWARD MEASURE 331 9.6. ESTIMATION OF THE REAL WORLD
TRANSITION PROBABILITIES 334 9.7. TERM STRUCTURE OF CREDIT SPREAD AND
MODEL CALIBRATION 337 9.8. MIGRATION PROCESS UNDER THE REAL-WORLD
PROBABILITY MEASURE 341 9.8.1. STOCHASTIC MONOTONICITIES IN DEFAULT
TIMES 344 9.8.2. ASYMPTOTIC BEHAVIOR .\ . .- 350 9.9. EXERCISES 352
CHAPTER 10. THE HEATH-JARROW-MORTON MODEL 355 10.1. INTRODUCTORY NOTES
355 10.2. HEATH-JARROW-MORTON MODEL 356 10^2.1. EVOLUTION OF FORWARD
RATE PROCESS 356 10.2.2. EVOLUTION OF THE SAVINGS ACCOUNT AND SHORT-TERM
INTEREST RATE PROCESS 358 10.2.3. EVOLUTION OF THE ZERO-COUPON
NON-DEFAULTABLE BOND PROCESS . . . 359 10.2.4. CONDITIONS ON THE DRIFT
AND VOLATILITY PARAMETERS FOR NON-ARBITRAGE 360 10.3. HEDGING STRATEGIES
FOR ZERO COUPON BONDS 362 10.4. EXERCISES 364 REFERENCES 365 APPENDICES
374 A. APPENDIX A 375 A.I. INTRODUCTORY THOUGHTS 375 A.2. GENESIS 376
A.3. THE DECISIVE STEPS 378 A.4. A BRIEF GLANCE TOWARDS THE FLOW OF
RESEARCH PATHS 387 B. APPENDIX B 391 B.I. INTRODUCTION 391 B.2. THE MAIN
THEOREM 392 INDEX 395 |
any_adam_object | 1 |
author | Vassiliou, Panos C. G. |
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spelling | Vassiliou, Panos C. G. Verfasser (DE-588)142769819 aut Discrete time asset pricing models in applied stochastic finance P. C. G. Vassiliou 1. publ. London ISTE Ltd [u.a.] 2010 XIII, 401 S. txt rdacontent n rdamedia nc rdacarrier Applied stochastic methods series Includes bibliographical references and index Securities / Prices / Mathematical models Capital assets pricing model Stochastic analysis Finance / Mathematical models Mathematisches Modell Finance Mathematical models Securities Prices Mathematical models Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s Stochastische Analysis (DE-588)4132272-1 s Capital-Asset-Pricing-Modell (DE-588)4121078-5 s DE-604 DE-601 pdf/application http://www.gbv.de/dms/zbw/612551563.pdf kostenfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018927898&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Vassiliou, Panos C. G. Discrete time asset pricing models in applied stochastic finance Securities / Prices / Mathematical models Capital assets pricing model Stochastic analysis Finance / Mathematical models Mathematisches Modell Finance Mathematical models Securities Prices Mathematical models Stochastische Analysis (DE-588)4132272-1 gnd Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd Finanzmathematik (DE-588)4017195-4 gnd |
subject_GND | (DE-588)4132272-1 (DE-588)4121078-5 (DE-588)4017195-4 |
title | Discrete time asset pricing models in applied stochastic finance |
title_auth | Discrete time asset pricing models in applied stochastic finance |
title_exact_search | Discrete time asset pricing models in applied stochastic finance |
title_full | Discrete time asset pricing models in applied stochastic finance P. C. G. Vassiliou |
title_fullStr | Discrete time asset pricing models in applied stochastic finance P. C. G. Vassiliou |
title_full_unstemmed | Discrete time asset pricing models in applied stochastic finance P. C. G. Vassiliou |
title_short | Discrete time asset pricing models in applied stochastic finance |
title_sort | discrete time asset pricing models in applied stochastic finance |
topic | Securities / Prices / Mathematical models Capital assets pricing model Stochastic analysis Finance / Mathematical models Mathematisches Modell Finance Mathematical models Securities Prices Mathematical models Stochastische Analysis (DE-588)4132272-1 gnd Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd Finanzmathematik (DE-588)4017195-4 gnd |
topic_facet | Securities / Prices / Mathematical models Capital assets pricing model Stochastic analysis Finance / Mathematical models Mathematisches Modell Finance Mathematical models Securities Prices Mathematical models Stochastische Analysis Capital-Asset-Pricing-Modell Finanzmathematik |
url | http://www.gbv.de/dms/zbw/612551563.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018927898&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT vassilioupanoscg discretetimeassetpricingmodelsinappliedstochasticfinance |