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1 | (4) |
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2 The Term Structure of Interest Rates |
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5 | (8) |
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2.1 Notation and Basic Interest Rate Relationships |
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5 | (2) |
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2.2 Data Set and Some Stylized Facts |
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7 | (6) |
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3 Discrete-Time Models of the Term Structure |
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13 | (42) |
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3.1 Arbitrage, the Pricing Kernel and the Term Structure |
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13 | (8) |
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21 | (18) |
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3.2.1 The One-Factor Vasicek Model |
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21 | (4) |
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3.2.2 The Gaussian Mixture Distribution |
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25 | (6) |
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3.2.3 A One-Factor Model with Mixture Innovations |
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31 | (3) |
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3.2.4 Comparison of the One-Factor Models |
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34 | (2) |
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3.2.5 Moments of the One-Factor Models |
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36 | (3) |
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3.3 Affine Multifactor Gaussian Mixture Models |
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39 | (16) |
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3.3.1 Model Structure and Derivation of Arbitrage-Free Yields |
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40 | (4) |
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3.3.2 Canonical Representation |
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44 | (6) |
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50 | (5) |
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4 Continuous-Time Models of the Term Structure |
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55 | (14) |
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4.1 The Martingale Approach to Bond Pricing |
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55 | (7) |
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4.1.1 One-Factor Models of the Short Rate |
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58 | (2) |
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4.1.2 Comments on the Market Price of Risk |
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60 | (1) |
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4.1.3 Multifactor Models of the Short Rate |
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61 | (1) |
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4.1.4 Martingale Modeling |
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62 | (1) |
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4.2 The Exponential-Affine Class |
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62 | (4) |
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62 | (2) |
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64 | (2) |
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4.3 The Heath-Jarrow-Morton Class |
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66 | (3) |
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69 | (14) |
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5.1 Structure of the Model |
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69 | (2) |
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5.2 Filtering, Prediction, Smoothing, and Parameter Estimation |
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71 | (3) |
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5.3 Linear Gaussian Models |
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74 | (9) |
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74 | (1) |
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74 | (5) |
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5.3.3 Maximum Likelihood Estimation |
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79 | (4) |
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6 State Space Models with a Gaussian Mixture |
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83 | (18) |
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83 | (3) |
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86 | (7) |
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6.3 The Approximate Filter AMF(k) |
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93 | (4) |
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97 | (4) |
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7 Simulation Results for the Mixture Model |
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101 | (34) |
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7.1 Sampling from a Unimodal Gaussian Mixture |
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102 | (15) |
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7.1.1 Data Generating Process |
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102 | (2) |
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7.1.2 Filtering and Prediction for Short Time Series |
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104 | (3) |
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7.1.3 Filtering and Prediction for Longer Time Series |
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107 | (5) |
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7.1.4 Estimation of Hyperparameters |
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112 | (5) |
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7.2 Sampling from a Bimodal Gaussian Mixture |
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117 | (9) |
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7.2.1 Data Generating Process |
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117 | (1) |
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7.2.2 Filtering and Prediction for Short Time Series |
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118 | (2) |
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7.2.3 Filtering and Prediction for Longer Time Series |
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120 | (1) |
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7.2.4 Estimation of Hyperparameters |
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121 | (5) |
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7.3 Sampling from a Student t Distribution |
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126 | (5) |
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7.3.1 Data Generating Process |
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126 | (1) |
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7.3.2 Estimation of Hyperparameters |
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127 | (4) |
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7.4 Summary and Discussion of Simulation Results |
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131 | (4) |
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8 Estimation of Term Structure Models in a State Space Framework |
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135 | (18) |
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8.1 Setting up the State Space Model |
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137 | (7) |
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8.1.1 Discrete-Time Models from the AMGM Class |
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137 | (2) |
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8.1.2 Continuous-Time Models |
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139 | (4) |
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8.1.3 General Form of the Measurement Equation |
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143 | (1) |
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8.2 A Survey of the Literature |
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144 | (2) |
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8.3 Estimation Techniques |
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146 | (3) |
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8.4 Model Adequacy and Interpretation of Results |
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149 | (4) |
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9 An Empirical Application |
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153 | (26) |
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9.1 Models and Estimation Approach |
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153 | (7) |
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160 | (14) |
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9.3 Conclusion and Extensions |
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174 | (5) |
10 Summary and Outlook |
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179 | (36) |
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A Properties of the Normal Distribution |
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181 | (4) |
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B Higher Order Stationarity of a VAR(1) |
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185 | (4) |
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C Derivations for the One-Factor Models in Discrete Time |
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189 | (8) |
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C.1 Sharpe Ratios for the One-Factor Models |
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189 | (2) |
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C.2 The Kurtosis Increases in the Variance Ratio |
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191 | (1) |
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C.3 Derivation of Formula (3.53) |
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192 | (1) |
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192 | (1) |
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C.5 Skewness and Kurtosis of Yields |
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193 | (1) |
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C.6 Moments of Differenced Factors |
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194 | (1) |
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C.7 Moments of Differenced Yields |
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195 | (2) |
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197 | (4) |
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E Derivations for the Multifactor Models in Discrete Time |
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201 | (8) |
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E.1 Properties of Factor Innovations |
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201 | (1) |
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202 | (2) |
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E.3 Moments of Differenced Factors |
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204 | (1) |
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E.4 Moments of Differenced Yields |
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205 | (4) |
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209 | (4) |
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G Random Draws from a Gaussian Mixture Distribution |
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213 | (2) |
References |
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215 | (6) |
List of Figures |
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221 | (2) |
List of Tables |
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223 | |