Introduction (Władysław Milo and Piotr Wdowiński) ............... 7
Part One: Bayesian Econometrics in Finance
1 Bayes Factors for Bivariate GARCH and SV Models (Jacek
Osiewalski, Anna Pajor and Mateusz Pipień) .................. 15
1.1. Introduction ........................................... 15
1.2. Statistical Methodology ................................ 17
1.3. The Competing Bayesian Models .......................... 19
1.3.1 Bivariate GARCH Specifications ................. 19
1.3.1.1 VECH and BEKK Models ................... 20
1.3.1.2 CCC and DCC Models ..................... 23
1.3.2 Bivariate Stochastic Volatility
Specifications .................................. 26
1.3.2.1 Stochastic Discount Factor Model -
SDF .................................... 26
1.3.2.2 Basic Stochastic Volatility Model -
BSV .................................... 27
1.3.2.3 Bivariate Stochastic Volatility
Model - JSV ............................ 27
1.3.2.4 Bivariate Stochastic Volatility
Model - TSV ............................ 28
1.4 The Data and Results of Model Comparison ............... 30
1.5 Concluding Remarks ..................................... 33
References .................................................. 34
2 A Bayesian Analysis of STUR Models (Jacek Kwiatkowski) ...... 37
2.1 Introduction ........................................... 37
2.2 Model and Bayesian Inference ........................... 38
2.3 Model Comparison and Forecasting ....................... 42
2.4 An Empirical Example ................................... 44
2.5 Conclusions ............................................ 47
References .................................................. 47
3 VECM-TSV Models for Two Polish Official Exchange Rates
(Anna Pajor) ................................................ 49
3.1 Introduction ........................................... 49
3.2 Multivariate Stochastic Volatility Process ............. 50
3.3 Model Frameworks ....................................... 53
3.4 Bayesian Inference for the Trivariate VECM-TSV Model ... 54
3.5 Empirical Results ...................................... 56
3.5.1 Posterior Results for the Parameters and
Unobserved Variables ............................ 57
3.5.2 Posterior Inference on Conditional Correlation
Coefficient and Volatilities .................... 59
3.6 Conclusions ............................................ 61
Appendix: MCMC Algorithm for Trivariate TSV Model - The
Full Conditional Distributions .............................. 62
References .................................................. 66
4 Application of Bayesian Inference in Value-at-Risk
Forecasting with the Use of Conditionally Asymmetric and
Fat-Tailed GARCH Models (Mateusz Pipień) .................... 67
4.1 Introduction ........................................... 67
4.2 Competing GARCH Specifications ......................... 68
4.3 VaR from Predictive Densites and Capital Charge for
Market Risk ............................................ 70
4.4 Evaluation of VaR Forecasts ............................ 72
4.5 Empirical Results ...................................... 74
4.6 Concluding Remarks ..................................... 78
References .................................................. 79
5 Bayesian Inference on Discretely Sampled Itô Processes
(Maciej Kostrzewski) ........................................ 81
5.1 Introduction ........................................... 81
5.2 Models ................................................. 82
5.2.1 The Vasiček Model (V) ........................... 82
5.2.2 The Black-Scholes Model (BS) .................... 83
5.2.3 The Cox-Ingersoll-Ross Model (CIR) .............. 83
5.2.4 The Extended Ornstein-Uhlenbeck Model (EOU) ..... 84
5.2.5 The Brennan-Schwartz Model (BSBS) ............... 84
5.3 Estimation of Parameters ............................... 85
5.3.1 The Hermit Series Expansion Method .............. 86
5.3.2 The Method Based on Solving the Fokker-Plack-
Kolmogorov Equations ............................ 87
5.4 The Bayesian Inference ................................. 88
5.5 Modeling and Forecasting the Fed Data .................. 90
5.6 Concluding Remarks ..................................... 95
References .................................................. 95
Part Two: Volatility in Financial Markets
6 Online Testing of Switching Volatility (David Bock) ......... 99
6.1 Introduction ........................................... 99
6.2 Notation and Specifications ........................... 101
6.3 Tests Based on a Moving Sum ........................... 103
6.3.1 I.I.D. Gaussian Process ........................ 103
6.3.2 I.I.D. Non-Gaussian Process .................... 105
6.3.3 GARCH(l.l) Process ............................ 105
6.4 Simulation Study ...................................... 106
6.4.1 Size Properties ................................ 107
6.4.2 Power Properties ............................... 110
6.4.2.1 The Size of the Shift ................. 110
6.4.2.2 The Time of the Shift ................. 112
6.5 Consequences of Having α < 1 .......................... 113
6.6 Monitoring the Volatility of the Hang Seng Index ...... 114
6.7 Discussion and Concluding Remarks ..................... 116
Appendix: Simulated Exact Critical Values of MOSUMQes and
MOSUMQgarch Yielding Sizes 10% ............................. 118
References ................................................. 120
7 Modeling the Realized Volatility with ARFIMA and
Unobserved Component Models: Results from the Polish
Financial Market (Malgorzata Doman) ........................ 123
7.1 Introduction .......................................... 123
7.2 Realized Volatility ................................... 124
7.3 The Data .............................................. 126
7.4 ARFIMA Models ......................................... 128
7.5 Unobserved Components Models .......................... 128
7.6 Empirical Results ..................................... 129
7.7 Conclusions ........................................... 136
References ................................................. 137
8 Forecasting the Conditional Skewness and Kurtosis of
the Polish Financial Returns (Ryszard Doman) ............... 139
8.1 Introduction .......................................... 139
8.2 Hansen's Skewed Student-t Distribution ................ 140
8.3 A GARCH Model Allowing for Time-Varying Conditional
Skewness and Kurtosis ................................. 141
8.4 The Data .............................................. 143
8.5 Estimation Results .................................... 144
8.6 The Dynamics of Volatility and Conditional Skewness
and Kurtosis .......................................... 145
8.7. Results Concerning the Forecasts ...................... 149
8.8 Conclusions ........................................... 153
References ................................................. 153
Part Three: Derivative Instruments
9. Optimal Futures Hedging Decisions in Fractionally
Cointegrated Markets (Piotr Humeńczuk) ..................... 157
9.1 Introduction .......................................... 157
9.2 Futures Hedging ....................................... 158
9.3 Cointegration Relationship ............................ 159
9.4 Hedge Ratio Estimation ................................ 160
9.5 Data Description ...................................... 164
9.6 Empirical Results ..................................... 164
9.7 Concluding Remarks .................................... 169
References ................................................. 169
10 Quasi-Monte Carlo Method in Pricing Barrier Options
(Tomasz Oczadły) ........................................... 171
10.1 Low-Discrepancy Numbers ............................... 171
10.2 Vanilla Barrier Options ............................... 173
10.3 Pricing Options Using Monte Carlo Approach ............ 175
10.4 Numerical Examination ................................. 177
10.5 Conclusions ........................................... 182
References ................................................. 183
11 The Cost-of-Carry Model for the FW20 Futures Contracts:
Threshold Cointegration Framework (Joanna Bruzda) .......... 185
11.1 Introduction .......................................... 185
11.2 Methodology ........................................... 188
11.3 Emprical Results ...................................... 195
11.4 Conclusions ........................................... 205
References ................................................. 205
Part Four: Modeling Stock Prices
12 Modeling and Predicting Japanese Stock Returns Based on
the ARFIMA-FIGARCH (Jun Nagayasu) .......................... 211
12.1 Introduction .......................................... 211
12.2 Stock Returns and Explanatory Variables ............... 212
12.3 Empirical Results ..................................... 216
12.3.1 Results from the Statistical Model ............. 216
12.3.2 Forecasting Performance ....................... 219
12.4 Summary and Discussion ................................ 221
References ................................................. 221
13 Asymmetry in the Adjustment of Main Capital Market
Indices in Poland {Pawel Milobędzki) ....................... 223
13.1 Introduction .......................................... 223
13.2 Indices and Their Characteristics ..................... 224
13.3 Testing for a Unit Root in the Case of Series
Asymmetry ............................................. 228
13.4 Conclusion ............................................ 230
Appendix ................................................... 231
References ................................................. 241
14 Test of the CAPM Model with Time-Varying Covariances for
the Polish Stock Market (Piotr Fiszeder) ................... 243
14.1 Introduction .......................................... 243
14.2 Model Specification .................................. 244
14.3 Test of the CAPM Model for the Polish Stock Market .... 247
14.3.1 The CAPM Model with a Constant Price of
Market Risk .................................... 247
14.3.2 Specification Tests of the CAPM Model with
a Constant Price of Market Risk ................ 250
14.3.3 Specification Tests of the CAPM Model with
Time-Varying Price of Market Risk .............. 254
14.4 Conclusions ........................................... 256
References ................................................. 256
15 Detecting Nonlinear Causality in Financial Markets
(Magdalena Osińska and Witold Orzeszko) .................... 259
15.1 Introduction .......................................... 259
15.2 The Foundations of the Methodology .................... 260
15.3 The Hiemstra-Jones Testing Procedure .................. 262
15.4 Case Study ............................................ 264
15.5 Detecting Nonlinear Causal Relations in Financial
Time Series ........................................... 269
15.6 Conclusions ........................................... 274
References ................................................. 275
16 Analysis of Influence of Russian Stock Market Into
Ukrainian Stock Market (Kostyantyn Stryzhychenko) ......... 277
16.1 Introduction .......................................... 277
16.2 Tasks ................................................. 278
16.3 Basic Definitions of the Cross-Spectral Analysis ...... 279
16.4 Results ............................................... 280
16.5 Conclusions ........................................... 284
References ................................................. 285
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