Statistics of Financial Markets: An Introduction

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Springer Science & Business Media, Jan 1, 2004 - Business & Economics - 424 pages
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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. From the reviews of the first edition: "The book starts ... with five eye-catching pages that reproduce a student’s handwritten notes for the examination that is based on this book. ... The material is well presented with a good balance between theoretical and applied aspects. ... The book is an excellent demonstration of the power of stochastics ... . The author’s goal is well achieved: this book can satisfy the needs of different groups of readers ... . " (Jordan Stoyanov, Journal of the Royal Statistical Society, Vol. 168 (4), 2005)
  

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Contents

1 Derivatives
5
11 Recommended Literature
12
2 Introduction to Option Management
13
22 Portfolio Insurance
25
23 Recommended Literature
33
3 Basic Concepts of Probability Theory
35
32 Expectation and Variance
38
33 Skewness and Kurtosis
39
1152 Estimation of the Covariance Function
190
1153 Estimation of the ACF
191
116 Portmanteau Statistics
192
117 Estimation of ARp Models
193
118 Estimation of MAq and ARMApq Models
194
119 Recommended Literature
199
12 Time Series with Stochastic Volatility
201
121 ARCH and GARCH Models
203

34 Random Vectors Dependence Correlation
40
35 Conditional Probabilities and Expectations
41
36 Recommended Literature
44
4 Stochastic Processes in Discrete Time
45
42 Trinomial Processes
49
43 General Random Walks
51
44 Geometric Random Walks
52
45 Binomial Models with State Dependent Increments
53
5 Stochastic Integrals and Differential Equations
55
52 Stochastic Integration
58
53 Stochastic Differential Equations
61
54 The Stock Price as a Stochastic Process
63
55 Itos Lemma
64
56 Recommended Literature
67
6 BlackScholes Option Pricing Model
69
62 BlackScholes Formulae for European Options
76
63 Risk Management and Hedging
82
631 Delta Hedging
84
632 Gamma and Theta
87
633 Rho and Vega
90
634 Historical and Implied Volatility
91
64 Recommended Literature
95
7 Binomial Model for European Options
97
71 CoxRossRubinstein Approach to Option Pricing
98
72 Discrete Dividends
103
722 Dividends as a Fixed Money Amount
104
73 Recommended Literature
107
8 American Options
109
82 The Trinomial Model for American Options
117
83 Recommended Literature
121
9 Exotic Options and Interest Rate Derivatives
123
912 Chooser Options or As you wish Options
124
913 Barrier Options
125
914 Asian Options
126
915 Lookback Options
128
92 Models for the Interest Rate and Interest Rate Derivatives
129
921 Bond Value with Known Time Dependent Interest Rate
130
923 The Bonds Value Equation
131
924 Solving the Zero Bonds Value Equation
133
Statistical Model of Financial Time Series
137
Definitions and Concepts
139
101 Certain Definitions
140
102 Statistical Analysis of German Stock Returns
147
103 Expectations and Efficient Markets
149
A Brief Summary
155
Theory of the Interest Rate Parity
156
The CoxlngersollRoss Model
158
The BlackScholes Model
160
1045 The Market Price of Risk
162
105 The Random Walk Hypothesis
165
106 Unit Root Tests
168
1062 The KPSS Test of Stationarity
170
1063 Variance Ratio Tests
172
11 ARIMA Time Series Models
177
111 Moving Average Processes
178
112 Autoregressive Process
179
113 ARMA Models
183
114 Partial Autocorrelation
185
115 Estimation Moments
188
1151 Estimation of the Mean Function
189
Definition and Properties
206
1212 Estimation of ARCH1 Models
213
Definition and Properties
217
1214 Estimation of an ARCHq Model
219
1215 Generalized ARCH GARCH
220
1216 Estimation of GARCHpq Models
223
122 Extensions of the GARCH Model
226
1221 Exponential GARCH
227
1222 Threshold ARCH Models
229
1223 Risk and Returns
230
1224 Estimation Results for the DAX Returns
231
123 Multivariate GARCH models
232
1231 The Vec Specification
233
1232 Die BEKK Spezifikation
236
1233 The CCC model
237
13 Nonparametric Concepts for Financial Time Series
245
131 Nonparametric Regression
246
132 Construction of the Estimator
249
133 Asymptotic Normality
252
134 Recommended Literature
267
Selected Financial Applications
269
14 Valuing Options with Flexible Volatility Estimators
271
141 Valuing Options with ARCHModels
272
142 A Monte Carlo Study
278
143 Application to the Valuation of DAX Calls
283
15 Value at Risk and Backtesting
289
151 Forecast and VaR Models
290
152 Backtesting with Expected Shortfall
293
153 Backtesting in Action
295
16 Copulas and ValueatRisk
303
161 Copulas
304
162 The Calculation of VaR and Copulas
307
163 Recommended Literature
311
17 Statistics of Extreme Risks
313
172 Statistics of Extreme Events
323
1721 The POT peaksoverthreshold Method
324
1722 The Hill Estimator
330
173 Estimators for Risk Measurements
332
174 Extreme Value Theory for Time Series
335
18 Neural Networks
341
181 From Perceptron to Nonlinear Neuron
343
182 Back Propagation
351
183 Neural Networks in Nonparametric Regression Analysis
354
184 Forecasts of Financial Time Series with Neural Networks
360
185 Quantifying Risk with Neural Networks
364
186 Recommended Literature
369
19 Volatility Risk of Option Portfolios
371
191 Description of the Data
372
192 Principal Component Analysis of the VDAXs Dynamics
376
193 Stability Analysis of the VDAXs Dynamics
379
194 Measure of the Implied Volatilitys Risk
380
195 Recommended Literature
383
20 Nonparametric Estimators for the Probability of Default
385
202 Semiparametric Model for Credit Rating
387
203 Credit Ratings with Neural Networks
391
A Technical Appendix
395
A2 Portfolio Strategies
400
Bibliography
407
Index
423
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Page xvii - A T transpose of matrix A X ~ D the random variable X has distribution D E[X] expected value of random variable X Var(X) variance of random variable X Cov(X, Y) covariance

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