Part I Financial Markets and Financial Time Series |
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3 | (4) |
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1.1 Financial markets and financial time series |
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3 | (1) |
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1.2 Econometric modeling of asset returns |
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4 | (1) |
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1.3 Applications of non-Gaussian econometrics |
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5 | (1) |
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1.4 Option pricing with non-Gaussian distributions |
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5 | (2) |
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2 Statistical Properties of Financial Market Data |
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7 | (26) |
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2.1 Definitions of returns |
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7 | (3) |
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8 | (1) |
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8 | (1) |
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9 | (1) |
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2.2 Distribution of returns |
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10 | (11) |
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2.2.1 Moments of a random variable |
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10 | (4) |
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14 | (2) |
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2.2.3 Testing for normality |
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16 | (5) |
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21 | (5) |
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2.3.1 Serial correlation in returns |
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22 | (1) |
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2.3.2 Serial correlation in volatility |
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23 | (2) |
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2.3.3 Volatility asymmetry |
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25 | (1) |
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2.3.4 Time-varying higher moments |
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26 | (1) |
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2.4 Linear dependence across returns |
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26 | (5) |
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2.4.1 Pearson's correlation coefficient |
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27 | (1) |
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2.4.2 Test for equality of two correlation coefficients |
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28 | (2) |
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2.4.3 Test for equality of two correlation matrices |
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30 | (1) |
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2.5 Multivariate higher moments |
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31 | (2) |
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2.5.1 Multivariate co-skewness and co-kurtosis |
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31 | (1) |
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2.5.2 Computing moments of portfolio returns |
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32 | (1) |
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3 Functioning of Financial Markets and Theoretical Models for Returns |
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33 | (46) |
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3.1 Functioning of financial markets |
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34 | (5) |
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3.1.1 Organization of financial markets |
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34 | (3) |
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37 | (2) |
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3.1.3 Components of the bid-ask spread |
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39 | (1) |
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3.2 Mandelbrot and the stable distribution |
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39 | (5) |
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40 | (1) |
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3.2.2 Stable distribution |
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41 | (3) |
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3.3 Clark's subordination model |
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44 | (4) |
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3.3.1 The idea of the model |
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44 | (2) |
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3.3.2 The density of returns under subordination |
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46 | (2) |
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3.4 A bivariate mixture-of-distribution model for return and volume |
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48 | (14) |
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3.4.1 A microstructure model for information arrivals |
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48 | (5) |
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3.4.2 Implications of the mixture of distributions hypothesis |
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53 | (4) |
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3.4.3 Testing the mixture of distribution hypothesis |
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57 | (4) |
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61 | (1) |
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3.5 A model of prices and quotes in a quote-driven market |
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62 | (17) |
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3.5.1 A model based on the trade flow |
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63 | (3) |
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3.5.2 Estimating the parameters |
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66 | (2) |
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68 | (5) |
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3.5.4 Extension to the liquidation of a large portfolio |
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73 | (6) |
Part II Econometric Modeling of Asset Returns |
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79 | (64) |
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4.1 Volatility at lower frequencies |
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79 | (2) |
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81 | (3) |
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81 | (1) |
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4.2.2 Kurtosis of an ARCH model |
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82 | (1) |
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4.2.3 Testing for ARCH effects |
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82 | (1) |
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83 | (1) |
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84 | (1) |
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84 | (10) |
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88 | (1) |
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4.3.2 Integrated GARCH model |
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89 | (1) |
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89 | (3) |
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4.3.4 Testing for GARCH effects |
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92 | (1) |
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4.3.5 Software to estimate ARCH and GARCH models |
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92 | (1) |
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93 | (1) |
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4.4 Asymmetric GARCH models |
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94 | (5) |
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94 | (1) |
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95 | (1) |
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95 | (1) |
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95 | (1) |
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96 | (1) |
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4.4.6 Partially non-parametric estimation |
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96 | (1) |
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4.4.7 Testing for asymmetric effects |
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97 | (2) |
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99 | (1) |
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4.5 GARCH model with jumps |
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99 | (9) |
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4.5.1 A model with time-varying jump intensity |
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101 | (4) |
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4.5.2 An empirical illustration |
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105 | (3) |
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4.6 Aggregation of GARCH processes |
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108 | (7) |
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4.6.1 Temporal aggregation |
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109 | (4) |
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4.6.2 Cross-sectional aggregation |
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113 | (1) |
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4.6.3 Estimation of the weak GARCH process |
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114 | (1) |
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4.7 Stochastic volatility |
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115 | (3) |
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4.7.1 From GARCH models to stochastic volatility models |
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115 | (2) |
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4.7.2 Estimation of the discrete time SV model |
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117 | (1) |
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118 | (25) |
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4.8.1 The difficulty to disentangle jumps |
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119 | (4) |
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4.8.2 Quadratic variation |
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123 | (1) |
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124 | (2) |
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126 | (2) |
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4.8.5 Estimation over finite time intervals |
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128 | (7) |
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4.8.6 Realized covariance |
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135 | (6) |
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4.8.7 Further related results |
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141 | (2) |
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5 Modeling Higher Moments |
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143 | (52) |
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144 | (8) |
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5.1.1 Higher moments of a GARCH process |
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145 | (3) |
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5.1.2 Quasi Maximum Likelihood Estimation |
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148 | (3) |
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5.1.3 The existence of distribution with given moments |
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151 | (1) |
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5.2 Distributions with higher moments |
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152 | (25) |
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5.2.1 Semi-parametric approach |
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153 | (2) |
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5.2.2 Series expansion about the normal distribution |
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155 | (4) |
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5.2.3 Skewed Student t distribution |
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159 | (7) |
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5.2.4 Generating asymmetric distributions |
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166 | (3) |
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5.2.5 Pearson IV distribution |
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169 | (3) |
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5.2.6 Entropy distribution |
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172 | (5) |
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5.3 Specification tests and inference |
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177 | (5) |
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5.3.1 Moment specification tests |
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177 | (2) |
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5.3.2 Adequacy tests based on density forecasts |
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179 | (1) |
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5.3.3 Adequacy tests based on interval forecasts |
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180 | (2) |
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182 | (6) |
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5.5 Modeling conditional higher moments |
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188 | (7) |
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5.5.1 Tests for autoregressive conditional higher moments |
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189 | (1) |
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5.5.2 Modeling higher moments directly |
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189 | (2) |
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5.5.3 Modeling the parameters of the distribution |
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191 | (4) |
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195 | (70) |
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6.1 Multivariate GARCH models |
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197 | (26) |
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6.1.1 Vectorial and diagonal GARCH models |
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198 | (2) |
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6.1.2 Dealing with large-dimensional systems |
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200 | (6) |
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6.1.3 Modeling conditional correlation |
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206 | (4) |
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210 | (2) |
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6.1.5 Specification tests |
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212 | (2) |
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6.1.6 Test of constant conditional correlation matrix |
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214 | (3) |
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217 | (6) |
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6.2 Modeling the multivariate distribution |
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223 | (17) |
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6.2.1 Standard multivariate distributions |
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225 | (5) |
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6.2.2 Skewed elliptical distribution |
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230 | (3) |
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6.2.3 Skewed Student t distribution |
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233 | (3) |
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236 | (3) |
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239 | (1) |
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240 | (1) |
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240 | (25) |
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6.3.1 Definitions and properties |
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241 | (1) |
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6.3.2 Measures of concordance |
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242 | (2) |
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6.3.3 Non-parametric copulas |
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244 | (1) |
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6.3.4 Review of some copula families |
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245 | (9) |
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254 | (4) |
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258 | (1) |
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6.3.7 Modeling the conditional dependency parameter |
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259 | (2) |
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261 | (4) |
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265 | (50) |
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7.1 Univariate tail estimation |
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266 | (34) |
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7.1.1 Distribution of extremes |
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266 | (10) |
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276 | (15) |
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7.1.3 The case of weakly dependent data |
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291 | (5) |
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7.1.4 Estimation of high quantiles |
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296 | (4) |
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7.2 Multivariate dependence |
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300 | (15) |
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7.2.1 Characterizing tail dependency |
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303 | (4) |
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7.2.2 Estimation and statistical inference on X and X |
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307 | (1) |
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7.2.3 Modeling dependency |
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308 | (1) |
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309 | (2) |
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7.2.5 Further investigations |
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311 | (4) |
Part III Applications of Non-Gaussian Econometrics |
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8 Risk Management and VaR |
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315 | (34) |
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8.1 Definitions and measures |
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316 | (5) |
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316 | (4) |
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8.1.2 Models for portfolio returns |
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320 | (1) |
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8.2 Historical simulation |
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321 | (1) |
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8.3 Semi-parametric approaches |
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322 | (8) |
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8.3.1 Extreme Value Theory (EVT) |
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324 | (4) |
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8.3.2 Quantile regression technique |
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328 | (2) |
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8.4 Parametric approaches |
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330 | (11) |
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8.4.1 RiskMetrics – J.P. Morgan |
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331 | (3) |
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8.4.2 The portfolio-level approach |
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334 | (3) |
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8.4.3 The asset-level approach |
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337 | (4) |
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341 | (1) |
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8.5.1 The "delta-only" method |
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341 | (1) |
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8.5.2 The "delta-gamma" method |
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341 | (1) |
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8.6 Comparison of VaR models |
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342 | (7) |
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8.6.1 Evaluation of VaR models |
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343 | (1) |
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8.6.2 Comparison of methods |
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343 | (1) |
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8.6.3 10-day VaR and scaling |
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344 | (1) |
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345 | (4) |
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349 | (16) |
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9.1 Portfolio allocation under non-normality |
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349 | (10) |
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9.1.1 Direct maximization of expected utility |
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350 | (3) |
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9.1.2 An approximate solution based on moments |
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353 | (6) |
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9.2 Portfolio allocation under downside risk |
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359 | (6) |
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360 | (1) |
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9.2.2 Downside risk as an additional constraint |
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360 | (1) |
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9.2.3 Downside risk as an optimization criterion |
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361 | (4) |
Part IV Option Pricing with Non-Gaussian Returns |
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10 Fundamentals of Option Pricing |
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365 | (18) |
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366 | (3) |
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10.2 The no-arbitrage approach to option pricing |
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369 | (8) |
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10.2.1 Choice of a stock price process |
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369 | (2) |
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10.2.2 The fundamental partial differential equation |
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371 | (2) |
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10.2.3 Solving the fundamental PDE |
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373 | (2) |
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10.2.4 The Black-Scholes-Merton formula |
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375 | (2) |
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10.3 Martingale measure and BSM formula |
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377 | (6) |
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10.3.1 Self-financing strategies and portfolio construction |
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377 | (1) |
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10.3.2 Change of numeraire |
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378 | (1) |
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10.3.3 Change of Brownian motion |
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378 | (1) |
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10.3.4 Evolution of St under Q |
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379 | (1) |
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10.3.5 The expected pay-off as a martingale |
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379 | (1) |
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10.3.6 The trading strategies |
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380 | (1) |
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10.3.7 Equivalent martingale measure |
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381 | (2) |
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11 Non-structural Option Pricing |
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383 | (34) |
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11.1 Difficulties with the standard BSM model |
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384 | (1) |
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11.2 Direct estimation of the risk-neutral density |
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385 | (4) |
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11.2.1 Expression for the RND |
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385 | (2) |
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11.2.2 Estimating the parameters of the RND |
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387 | (2) |
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389 | (6) |
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11.3.1 Mixture of log-normal distributions |
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389 | (5) |
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11.3.2 Mixtures of hypergeometric functions |
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394 | (1) |
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11.3.3 Generalized beta distribution |
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395 | (1) |
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11.4 Semi-parametric methods |
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395 | (7) |
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11.4.1 Edgeworth expansions |
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395 | (4) |
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11.4.2 Hermite polynomials |
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399 | (3) |
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11.5 Non-parametric methods |
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402 | (7) |
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402 | (4) |
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11.5.2 Tree-based methods |
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406 | (1) |
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11.5.3 Maximum entropy principle |
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407 | (1) |
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408 | (1) |
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11.6 Comparison of various methods |
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409 | (5) |
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11.7 Relationship with real probability |
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414 | (3) |
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11.7.1 The link between RNDs and objective densities |
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414 | (2) |
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11.7.2 Empirical findings |
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416 | (1) |
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12 Structural Option Pricing |
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417 | (34) |
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12.1 Stochastic volatility model |
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417 | (8) |
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12.1.1 The square root process |
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418 | (1) |
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12.1.2 Solving the PDE based on characteristic function |
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419 | (3) |
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12.1.3 A new partial differential equation |
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422 | (3) |
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12.2 Option pricing with stochastic volatility |
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425 | (7) |
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12.2.1 Hull and White (1987, 1988) |
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425 | (1) |
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426 | (2) |
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12.2.3 Characteristic function of the SV model |
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428 | (1) |
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429 | (3) |
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432 | (9) |
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12.3.1 Stochastic process with jumps |
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432 | (2) |
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12.3.2 Diffusion with double exponential jumps |
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434 | (2) |
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12.3.3 Combining stochastic volatility with jumps |
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436 | (4) |
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12.3.4 Jumpy affine models |
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440 | (1) |
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12.4 Models with even wilder jumps: Levy option pricing |
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441 | (10) |
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12.4.1 Commonly used Levy processes |
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443 | (1) |
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12.4.2 Choice of the time-changing process |
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444 | (1) |
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445 | (1) |
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12.4.4 Pricing options with risk-neutral characteristic function |
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446 | (1) |
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447 | (4) |
Part V Appendices on Option Pricing Mathematics |
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13 Brownian Motion and Stochastic Calculus |
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451 | (20) |
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13.1 Law of large numbers and the central limit theorem |
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451 | (2) |
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453 | (1) |
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13.3 Construction of the Brownian motion |
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453 | (3) |
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13.4 Properties of the Brownian motion |
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456 | (1) |
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13.5 Stochastic integration |
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457 | (2) |
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13.6 Stochastic differential equations |
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459 | (1) |
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460 | (2) |
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13.8 Multivariate extension of Ito's lemma |
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462 | (1) |
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13.9 Transition probabilities and partial differential equations |
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463 | (1) |
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13.10 Kolmogorov backward and forward equations |
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464 | (2) |
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13.11 PDE associated with diffusions |
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466 | (2) |
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13.12 Feynman-Kac formula |
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468 | (3) |
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14 Martingale and Changing Measure |
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471 | (6) |
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471 | (1) |
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14.2 Changing probability of a normal distribution |
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472 | (1) |
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14.3 Radon-Nikodym derivative |
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473 | (1) |
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474 | (1) |
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14.5 Martingale representation theorem |
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475 | (2) |
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15 Characteristic Functions and Fourier Transforms |
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477 | (10) |
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15.1 Characteristic functions |
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477 | (6) |
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478 | (1) |
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15.1.2 Moments and the characteristic function |
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478 | (1) |
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15.1.3 Convolution theorem |
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479 | (1) |
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480 | (1) |
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480 | (3) |
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15.2 Fourier transform and characteristic function |
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483 | (4) |
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487 | (14) |
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16.1 Counting and marked point process |
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487 | (2) |
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489 | (5) |
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16.2.1 Construction of the Poisson distribution |
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489 | (2) |
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16.2.2 Properties of the Poisson distribution |
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491 | (1) |
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16.2.3 Moments of pure Poisson process |
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492 | (1) |
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16.2.4 Compound Poisson process |
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493 | (1) |
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16.3 The exponential distribution |
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494 | (3) |
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16.3.1 Definition and properties |
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494 | (1) |
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16.3.2 Moments of the exponential variable |
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495 | (1) |
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16.3.3 Hazard and survivor functions |
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496 | (1) |
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16.4 Duration between Poisson jumps |
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497 | (1) |
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16.5 Compensated Poisson processes |
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498 | (3) |
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501 | (6) |
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17.1 Construction of the Levy process |
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501 | (4) |
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17.2 Properties of Levy processes |
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505 | (2) |
References |
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507 | (28) |
Index |
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535 | |