Verfügbarkeit: Statistics of financial markets

Statistics of financial markets: an introduction

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Franke, Jürgen 1952- (VerfasserIn), Härdle, Wolfgang 1953- (VerfasserIn), Hafner, Christian M. 1967- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2008
Ausgabe:	2. ed.
Schriftenreihe:	Universitext
Schlagworte:	Estatística Finanças Modelos matemáticos Mathematisches Modell Finance > Mathematical models Finance > Statistical methods CD-ROM Statistik Financial Engineering Optionspreistheorie Kreditmarkt Finanzmathematik Lehrbuch
Online-Zugang:	Inhaltsverzeichnis Inhaltsverzeichnis
Beschreibung:	XXII, 501 S. graph. Darst.
ISBN:	9783540762690 3540762698 9783540762720

Internformat

MARC


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Datensatz im Suchindex

_version_	1804137253435342848
adam_text	CONTENTS PREFACE TO THE SECOND EDITION XI PREFACE TO THE FIRST EDITION XIII I OPTION PRICING 1 1 DERIVATIVES 3 1.1 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 10 2 INTRODUCTION TO OPTION MANAGEMENT 11 2.1 ARBITRAGE RELATIONS . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 PORTFOLIO INSURANCE . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 BINARY ONE-PERIOD MODEL . . . . . . . . . . . . . . . . . . . . 30 2.4 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 35 3 BASIC CONCEPTS OF PROBABILITY THEORY 37 3.1 REAL VALUED RANDOM VARIABLES . . . . . . . . . . . . . . . . . 37 3.2 EXPECTATION AND VARIANCE . . . . . . . . . . . . . . . . . . . . 39 3.3 SKEWNESS AND KURTOSIS . . . . . . . . . . . . . . . . . . . . . . 41 3.4 RANDOM VECTORS, DEPENDENCE, CORRELATION . . . . . . . . . . . 42 3.5 CONDITIONAL PROBABILITIES AND EXPECTATIONS . . . . . . . . . . 43 3.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 45 4 STOCHASTIC PROCESSES IN DISCRETE TIME 47 4.1 BINOMIAL PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2 TRINOMIAL PROCESSES . . . . . . . . . . . . . . . . . . . . . . . 51 4.3 GENERAL RANDOM WALKS . . . . . . . . . . . . . . . . . . . . . 53 4.4 GEOMETRIC RANDOM WALKS . . . . . . . . . . . . . . . . . . . . 54 4.5 BINOMIAL MODELS WITH STATE DEPENDENT INCREMENTS . . . . . . 55 4.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 56 5 STOCHASTIC INTEGRALS AND DIFFERENTIAL EQUATIONS 57 5.1 WIENER PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2 STOCHASTIC INTEGRATION . . . . . . . . . . . . . . . . . . . . . . 61 XVIII CONTENTS 5.3 STOCHASTIC DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . 63 5.4 THE STOCK PRICE AS A STOCHASTIC PROCESS . . . . . . . . . . . . 66 5.5 IT* OS LEMMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 72 6 BLACKSCHOLES OPTION PRICING MODEL 73 6.1 BLACKSCHOLES DIFFERENTIAL EQUATION . . . . . . . . . . . . . . . 73 6.2 BLACKSCHOLES FORMULA FOR EUROPEAN OPTIONS . . . . . . . . . 80 6.2.1 NUMERICAL APPROXIMATION . . . . . . . . . . . . . . . . 84 6.3 SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.3.1 LINEAR CONGRUENTIAL GENERATOR . . . . . . . . . . . . . 88 6.3.2 FIBONACCI GENERATORS . . . . . . . . . . . . . . . . . . 93 6.3.3 INVERSION METHOD . . . . . . . . . . . . . . . . . . . . . 94 6.3.4 BOX-MULLER METHOD . . . . . . . . . . . . . . . . . . . 95 6.3.5 VARIANT OF MARSAGLIA METHOD . . . . . . . . . . . . . . 97 6.4 RISK MANAGEMENT AND HEDGING . . . . . . . . . . . . . . . . . 98 6.4.1 DELTA HEDGING . . . . . . . . . . . . . . . . . . . . . . 101 6.4.2 GAMMA AND THETA . . . . . . . . . . . . . . . . . . . . 104 6.4.3 RHO AND VEGA . . . . . . . . . . . . . . . . . . . . . . . 107 6.4.4 VOLGA AND VANNA . . . . . . . . . . . . . . . . . . . . . 108 6.4.5 HISTORICAL AND IMPLIED VOLATILITY . . . . . . . . . . . . 110 6.4.6 REALISED VOLATILITY . . . . . . . . . . . . . . . . . . . . 114 6.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 115 7 BINOMIAL MODEL FOR EUROPEAN OPTIONS 117 7.1 COXROSSRUBINSTEIN APPROACH TO OPTION PRICING . . . . . . 118 7.2 DISCRETE DIVIDENDS . . . . . . . . . . . . . . . . . . . . . . . . 122 7.2.1 DIVIDENDS AS A PERCENTAGE OF THE STOCK PRICE . . . . . 123 7.2.2 DIVIDENDS AS A FIXED AMOUNT OF MONEY . . . . . . . . 124 7.3 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 127 8 AMERICAN OPTIONS 129 8.1 ARBITRAGE RELATIONSHIP FOR AMERICAN OPTIONS . . . . . . . . . 129 8.2 THE TRINOMIAL MODEL FOR AMERICAN OPTIONS . . . . . . . . . . 136 8.3 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 141 9 EXOTIC OPTIONS 143 9.1 COMPOUND OPTIONS, OPTION ON OPTION . . . . . . . . . . . . . 143 9.2 CHOOSER OPTIONS OR AS YOU WISH OPTIONS . . . . . . . . . . 146 9.3 BARRIER OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 146 9.4 ASIAN OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 9.5 LOOKBACK OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . 150 9.6 CLIQUET OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 152 CONTENTS XIX 9.7 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 153 10 MODELS FOR THE INTEREST RATE AND INTEREST RATE DERIVATIVES 155 10.1 BOND VALUE WITH KNOWN TIME DEPENDENT INTEREST RATE . . . 155 10.2 STOCHASTIC INTEREST RATE MODEL . . . . . . . . . . . . . . . . . 156 10.3 THE BOND VALUATION EQUATION . . . . . . . . . . . . . . . . . . 157 10.4 SOLVING THE ZERO BOND VALUATION EQUATION . . . . . . . . . . . 159 10.5 VALUATION OF BOND OPTIONS . . . . . . . . . . . . . . . . . . . 160 10.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 161 II STATISTICAL MODELS OF FINANCIAL TIME SERIES 163 11 INTRODUCTION: DEFINITIONS AND CONCEPTS 165 11.1 SOME DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . 166 11.2 STATISTICAL ANALYSIS OF GERMAN STOCK RETURNS . . . . . . . . . 173 11.3 EXPECTATIONS AND EFFICIENT MARKETS . . . . . . . . . . . . . . . 175 11.4 ECONOMETRIC MODELS: A BRIEF SUMMARY . . . . . . . . . . . . 181 11.4.1 STOCK PRICES: THE CAPM . . . . . . . . . . . . . . . . 181 11.4.2 EXCHANGE RATE: THEORY OF THE INTEREST RATE PARITY . . 182 11.4.3 TERM STRUCTURE: THE COX-INGERSOLL-ROSS MODEL . . . . 184 11.4.4 OPTIONS: THE BLACK-SCHOLES MODEL . . . . . . . . . . . 186 11.4.5 THE MARKET PRICE OF RISK . . . . . . . . . . . . . . . . 188 11.5 THE RANDOM WALK HYPOTHESIS . . . . . . . . . . . . . . . . . 191 11.6 UNIT ROOT TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . 193 11.6.1 DICKEY-FULLER TESTS . . . . . . . . . . . . . . . . . . . . 194 11.6.2 THE KPSS TEST OF STATIONARITY . . . . . . . . . . . . . 196 11.6.3 VARIANCE RATIO TESTS . . . . . . . . . . . . . . . . . . . 198 11.7 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 200 12 ARIMA TIME SERIES MODELS 203 12.1 MOVING AVERAGE PROCESSES . . . . . . . . . . . . . . . . . . . . 204 12.2 AUTOREGRESSIVE PROCESS . . . . . . . . . . . . . . . . . . . . . . 205 12.3 ARMA MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . 209 12.4 PARTIAL AUTOCORRELATION . . . . . . . . . . . . . . . . . . . . . 211 12.5 ESTIMATION OF MOMENTS . . . . . . . . . . . . . . . . . . . . . 214 12.5.1 ESTIMATION OF THE MEAN FUNCTION . . . . . . . . . . . . 215 12.5.2 ESTIMATION OF THE COVARIANCE FUNCTION . . . . . . . . . 216 12.5.3 ESTIMATION OF THE ACF . . . . . . . . . . . . . . . . . . 217 12.6 PORTMANTEAU STATISTICS . . . . . . . . . . . . . . . . . . . . . . 218 12.7 ESTIMATION OF AR( P ) MODELS . . . . . . . . . . . . . . . . . . . 219 12.8 ESTIMATION OF MA( Q ) AND ARMA( P, Q ) MODELS . . . . . . . . . 220 XX CONTENTS 12.9 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 225 13 TIME SERIES WITH STOCHASTIC VOLATILITY 227 13.1 ARCH AND GARCH MODELS . . . . . . . . . . . . . . . . . . . 229 13.1.1 ARCH(1): DEFINITION AND PROPERTIES . . . . . . . . . . 231 13.1.2 ESTIMATION OF ARCH(1) MODELS . . . . . . . . . . . . . 239 13.1.3 ARCH( Q ): DEFINITION AND PROPERTIES . . . . . . . . . . 242 13.1.4 ESTIMATION OF AN ARCH( Q ) MODEL . . . . . . . . . . . 244 13.1.5 GENERALISED ARCH (GARCH) . . . . . . . . . . . . . . 245 13.1.6 ESTIMATION OF GARCH( P, Q ) MODELS . . . . . . . . . . 248 13.2 EXTENSIONS OF THE GARCH MODEL . . . . . . . . . . . . . . . . 252 13.2.1 EXPONENTIAL GARCH . . . . . . . . . . . . . . . . . . . 252 13.2.2 THRESHOLD ARCH MODELS . . . . . . . . . . . . . . . . 254 13.2.3 RISK AND RETURNS . . . . . . . . . . . . . . . . . . . . . 255 13.2.4 ESTIMATION RESULTS FOR THE DAX RETURNS . . . . . . . 256 13.3 SHORTFALLS OF GARCH . . . . . . . . . . . . . . . . . . . . . . . 258 13.3.1 RECENT CHALLENGES TO GARCH MODELS . . . . . . . . . 258 13.3.2 NEXT-DAY VOLATILITY FORECASTING FOR DAX RETURNS . . 265 13.4 MULTIVARIATE GARCH MODELS . . . . . . . . . . . . . . . . . . 268 13.4.1 THE VEC SPECIFICATION . . . . . . . . . . . . . . . . . . 268 13.4.2 THE BEKK SPECIFICATION . . . . . . . . . . . . . . . . . 271 13.4.3 THE CCC MODEL . . . . . . . . . . . . . . . . . . . . . 272 13.4.4 THE DCC MODEL . . . . . . . . . . . . . . . . . . . . . 272 13.4.5 AN EMPIRICAL ILLUSTRATION . . . . . . . . . . . . . . . . 273 13.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 277 14 NON-PARAMETRIC CONCEPTS FOR FINANCIAL TIME SERIES 279 14.1 NONPARAMETRIC REGRESSION . . . . . . . . . . . . . . . . . . . . 280 14.2 CONSTRUCTION OF THE ESTIMATOR . . . . . . . . . . . . . . . . . . 283 14.3 ASYMPTOTIC NORMALITY . . . . . . . . . . . . . . . . . . . . . . 286 14.4 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 301 III SELECTED FINANCIAL APPLICATIONS 303 15 PRICING OPTIONS WITH FLEXIBLE VOLATILITY ESTIMATORS 305 15.1 PRICING OPTIONS WITH ARCH-MODELS . . . . . . . . . . . . . . 305 15.2 A MONTE CARLO STUDY . . . . . . . . . . . . . . . . . . . . . . 312 15.3 APPLICATION TO THE VALUATION OF DAX CALLS . . . . . . . . . . 315 15.4 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 319 16 VALUE AT RISK AND BACKTESTING 321 16.1 FORECAST AND VAR MODELS . . . . . . . . . . . . . . . . . . . . 323 CONTENTS XXI 16.2 BACKTESTING WITH EXPECTED SHORTFALL . . . . . . . . . . . . . . 325 16.3 BACKTESTING IN ACTION . . . . . . . . . . . . . . . . . . . . . . 326 16.4 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 331 17 COPULAE AND VALUE AT RISK 333 17.1 COPULAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 17.1.1 GAUSSIAN COPULA . . . . . . . . . . . . . . . . . . . . . 339 17.1.2 STUDENTS T -COPULA . . . . . . . . . . . . . . . . . . . . 341 17.1.3 ARCHIMEDEAN COPULAE . . . . . . . . . . . . . . . . . . 342 17.1.4 MULTIVARIATE ARCHIMEDEAN COPULAE . . . . . . . . . . . 343 17.1.5 DISTRIBUTIONS CONSTRUCTED WITH COPULAE . . . . . . . . 345 17.1.6 MONTE CARLO SIMULATION . . . . . . . . . . . . . . . . . 345 17.2 COPULA ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . 349 17.2.1 MAXIMUM LIKELIHOOD ESTIMATION . . . . . . . . . . . . 351 17.2.2 IFM - INFERENCE FOR MARGINS . . . . . . . . . . . . . . . 351 17.2.3 CML - CANONICAL MAXIMUM LIKELIHOOD . . . . . . . . 351 17.2.4 GAUSSIAN COPULA ESTIMATION . . . . . . . . . . . . . . 352 17.2.5 T -COPULA ESTIMATION . . . . . . . . . . . . . . . . . . . 353 17.3 VALUE-AT-RISK AND COPULAE . . . . . . . . . . . . . . . . . . . 354 17.3.1 VALUE-AT-RISK . . . . . . . . . . . . . . . . . . . . . . . 354 17.3.2 VAR ESTIMATION WITH COPULAE . . . . . . . . . . . . . . 355 17.3.3 TIME-VARYING COPULAE AND BACKTESTING . . . . . . . . 356 17.4 EMPIRICAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . 356 17.4.1 AN EXCHANGE RATE PORTFOLIO . . . . . . . . . . . . . . . 356 17.4.2 5 -DIMENSIONAL EXCHANGE RATE PORTFOLIO . . . . . . . . 361 17.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 368 18 STATISTICS OF EXTREME RISKS 371 18.1 LIMIT BEHAVIOUR OF MAXIMA . . . . . . . . . . . . . . . . . . . 371 18.2 STATISTICS OF EXTREME EVENTS . . . . . . . . . . . . . . . . . . . 380 18.2.1 THE POT (PEAKS-OVER-THRESHOLD) METHOD . . . . . . 382 18.2.2 THE HILL ESTIMATOR . . . . . . . . . . . . . . . . . . . . 388 18.3 ESTIMATORS FOR RISK MEASUREMENTS . . . . . . . . . . . . . . . 390 18.4 EXTREME VALUE THEORY FOR TIME SERIES . . . . . . . . . . . . . 392 18.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 396 19 NEURAL NETWORKS 399 19.1 FROM PERCEPTRON TO NON-LINEAR NEURON . . . . . . . . . . . . . 400 19.2 BACK PROPAGATION . . . . . . . . . . . . . . . . . . . . . . . . . 409 19.3 NEURAL NETWORKS IN NON-PARAMETRIC REGRESSION ANALYSIS . . . 411 19.4 FORECASTS OF FINANCIAL TIME SERIES WITH NEURAL NETWORKS . . . 418 19.5 QUANTIFYING RISK WITH NEURAL NETWORKS . . . . . . . . . . . . 422 XXII CONTENTS 19.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 427 20 VOLATILITY RISK OF OPTION PORTFOLIOS 429 20.1 DESCRIPTION OF THE DATA . . . . . . . . . . . . . . . . . . . . . 430 20.2 PRINCIPAL COMPONENT ANALYSIS OF THE VDAXS DYNAMICS . . . 434 20.3 STABILITY ANALYSIS OF THE VDAXS DYNAMICS . . . . . . . . . . 437 20.4 MEASURE OF THE IMPLIED VOLATILITYS RISK . . . . . . . . . . . . 438 20.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 441 21 NONPARAMETRIC ESTIMATORS FOR THE PROBABILITY OF DEFAULT 443 21.1 LOGISTIC REGRESSION . . . . . . . . . . . . . . . . . . . . . . . . 443 21.2 SEMI-PARAMETRIC MODEL FOR CREDIT RATING . . . . . . . . . . . 445 21.3 CREDIT RATINGS WITH NEURAL NETWORKS . . . . . . . . . . . . . . 449 22 CREDIT RISK MANAGEMENT 451 22.1 BASIC CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . 451 22.2 THE BERNOULLI MODEL . . . . . . . . . . . . . . . . . . . . . . . 453 22.3 THE POISSON MODEL . . . . . . . . . . . . . . . . . . . . . . . . 454 22.4 THE INDUSTRIAL MODELS . . . . . . . . . . . . . . . . . . . . . . 455 22.5 ONE FACTOR MODELS . . . . . . . . . . . . . . . . . . . . . . . . 460 22.6 COPULAE AND LOSS DISTRIBUTIONS . . . . . . . . . . . . . . . . . 462 A TECHNICAL APPENDIX 467 APPENDIX 467 A.1 INTEGRATION THEORY . . . . . . . . . . . . . . . . . . . . . . . . 467 A.2 PORTFOLIO STRATEGIES . . . . . . . . . . . . . . . . . . . . . . . . 472 FREQUENTLY USED NOTATIONS 479 BIBLIOGRAPHY 481 INDEX 497
adam_txt	CONTENTS PREFACE TO THE SECOND EDITION XI PREFACE TO THE FIRST EDITION XIII I OPTION PRICING 1 1 DERIVATIVES 3 1.1 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 10 2 INTRODUCTION TO OPTION MANAGEMENT 11 2.1 ARBITRAGE RELATIONS . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 PORTFOLIO INSURANCE . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 BINARY ONE-PERIOD MODEL . . . . . . . . . . . . . . . . . . . . 30 2.4 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 35 3 BASIC CONCEPTS OF PROBABILITY THEORY 37 3.1 REAL VALUED RANDOM VARIABLES . . . . . . . . . . . . . . . . . 37 3.2 EXPECTATION AND VARIANCE . . . . . . . . . . . . . . . . . . . . 39 3.3 SKEWNESS AND KURTOSIS . . . . . . . . . . . . . . . . . . . . . . 41 3.4 RANDOM VECTORS, DEPENDENCE, CORRELATION . . . . . . . . . . . 42 3.5 CONDITIONAL PROBABILITIES AND EXPECTATIONS . . . . . . . . . . 43 3.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 45 4 STOCHASTIC PROCESSES IN DISCRETE TIME 47 4.1 BINOMIAL PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2 TRINOMIAL PROCESSES . . . . . . . . . . . . . . . . . . . . . . . 51 4.3 GENERAL RANDOM WALKS . . . . . . . . . . . . . . . . . . . . . 53 4.4 GEOMETRIC RANDOM WALKS . . . . . . . . . . . . . . . . . . . . 54 4.5 BINOMIAL MODELS WITH STATE DEPENDENT INCREMENTS . . . . . . 55 4.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 56 5 STOCHASTIC INTEGRALS AND DIFFERENTIAL EQUATIONS 57 5.1 WIENER PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2 STOCHASTIC INTEGRATION . . . . . . . . . . . . . . . . . . . . . . 61 XVIII CONTENTS 5.3 STOCHASTIC DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . 63 5.4 THE STOCK PRICE AS A STOCHASTIC PROCESS . . . . . . . . . . . . 66 5.5 IT* OS LEMMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 72 6 BLACKSCHOLES OPTION PRICING MODEL 73 6.1 BLACKSCHOLES DIFFERENTIAL EQUATION . . . . . . . . . . . . . . . 73 6.2 BLACKSCHOLES FORMULA FOR EUROPEAN OPTIONS . . . . . . . . . 80 6.2.1 NUMERICAL APPROXIMATION . . . . . . . . . . . . . . . . 84 6.3 SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.3.1 LINEAR CONGRUENTIAL GENERATOR . . . . . . . . . . . . . 88 6.3.2 FIBONACCI GENERATORS . . . . . . . . . . . . . . . . . . 93 6.3.3 INVERSION METHOD . . . . . . . . . . . . . . . . . . . . . 94 6.3.4 BOX-MULLER METHOD . . . . . . . . . . . . . . . . . . . 95 6.3.5 VARIANT OF MARSAGLIA METHOD . . . . . . . . . . . . . . 97 6.4 RISK MANAGEMENT AND HEDGING . . . . . . . . . . . . . . . . . 98 6.4.1 DELTA HEDGING . . . . . . . . . . . . . . . . . . . . . . 101 6.4.2 GAMMA AND THETA . . . . . . . . . . . . . . . . . . . . 104 6.4.3 RHO AND VEGA . . . . . . . . . . . . . . . . . . . . . . . 107 6.4.4 VOLGA AND VANNA . . . . . . . . . . . . . . . . . . . . . 108 6.4.5 HISTORICAL AND IMPLIED VOLATILITY . . . . . . . . . . . . 110 6.4.6 REALISED VOLATILITY . . . . . . . . . . . . . . . . . . . . 114 6.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 115 7 BINOMIAL MODEL FOR EUROPEAN OPTIONS 117 7.1 COXROSSRUBINSTEIN APPROACH TO OPTION PRICING . . . . . . 118 7.2 DISCRETE DIVIDENDS . . . . . . . . . . . . . . . . . . . . . . . . 122 7.2.1 DIVIDENDS AS A PERCENTAGE OF THE STOCK PRICE . . . . . 123 7.2.2 DIVIDENDS AS A FIXED AMOUNT OF MONEY . . . . . . . . 124 7.3 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 127 8 AMERICAN OPTIONS 129 8.1 ARBITRAGE RELATIONSHIP FOR AMERICAN OPTIONS . . . . . . . . . 129 8.2 THE TRINOMIAL MODEL FOR AMERICAN OPTIONS . . . . . . . . . . 136 8.3 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 141 9 EXOTIC OPTIONS 143 9.1 COMPOUND OPTIONS, OPTION ON OPTION . . . . . . . . . . . . . 143 9.2 CHOOSER OPTIONS OR AS YOU WISH OPTIONS . . . . . . . . . . 146 9.3 BARRIER OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 146 9.4 ASIAN OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 9.5 LOOKBACK OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . 150 9.6 CLIQUET OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 152 CONTENTS XIX 9.7 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 153 10 MODELS FOR THE INTEREST RATE AND INTEREST RATE DERIVATIVES 155 10.1 BOND VALUE WITH KNOWN TIME DEPENDENT INTEREST RATE . . . 155 10.2 STOCHASTIC INTEREST RATE MODEL . . . . . . . . . . . . . . . . . 156 10.3 THE BOND VALUATION EQUATION . . . . . . . . . . . . . . . . . . 157 10.4 SOLVING THE ZERO BOND VALUATION EQUATION . . . . . . . . . . . 159 10.5 VALUATION OF BOND OPTIONS . . . . . . . . . . . . . . . . . . . 160 10.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 161 II STATISTICAL MODELS OF FINANCIAL TIME SERIES 163 11 INTRODUCTION: DEFINITIONS AND CONCEPTS 165 11.1 SOME DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . 166 11.2 STATISTICAL ANALYSIS OF GERMAN STOCK RETURNS . . . . . . . . . 173 11.3 EXPECTATIONS AND EFFICIENT MARKETS . . . . . . . . . . . . . . . 175 11.4 ECONOMETRIC MODELS: A BRIEF SUMMARY . . . . . . . . . . . . 181 11.4.1 STOCK PRICES: THE CAPM . . . . . . . . . . . . . . . . 181 11.4.2 EXCHANGE RATE: THEORY OF THE INTEREST RATE PARITY . . 182 11.4.3 TERM STRUCTURE: THE COX-INGERSOLL-ROSS MODEL . . . . 184 11.4.4 OPTIONS: THE BLACK-SCHOLES MODEL . . . . . . . . . . . 186 11.4.5 THE MARKET PRICE OF RISK . . . . . . . . . . . . . . . . 188 11.5 THE RANDOM WALK HYPOTHESIS . . . . . . . . . . . . . . . . . 191 11.6 UNIT ROOT TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . 193 11.6.1 DICKEY-FULLER TESTS . . . . . . . . . . . . . . . . . . . . 194 11.6.2 THE KPSS TEST OF STATIONARITY . . . . . . . . . . . . . 196 11.6.3 VARIANCE RATIO TESTS . . . . . . . . . . . . . . . . . . . 198 11.7 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 200 12 ARIMA TIME SERIES MODELS 203 12.1 MOVING AVERAGE PROCESSES . . . . . . . . . . . . . . . . . . . . 204 12.2 AUTOREGRESSIVE PROCESS . . . . . . . . . . . . . . . . . . . . . . 205 12.3 ARMA MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . 209 12.4 PARTIAL AUTOCORRELATION . . . . . . . . . . . . . . . . . . . . . 211 12.5 ESTIMATION OF MOMENTS . . . . . . . . . . . . . . . . . . . . . 214 12.5.1 ESTIMATION OF THE MEAN FUNCTION . . . . . . . . . . . . 215 12.5.2 ESTIMATION OF THE COVARIANCE FUNCTION . . . . . . . . . 216 12.5.3 ESTIMATION OF THE ACF . . . . . . . . . . . . . . . . . . 217 12.6 PORTMANTEAU STATISTICS . . . . . . . . . . . . . . . . . . . . . . 218 12.7 ESTIMATION OF AR( P ) MODELS . . . . . . . . . . . . . . . . . . . 219 12.8 ESTIMATION OF MA( Q ) AND ARMA( P, Q ) MODELS . . . . . . . . . 220 XX CONTENTS 12.9 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 225 13 TIME SERIES WITH STOCHASTIC VOLATILITY 227 13.1 ARCH AND GARCH MODELS . . . . . . . . . . . . . . . . . . . 229 13.1.1 ARCH(1): DEFINITION AND PROPERTIES . . . . . . . . . . 231 13.1.2 ESTIMATION OF ARCH(1) MODELS . . . . . . . . . . . . . 239 13.1.3 ARCH( Q ): DEFINITION AND PROPERTIES . . . . . . . . . . 242 13.1.4 ESTIMATION OF AN ARCH( Q ) MODEL . . . . . . . . . . . 244 13.1.5 GENERALISED ARCH (GARCH) . . . . . . . . . . . . . . 245 13.1.6 ESTIMATION OF GARCH( P, Q ) MODELS . . . . . . . . . . 248 13.2 EXTENSIONS OF THE GARCH MODEL . . . . . . . . . . . . . . . . 252 13.2.1 EXPONENTIAL GARCH . . . . . . . . . . . . . . . . . . . 252 13.2.2 THRESHOLD ARCH MODELS . . . . . . . . . . . . . . . . 254 13.2.3 RISK AND RETURNS . . . . . . . . . . . . . . . . . . . . . 255 13.2.4 ESTIMATION RESULTS FOR THE DAX RETURNS . . . . . . . 256 13.3 SHORTFALLS OF GARCH . . . . . . . . . . . . . . . . . . . . . . . 258 13.3.1 RECENT CHALLENGES TO GARCH MODELS . . . . . . . . . 258 13.3.2 NEXT-DAY VOLATILITY FORECASTING FOR DAX RETURNS . . 265 13.4 MULTIVARIATE GARCH MODELS . . . . . . . . . . . . . . . . . . 268 13.4.1 THE VEC SPECIFICATION . . . . . . . . . . . . . . . . . . 268 13.4.2 THE BEKK SPECIFICATION . . . . . . . . . . . . . . . . . 271 13.4.3 THE CCC MODEL . . . . . . . . . . . . . . . . . . . . . 272 13.4.4 THE DCC MODEL . . . . . . . . . . . . . . . . . . . . . 272 13.4.5 AN EMPIRICAL ILLUSTRATION . . . . . . . . . . . . . . . . 273 13.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 277 14 NON-PARAMETRIC CONCEPTS FOR FINANCIAL TIME SERIES 279 14.1 NONPARAMETRIC REGRESSION . . . . . . . . . . . . . . . . . . . . 280 14.2 CONSTRUCTION OF THE ESTIMATOR . . . . . . . . . . . . . . . . . . 283 14.3 ASYMPTOTIC NORMALITY . . . . . . . . . . . . . . . . . . . . . . 286 14.4 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 301 III SELECTED FINANCIAL APPLICATIONS 303 15 PRICING OPTIONS WITH FLEXIBLE VOLATILITY ESTIMATORS 305 15.1 PRICING OPTIONS WITH ARCH-MODELS . . . . . . . . . . . . . . 305 15.2 A MONTE CARLO STUDY . . . . . . . . . . . . . . . . . . . . . . 312 15.3 APPLICATION TO THE VALUATION OF DAX CALLS . . . . . . . . . . 315 15.4 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 319 16 VALUE AT RISK AND BACKTESTING 321 16.1 FORECAST AND VAR MODELS . . . . . . . . . . . . . . . . . . . . 323 CONTENTS XXI 16.2 BACKTESTING WITH EXPECTED SHORTFALL . . . . . . . . . . . . . . 325 16.3 BACKTESTING IN ACTION . . . . . . . . . . . . . . . . . . . . . . 326 16.4 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 331 17 COPULAE AND VALUE AT RISK 333 17.1 COPULAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 17.1.1 GAUSSIAN COPULA . . . . . . . . . . . . . . . . . . . . . 339 17.1.2 STUDENTS T -COPULA . . . . . . . . . . . . . . . . . . . . 341 17.1.3 ARCHIMEDEAN COPULAE . . . . . . . . . . . . . . . . . . 342 17.1.4 MULTIVARIATE ARCHIMEDEAN COPULAE . . . . . . . . . . . 343 17.1.5 DISTRIBUTIONS CONSTRUCTED WITH COPULAE . . . . . . . . 345 17.1.6 MONTE CARLO SIMULATION . . . . . . . . . . . . . . . . . 345 17.2 COPULA ESTIMATION . . . . . . . . . . . . . . . . . . . . . . . . 349 17.2.1 MAXIMUM LIKELIHOOD ESTIMATION . . . . . . . . . . . . 351 17.2.2 IFM - INFERENCE FOR MARGINS . . . . . . . . . . . . . . . 351 17.2.3 CML - CANONICAL MAXIMUM LIKELIHOOD . . . . . . . . 351 17.2.4 GAUSSIAN COPULA ESTIMATION . . . . . . . . . . . . . . 352 17.2.5 T -COPULA ESTIMATION . . . . . . . . . . . . . . . . . . . 353 17.3 VALUE-AT-RISK AND COPULAE . . . . . . . . . . . . . . . . . . . 354 17.3.1 VALUE-AT-RISK . . . . . . . . . . . . . . . . . . . . . . . 354 17.3.2 VAR ESTIMATION WITH COPULAE . . . . . . . . . . . . . . 355 17.3.3 TIME-VARYING COPULAE AND BACKTESTING . . . . . . . . 356 17.4 EMPIRICAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . 356 17.4.1 AN EXCHANGE RATE PORTFOLIO . . . . . . . . . . . . . . . 356 17.4.2 5 -DIMENSIONAL EXCHANGE RATE PORTFOLIO . . . . . . . . 361 17.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 368 18 STATISTICS OF EXTREME RISKS 371 18.1 LIMIT BEHAVIOUR OF MAXIMA . . . . . . . . . . . . . . . . . . . 371 18.2 STATISTICS OF EXTREME EVENTS . . . . . . . . . . . . . . . . . . . 380 18.2.1 THE POT (PEAKS-OVER-THRESHOLD) METHOD . . . . . . 382 18.2.2 THE HILL ESTIMATOR . . . . . . . . . . . . . . . . . . . . 388 18.3 ESTIMATORS FOR RISK MEASUREMENTS . . . . . . . . . . . . . . . 390 18.4 EXTREME VALUE THEORY FOR TIME SERIES . . . . . . . . . . . . . 392 18.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 396 19 NEURAL NETWORKS 399 19.1 FROM PERCEPTRON TO NON-LINEAR NEURON . . . . . . . . . . . . . 400 19.2 BACK PROPAGATION . . . . . . . . . . . . . . . . . . . . . . . . . 409 19.3 NEURAL NETWORKS IN NON-PARAMETRIC REGRESSION ANALYSIS . . . 411 19.4 FORECASTS OF FINANCIAL TIME SERIES WITH NEURAL NETWORKS . . . 418 19.5 QUANTIFYING RISK WITH NEURAL NETWORKS . . . . . . . . . . . . 422 XXII CONTENTS 19.6 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 427 20 VOLATILITY RISK OF OPTION PORTFOLIOS 429 20.1 DESCRIPTION OF THE DATA . . . . . . . . . . . . . . . . . . . . . 430 20.2 PRINCIPAL COMPONENT ANALYSIS OF THE VDAXS DYNAMICS . . . 434 20.3 STABILITY ANALYSIS OF THE VDAXS DYNAMICS . . . . . . . . . . 437 20.4 MEASURE OF THE IMPLIED VOLATILITYS RISK . . . . . . . . . . . . 438 20.5 RECOMMENDED LITERATURE . . . . . . . . . . . . . . . . . . . . 441 21 NONPARAMETRIC ESTIMATORS FOR THE PROBABILITY OF DEFAULT 443 21.1 LOGISTIC REGRESSION . . . . . . . . . . . . . . . . . . . . . . . . 443 21.2 SEMI-PARAMETRIC MODEL FOR CREDIT RATING . . . . . . . . . . . 445 21.3 CREDIT RATINGS WITH NEURAL NETWORKS . . . . . . . . . . . . . . 449 22 CREDIT RISK MANAGEMENT 451 22.1 BASIC CONCEPTS . . . . . . . . . . . . . . . . . . . . . . . . . . 451 22.2 THE BERNOULLI MODEL . . . . . . . . . . . . . . . . . . . . . . . 453 22.3 THE POISSON MODEL . . . . . . . . . . . . . . . . . . . . . . . . 454 22.4 THE INDUSTRIAL MODELS . . . . . . . . . . . . . . . . . . . . . . 455 22.5 ONE FACTOR MODELS . . . . . . . . . . . . . . . . . . . . . . . . 460 22.6 COPULAE AND LOSS DISTRIBUTIONS . . . . . . . . . . . . . . . . . 462 A TECHNICAL APPENDIX 467 APPENDIX 467 A.1 INTEGRATION THEORY . . . . . . . . . . . . . . . . . . . . . . . . 467 A.2 PORTFOLIO STRATEGIES . . . . . . . . . . . . . . . . . . . . . . . . 472 FREQUENTLY USED NOTATIONS 479 BIBLIOGRAPHY 481 INDEX 497
any_adam_object	1
any_adam_object_boolean	1
author	Franke, Jürgen 1952- Härdle, Wolfgang 1953- Hafner, Christian M. 1967-
author_GND	(DE-588)141577177 (DE-588)110357116 (DE-588)115629793
author_facet	Franke, Jürgen 1952- Härdle, Wolfgang 1953- Hafner, Christian M. 1967-
author_role	aut aut aut
author_sort	Franke, Jürgen 1952-
author_variant	j f jf w h wh c m h cm cmh
building	Verbundindex
bvnumber	BV023029589
callnumber-first	H - Social Science
callnumber-label	HG176
callnumber-raw	HG176.5
callnumber-search	HG176.5
callnumber-sort	HG 3176.5
callnumber-subject	HG - Finance
classification_rvk	QK 600 QK 660 QP 890 SK 980
classification_tum	WIR 651f
ctrlnum	(OCoLC)221661723 (DE-599)DNB986058033
dewey-full	332.01/5195 332.0151
dewey-hundreds	300 - Social sciences
dewey-ones	332 - Financial economics
dewey-raw	332.01/5195 332.0151
dewey-search	332.01/5195 332.0151
dewey-sort	3332.01 45195
dewey-tens	330 - Economics
discipline	Mathematik Wirtschaftswissenschaften
discipline_str_mv	Mathematik Wirtschaftswissenschaften
edition	2. ed.
format	Book
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genre_facet	Lehrbuch
id	DE-604.BV023029589
illustrated	Illustrated
index_date	2024-07-02T19:16:26Z
indexdate	2024-07-09T21:09:21Z
institution	BVB
isbn	9783540762690 3540762698 9783540762720
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016233494
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physical	XXII, 501 S. graph. Darst.
publishDate	2008
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spelling	Franke, Jürgen 1952- Verfasser (DE-588)141577177 aut Statistics of financial markets an introduction Jürgen Franke ; Wolfgang Härdle ; Christian M. Hafner 2. ed. Berlin [u.a.] Springer 2008 XXII, 501 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Estatística larpcal Finanças larpcal Modelos matemáticos larpcal Mathematisches Modell Finance Mathematical models Finance Statistical methods CD-ROM (DE-588)4139307-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Financial Engineering (DE-588)4208404-0 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Financial Engineering (DE-588)4208404-0 s Finanzmathematik (DE-588)4017195-4 s DE-604 Kreditmarkt (DE-588)4073788-3 s Optionspreistheorie (DE-588)4135346-8 s Mathematisches Modell (DE-588)4114528-8 s Statistik (DE-588)4056995-0 s CD-ROM (DE-588)4139307-7 s 1\p DE-604 Härdle, Wolfgang 1953- Verfasser (DE-588)110357116 aut Hafner, Christian M. 1967- Verfasser (DE-588)115629793 aut http://d-nb.info/986058033/04 Inhaltsverzeichnis SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016233494&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Franke, Jürgen 1952- Härdle, Wolfgang 1953- Hafner, Christian M. 1967- Statistics of financial markets an introduction Estatística larpcal Finanças larpcal Modelos matemáticos larpcal Mathematisches Modell Finance Mathematical models Finance Statistical methods CD-ROM (DE-588)4139307-7 gnd Statistik (DE-588)4056995-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd Financial Engineering (DE-588)4208404-0 gnd Optionspreistheorie (DE-588)4135346-8 gnd Kreditmarkt (DE-588)4073788-3 gnd Finanzmathematik (DE-588)4017195-4 gnd
subject_GND	(DE-588)4139307-7 (DE-588)4056995-0 (DE-588)4114528-8 (DE-588)4208404-0 (DE-588)4135346-8 (DE-588)4073788-3 (DE-588)4017195-4 (DE-588)4123623-3
title	Statistics of financial markets an introduction
title_auth	Statistics of financial markets an introduction
title_exact_search	Statistics of financial markets an introduction
title_exact_search_txtP	Statistics of financial markets an introduction
title_full	Statistics of financial markets an introduction Jürgen Franke ; Wolfgang Härdle ; Christian M. Hafner
title_fullStr	Statistics of financial markets an introduction Jürgen Franke ; Wolfgang Härdle ; Christian M. Hafner
title_full_unstemmed	Statistics of financial markets an introduction Jürgen Franke ; Wolfgang Härdle ; Christian M. Hafner
title_short	Statistics of financial markets
title_sort	statistics of financial markets an introduction
title_sub	an introduction
topic	Estatística larpcal Finanças larpcal Modelos matemáticos larpcal Mathematisches Modell Finance Mathematical models Finance Statistical methods CD-ROM (DE-588)4139307-7 gnd Statistik (DE-588)4056995-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd Financial Engineering (DE-588)4208404-0 gnd Optionspreistheorie (DE-588)4135346-8 gnd Kreditmarkt (DE-588)4073788-3 gnd Finanzmathematik (DE-588)4017195-4 gnd
topic_facet	Estatística Finanças Modelos matemáticos Mathematisches Modell Finance Mathematical models Finance Statistical methods CD-ROM Statistik Financial Engineering Optionspreistheorie Kreditmarkt Finanzmathematik Lehrbuch
url	http://d-nb.info/986058033/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016233494&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT frankejurgen statisticsoffinancialmarketsanintroduction AT hardlewolfgang statisticsoffinancialmarketsanintroduction AT hafnerchristianm statisticsoffinancialmarketsanintroduction

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