Statistics of Financial Markets: An Introduction

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

 

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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

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

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