Statistics of Financial Markets : An Introduction

by Franke, Jurgen; Hardle, Wolfgang Karl; Hafner, Christian M.

• ISBN13: 9783540762690
• ISBN10: 3540762698
• Edition: 2nd
• Format: Paperback
• Copyright: 2008-02-01
• Publisher: Springer Verlag

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.

Author Biography

Christian M. Hafner is a professor of econometrics and statistics at the University catholique de Louvain.

Table of Contents

Preface to the Second Edition	p. xi
Preface to the First Edition	p. xiii
Option Pricing	p. 1
Derivatives	p. 3
Recommended Literature	p. 10
Introduction to Option Management	p. 11
Arbitrage Relations	p. 11
Portfolio Insurance	p. 23
Binary One-Period Model	p. 30
Recommended Literature	p. 35
Basic Concepts of Probability Theory	p. 37
Real Valued Random Variables	p. 37
Expectation and Variance	p. 39
Skewness and Kurtosis	p. 41
Random Vectors, Dependence, Correlation	p. 42
Conditional Probabilities and Expectations	p. 43
Recommended Literature	p. 45
Stochastic Processes in Discrete Time	p. 47
Binomial Processes	p. 47
Trinomial Processes	p. 51
General Random Walks	p. 53
Geometric Random Walks	p. 54
Binomial Models with State Dependent Increments	p. 55
Recommended Literature	p. 56
Stochastic Integrals and Differential Equations	p. 57
Wiener Process	p. 57
Stochastic Integration	p. 61
Stochastic Differential Equations	p. 63
The Stock Price as a Stochastic Process	p. 66
Ito's Lemma	p. 69
Recommended Literature	p. 72
Black-Scholes Option Pricing Model	p. 73
Black-Scholes Differential Equation	p. 73
Black-Scholes Formula for European Options	p. 80
Numerical Approximation	p. 84
Simulation	p. 87
Linear Congruential Generator	p. 88
Fibonacci Generators	p. 93
Inversion Method	p. 94
Box-Muller Method	p. 95
Variant of Marsaglia Method	p. 97
Risk Management and Hedging	p. 98
Delta Hedging	p. 101
Gamma and Theta	p. 104
Rho and Vega	p. 107
Volga and Vanna	p. 108
Historical and Implied Volatility	p. 110
Realised Volatility	p. 114
Recommended Literature	p. 115
Binomial Model for European Options	p. 117
Cox-Ross-Rubinstein Approach to Option Pricing	p. 118
Discrete Dividends	p. 122
Dividends as a Percentage of the Stock Price	p. 123
Dividends as a Fixed Amount of Money	p. 124
Recommended Literature	p. 127
American Options	p. 129
Arbitrage Relationship for American Options	p. 129
The Trinomial Model for American Options	p. 136
Recommended Literature	p. 141
Exotic Options	p. 143
Compound Options, Option on Option	p. 143
Chooser Options or "As You Wish" Options	p. 146
Barrier Options	p. 146
Asian Options	p. 148
Lookback Options	p. 150
Cliquet Options	p. 152
Recommended Literature	p. 153
Models for the Interest Rate and Interest Rate Derivatives	p. 155
Bond Value with Known Time Dependent Interest Rate	p. 155
Stochastic Interest Rate Model	p. 156
The Bond Valuation Equation	p. 157
Solving the Zero Bond Valuation Equation	p. 159
Valuation of Bond Options	p. 160
Recommended Literature	p. 161
Statistical Models of Financial Time Series	p. 163
Introduction: Definitions and Concepts	p. 165
Some Definitions	p. 166
Statistical Analysis of German Stock Returns	p. 173
Expectations and Efficient Markets	p. 175
Econometric Models: A Brief Summary	p. 181
Stock Prices: the CAPM	p. 181
Exchange Rate: Theory of the Interest Rate Parity	p. 182
Term Structure: The Cox-Ingersoll-Ross Model	p. 184
Options: The Black-Scholes Model	p. 186
The Market Price of Risk	p. 188
The Random Walk Hypothesis	p. 191
Unit Root Tests	p. 193
Dickey-Fuller Tests	p. 194
The KPSS Test of Stationarity	p. 196
Variance Ratio Tests	p. 198
Recommended Literature	p. 200
ARIMA Time Series Models	p. 203
Moving Average Processes	p. 204
Autoregressive Process	p. 205
ARMA Models	p. 209
Partial Autocorrelation	p. 211
Estimation of Moments	p. 214
Estimation of the Mean Function	p. 215
Estimation of the Covariance Function	p. 216
Estimation of the ACF	p. 217
Portmanteau Statistics	p. 218
Estimation of AR(p) Models	p. 219
Estimation of MA(q) and ARMA(p, q) Models	p. 220
Recommended Literature	p. 225
Time Series with Stochastic Volatility	p. 227
ARCH and GARCH Models	p. 229
ARCH(1): Definition and Properties	p. 231
Estimation of ARCH(1) Models	p. 239
ARCH(q): Definition and Properties	p. 242
Estimation of an ARCH(q) Model	p. 244
Generalised ARCH (GARCH)	p. 245
Estimation of GARCH(p, q) Models	p. 248
Extensions of the GARCH Model	p. 252
Exponential GARCH	p. 252
Threshold ARCH Models	p. 254
Risk and Returns	p. 255
Estimation Results for the DAX Returns	p. 256
Shortfalls of GARCH	p. 258
Recent Challenges to GARCH Models	p. 258
Next-Day Volatility Forecasting for DAX Returns	p. 265
Multivariate GARCH Models	p. 268
The Vec Specification	p. 268
The BEKK Specification	p. 271
The CCC Model	p. 272
The DCC Model	p. 272
An Empirical Illustration	p. 273
Recommended Literature	p. 277
Non-parametric Concepts for Financial Time Series	p. 279
Nonparametric Regression	p. 280
Construction of the Estimator	p. 283
Asymptotic Normality	p. 286
Recommended Literature	p. 301
Selected Financial Applications	p. 303
Pricing Options with Flexible Volatility Estimators	p. 305
Pricing Options with ARCH-Models	p. 305
A Monte Carlo Study	p. 312
Application to the Valuation of DAX Calls	p. 315
Recommended Literature	p. 319
Value at Risk and Backtesting	p. 321
Forecast and VaR Models	p. 323
Backtesting with Expected Shortfall	p. 325
Backtesting in Action	p. 326
Recommended Literature	p. 331
Copulae and Value at Risk	p. 333
Copulae	p. 335
Gaussian Copula	p. 339
Student's t-Copula	p. 341
Archimedean Copulae	p. 342
Multivariate Archimedean Copulae	p. 343
Distributions Constructed with Copulae	p. 345
Monte Carlo Simulation	p. 345
Copula Estimation	p. 349
Maximum Likelihood Estimation	p. 351
IFM - Inference for Margins	p. 351
CML - Canonical Maximum Likelihood	p. 351
Gaussian Copula Estimation	p. 352
t-Copula Estimation	p. 353
Value-at-Risk and Copulae	p. 354
Value-at-Risk	p. 354
VaR Estimation with Copulae	p. 355
Time-Varying Copulae and Backtesting	p. 356
Empirical Results	p. 356
An Exchange Rate Portfolio	p. 356
5-dimensional Exchange Rate Portfolio	p. 361
Recommended Literature	p. 368
Statistics of Extreme Risks	p. 371
Limit Behaviour of Maxima	p. 371
Statistics of Extreme Events	p. 380
The POT (Peaks-Over-Threshold) Method	p. 382
The Hill Estimator	p. 388
Estimators for Risk Measurements	p. 390
Extreme Value Theory for Time Series	p. 392
Recommended Literature	p. 396
Neural Networks	p. 399
From Perceptron to Non-linear Neuron	p. 400
Back Propagation	p. 409
Neural Networks in Non-parametric Regression Analysis	p. 411
Forecasts of Financial Time Series with Neural Networks	p. 418
Quantifying Risk with Neural Networks	p. 422
Recommended Literature	p. 427
Volatility Risk of Option Portfolios	p. 429
Description of the Data	p. 430
Principal Component Analysis of the VDAX's Dynamics	p. 434
Stability Analysis of the VDAX's Dynamics	p. 437
Measure of the Implied Volatility's Risk	p. 438
Recommended Literature	p. 441
Nonparametric Estimators for the Probability of Default	p. 443
Logistic Regression	p. 443
Semi-parametric Model for Credit Rating	p. 445
Credit Ratings with Neural Networks	p. 449
Credit Risk Management	p. 451
Basic Concepts	p. 451
The Bernoulli Model	p. 453
The Poisson Model	p. 454
The Industrial Models	p. 455
One Factor Models	p. 460
Copulae and Loss Distributions	p. 462
Technical Appendix	p. 467
Appendix	p. 467
Integration Theory	p. 467
Portfolio Strategies	p. 472
Frequently Used Notations	p. 479
Bibliography	p. 481
Index	p. 497
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