Statistics of financial markets : an introduction / Jürgen Franke, Wolfgang Härdle, Christian M. Hafner.

Format:

Book

Author/Creator:

Franke, Jürgen, 1952-

Contributor:

Härdle, Wolfgang.

Hafner, Christian.

Series:

Universitext

Language:

English

Subjects (All):

Finance--Statistical methods.

Finance.

Finance--Mathematical models.

Physical Description:

xxii, 501 pages : illustrations, facsimiles ; 24 cm.

Place of Publication:

Berlin : Springer, 2008.

Summary:

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.

Contents:

I Option Pricing 1

1 Derivatives 3

2 Introduction to Option Management 11

2.1 Arbitrage Relations 11

2.2 Portfolio Insurance 23

2.3 Binary One-Period Model 30

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

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

5 Stochastic Integrals and Differential Equations 57

5.1 Wiener Process 57

5.2 Stochastic Integration 61

5.3 Stochastic Differential Equations 63

5.4 The Stock Price as a Stochastic Process 66

5.5 Ito's Lemma 69

6 Black-Scholes Option Pricing Model 73

6.1 Black-Scholes Differential Equation 73

6.2 Black-Scholes 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

7 Binomial Model for European Options 117

7.1 Cox-Ross-Rubinstein 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

8 American Options 129

8.1 Arbitrage Relationship for American Options 129

8.2 The Trinomial Model for American Options 136

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

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

II Statistical Models of Financial Time Series 163

11 Introduction: Definitions and Concepts 165

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

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

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

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

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

16 Value at Risk and Backtesting 321

16.1 Forecast and VaR Models 323

16.2 Backtesting with Expected Shortfall 325

16.3 Backtesting in Action 326

17 Copulae and Value at Risk 333

17.1 Copulae 335

17.1.1 Gaussian Copula 339

17.1.2 Student's 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

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

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

20 Volatility Risk of Option Portfolios 429

20.1 Description of the Data 430

20.2 Principal Component Analysis of the VDAX's Dynamics 434

20.3 Stability Analysis of the VDAX's Dynamics 437

20.4 Measure of the Implied Volatility's Risk 438

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

22.2 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.1 Integration Theory 467

A.2 Portfolio Strategies 472.

Notes:

Includes bibliographical references (pages [481]-495) and index.

ISBN:

9783540762690

3540762698

OCLC:

181090576