# Statistics of Financial Markets: An Introduction

Springer Science & Business Media, Jan 4, 2008 - Business & Economics - 502 pages

Statistics of Financial Markets offers a vivid yet concise introduction to the growing field of statistical applications in finance. The reader will learn the basic methods to evaluate option contracts, to analyse financial time series, to select portfolios and manage risks making realistic assumptions of the market behaviour.

The focus is both on fundamentals of mathematical finance and financial time series analysis and on applications to given problems of financial markets, making the book the ideal basis for lectures, seminars and crash courses on the topic.

For the second edition the book has been updated and extensively revised. Several new aspects have been included, among others a chapter on credit risk management.

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### Contents

 Derivatives 3 11 Recommended Literature 10 Introduction to Option Management 11 22 Portfolio Insurance 23 23 Binary OnePeriod Model 30 24 Recommended Literature 35 Basic Concepts of Probability Theory 37 32 Expectation and Variance 39
 127 Estimation of ARp Models 219 128 Estimation of MAqandARMApq Models 220 129 Recommended Literature 225 Time Series with Stochastic Volatility 227 131 ARCH and GARCH Models 229 Deﬁnition and Properties 231 1312 Estimation of ARCH1 Models 239 Deﬁnition and Properties 242

 33 Skewness and Kurtosis 41 34 Random Vectors Dependence Correlation 42 35 Conditional Probabilities and Expectations 43 36 Recommended Literature 45 Stochastic Processes in Discrete Time 47 42 Trinomial Processes 51 43 General Random Walks 53 44 Geometric Random Walks 54 45 Binomial Models with State Dependent Increments 55 46 Recommended Literature 56 Stochastic Integrals and Diﬀerential Equations 57 52 Stochastic Integration 61 53 Stochastic Diﬀerential Equations 63 54 The Stock Price as a Stochastic Process 66 55 Itˆos Lemma 69 56 Recommended Literature 72 6 BlackScholes Option Pricing Model 73 62 BlackScholes Formula for European Options 80 621 Numerical Approximation 84 63 Simulation 87 631 Linear Congruential Generator 88 632 Fibonacci Generators 93 633 Inversion Method 94 634 BoxMuller Method 95 635 Variant of Marsaglia Method 97 64 Risk Management and Hedging 98 641 Delta Hedging 101 642 Gamma and Theta 104 643 Rho and Vega 107 644 Volga and Vanna 108 645 Historical and Implied Volatility 110 646 Realised Volatility 114 65 Recommended Literature 115 Binomial Model for European Options 116 71 CoxRossRubinstein Approach to Option Pricing 118 72 Discrete Dividends 122 721 Dividends as a Percentage of the Stock Price 123 722 Dividends as a Fixed Amount of Money 124 73 Recommended Literature 127 American Options 129 82 The Trinomial Model for American Options 136 83 Recommended Literature 141 Exotic Options 142 92 Chooser Options or As You Wish Options 146 94 Asian Options 148 95 Lookback Options 150 96 Cliquet Options 152 97 Recommended Literature 153 Models for the Interest Rate and Interest Rate Derivatives 155 102 Stochastic Interest Rate Model 156 103 The Bond Valuation Equation 157 104 Solving the Zero Bond Valuation Equation 159 105 Valuation of Bond Options 160 106 Recommended Literature 161 Statistical Models of Financial Time Series 162 Introduction Deﬁnitions and Concepts 165 111 Some Deﬁnitions 166 112 Statistical Analysis of German Stock Returns 173 113 Expectations and Efficient Markets 175 A Brief Summary 181 Theory of the Interest Rate Parity 182 The CoxIngersollRoss Model 184 The BlackScholes Model 186 1145 The Market Price of Risk 188 115 The Random Walk Hypothesis 191 116 UnitRootTests 193 1161 DickeyFuller Tests 194 1162 The KPSS Test of Stationarity 196 1163 Variance Ratio Tests 198 117 Recommended Literature 200 ARIMA Time Series Models 202 121 Moving Average Processes 204 122 Autoregressive Process 205 123 ARMA Models 209 124 Partial Autocorrelation 211 125 Estimation of Moments 214 1251 Estimation of the Mean Function 215 1252 Estimation of the Covariance Function 216 1253 Estimation of the ACF 217 126 Portmanteau Statistics 218
 1314 Estimation of an ARCHq Model 244 1315 Generalised ARCH GARCH 245 1316 Estimation of GARCHpq Models 248 132 Extensions of the GARCH Model 252 1322 Threshold ARCH Models 254 1323 Risk and Returns 255 1324 Estimation Results for the DAX Returns 256 133 Shortfalls of GARCH 258 1332 NextDay Volatility Forecasting for DAX Returns 265 134 Multivariate GARCH Models 268 1342 The BEKK Speciﬁcation 271 1343 The CCC Model 272 1345 An Empirical Illustration 273 135 Recommended Literature 277 Nonparametric Concepts for Financial Time Series 279 141 Nonparametric Regression 280 142 Construction of the Estimator 283 143 Asymptotic Normality 286 144 Recommended Literature 301 Selected Financial Applications 303 Pricing Options with Flexible Volatility Estimators 304 152 A Monte Carlo Study 312 153 Application to the Valuation of DAX Calls 315 154 Recommended Literature 319 Value at Risk and Backtesting 321 161 Forecast and VaR Models 323 162 Backtesting with Expected Shortfall 325 163 Backtesting in Action 326 164 Recommended Literature 331 Copulae and Value at Risk 333 171 Copulae 335 1711 Gaussian Copula 339 1712 Students tCopula 341 1713 Archimedean Copulae 342 1714 Multivariate Archimedean Copulae 343 1715 Distributions Constructed with Copulae 345 172 Copula Estimation 349 1721 Maximum Likelihood Estimation 351 1724 Gaussian Copula Estimation 352 1725 tCopula Estimation 353 173 ValueatRisk and Copulae 354 1732 VaR Estimation with Copulae 355 1733 TimeVarying Copulae and Backtesting 356 1742 5dimensional Exchange Rate Portfolio 361 175 Recommended Literature 368 18 Statistics of Extreme Risks 371 182 Statistics of Extreme Events 380 1821 The POT PeaksOverThreshold Method 382 1822 The Hill Estimator 388 183 Estimators for Risk Measurements 390 184 Extreme Value Theory for Time Series 392 185 Recommended Literature 396 Neural Networks 398 191 From Perceptron to Nonlinear Neuron 400 192 Back Propagation 409 193 Neural Networks in Nonparametric Regression Analysis 411 194 Forecasts of Financial Time Series with Neural Networks 418 195 Quantifying Risk with Neural Networks 422 196 Recommended Literature 427 Volatility Risk of Option Portfolios 429 201 Description of the Data 430 202 Principal Component Analysis of the VDAXs Dynamics 434 203 Stability Analysis of the VDAXs Dynamics 437 204 Measure of the Implied Volatilitys Risk 438 205 Recommended Literature 441 Nonparametric Estimators for the Probability of Default 442 212 Semiparametric Model for Credit Rating 445 213 Credit Ratings with Neural Networks 449 22 Credit Risk Management 451 222 The Bernoulli Model 453 223 The Poisson Model 454 224 The Industrial Models 455 225 One Factor Models 460 226 Copulae and Loss Distributions 462 Technical Appendix 467 A2 Portfolio Strategies 472 Frequently Used Notations 479 Bibliography 481 Index 496 Copyright

### Popular passages

Page 481 - Abberger, K. (1997). Quantile smoothing in financial time series, Statistical Papers 38: 125-148. Anders, U. (1997). Statistische neuronale Netze, Vahlen, Miinchen.