Handbook of Modeling High–Frequency Data in Finance

Preface xi
<p>Contributors xiii</p>
<p>Part One Analysis of Empirical Data 1</p>
<p>1 Estimation of NIG and VG Models for High Frequency Financial Data 3<br /> Jos&eacute; E. Figueroa–L&oacute;pez, Steven R. Lancette, Kiseop Lee, and Yanhui Mi</p>
<p>1.1 Introduction, 3</p>
<p>1.2 The Statistical Models, 6</p>
<p>1.3 Parametric Estimation Methods, 9</p>
<p>1.4 Finite–Sample Performance via Simulations, 14</p>
<p>1.5 Empirical Results, 18</p>
<p>1.6 Conclusion, 22</p>
<p>References, 24</p>
<p>2 A Study of Persistence of Price Movement using High Frequency Financial Data 27<br /> Dragos Bozdog, Ionut&cedil; Florescu, Khaldoun Khashanah, and Jim Wang</p>
<p>2.1 Introduction, 27</p>
<p>2.2 Methodology, 29</p>
<p>2.3 Results, 35</p>
<p>2.4 Rare Events Distribution, 41</p>
<p>2.5 Conclusions, 44</p>
<p>References, 45</p>
<p>3 Using Boosting for Financial Analysis and Trading 47<br /> Germ&aacute;n Creamer</p>
<p>3.1 Introduction, 47</p>
<p>3.2 Methods, 48</p>
<p>3.3 Performance Evaluation, 53</p>
<p>3.4 Earnings Prediction and Algorithmic Trading, 60</p>
<p>3.5 Final Comments and Conclusions, 66</p>
<p>References, 69</p>
<p>4 Impact of Correlation Fluctuations on Securitized structures 75<br /> Eric Hillebrand, Ambar N. Sengupta, and Junyue Xu</p>
<p>4.1 Introduction, 75</p>
<p>4.2 Description of the Products and Models, 77</p>
<p>4.3 Impact of Dynamics of Default Correlation on</p>
<p>Low–Frequency Tranches, 79</p>
<p>4.4 Impact of Dynamics of Default Correlation on High–Frequency Tranches, 87</p>
<p>4.5 Conclusion, 92</p>
<p>References, 94</p>
<p>5 Construction of Volatility Indices Using A Multinomial Tree&nbsp;Approximation Method 97<br /> Dragos Bozdog, Ionut&cedil; Florescu, Khaldoun Khashanah, and Hongwei Qiu</p>
<p>5.1 Introduction, 97</p>
<p>5.2 New Methodology, 99</p>
<p>5.3 Results and Discussions, 101</p>
<p>5.4 Summary and Conclusion, 110</p>
<p>References, 115</p>
<p>Part Two Long Range Dependence Models 117</p>
<p>6 Long Correlations Applied to the Study of Memory Effects in High Frequency (TICK) Data, the Dow Jones Index, and International Indices 119<br /> Ernest Barany and Maria Pia Beccar Varela</p>
<p>6.1 Introduction, 119</p>
<p>6.2 Methods Used for Data Analysis, 122</p>
<p>6.3 Data, 128</p>
<p>6.4 Results and Discussions, 132</p>
<p>6.5 Conclusion, 150</p>
<p>References, 160</p>
<p>7 Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales 163<br /> Alec N. Kercheval and Yang Liu</p>
<p>7.1 Introduction, 163</p>
<p>7.2 The Skewed t Distributions, 165</p>
<p>7.3 Risk Forecasts on a Fixed Timescale, 176</p>
<p>7.4 Multiple Timescale Forecasts, 185</p>
<p>7.5 Backtesting, 188</p>
<p>7.6 Further Analysis: Long–Term GARCH and Comparisons using Simulated Data, 203</p>
<p>7.7 Conclusion, 216</p>
<p>References, 217</p>
<p>8 Parameter Estimation and Calibration for Long–Memory Stochastic Volatility Models 219<br /> Alexandra Chronopoulou</p>
<p>8.1 Introduction, 219</p>
<p>8.2 Statistical Inference Under the LMSV Model, 222</p>
<p>8.3 Simulation Results, 227</p>
<p>8.4 Application to the S&amp;P Index, 228</p>
<p>8.5 Conclusion, 229</p>
<p>References, 230</p>
<p>Part Three Analytical Results 233</p>
<p>9 A Market Microstructure Model of Ultra High Frequency Trading 235<br /> Carlos A. Ulibarri and Peter C. Anselmo</p>
<p>9.1 Introduction, 235</p>
<p>9.2 Microstructural Model, 237</p>
<p>9.3 Static Comparisons, 239</p>
<p>9.4 Questions for Future Research, 241</p>
<p>References, 242</p>
<p>10 Multivariate Volatility Estimation with High Frequency Data Using Fourier Method 243<br /> Maria Elvira Mancino and Simona Sanfelici</p>
<p>10.1 Introduction, 243</p>
<p>10.2 Fourier Estimator of Multivariate Spot Volatility, 246</p>
<p>10.3 Fourier Estimator of Integrated Volatility in the Presence of Microstructure Noise, 252</p>
<p>10.4 Fourier Estimator of Integrated Covariance in the Presence of Microstructure Noise, 263</p>
<p>10.5 Forecasting Properties of Fourier Estimator, 272</p>
<p>10.6 Application: Asset Allocation, 286</p>
<p>References, 290</p>
<p>11 The "Retirement" Problem 295<br /> Cristian Pasarica</p>
<p>11.1 Introduction, 295</p>
<p>11.2 The Market Model, 296</p>
<p>11.3 Portfolio and Wealth Processes, 297</p>
<p>11.4 Utility Function, 299</p>
<p>11.5 The Optimization Problem in the Case (_{t ,T}]&nbsp; 0, 299</p>
<p>11.6 Duality Approach, 300</p>
<p>11.7 Infinite Horizon Case, 305</p>
<p>References, 324</p>
<p>12 Stochastic Differential Equations and Levy Models with Applications to High Frequency Data 327<br /> Ernest Barany and Maria Pia Beccar Varela</p>
<p>12.1 Solutions to Stochastic Differential Equations, 327</p>
<p>12.2 Stable Distributions, 334</p>
<p>12.3 The Levy Flight Models, 336</p>
<p>12.4 Numerical Simulations and Levy Models: Applications to Models Arising in Financial Indices and High Frequency Data, 340</p>
<p>12.5 Discussion and Conclusions, 345</p>
<p>References, 346</p>
<p>13 Solutions to Integro–Differential Parabolic Problem Arising on Financial Mathematics 347<br /> Maria C. Mariani, Marc Salas, and Indranil SenGupta</p>
<p>13.1 Introduction, 347</p>
<p>13.2 Method of Upper and Lower Solutions, 351</p>
<p>13.3 Another Iterative Method, 364</p>
<p>13.4 Integro–Differential Equations in a L&eacute;vy Market, 375</p>
<p>References, 380</p>
<p>14 Existence of Solutions for Financial Models with Transaction Costs and Stochastic Volatility 383<br /> Maria C. Mariani, Emmanuel K. Ncheuguim, and Indranil SenGupta</p>
<p>14.1 Model with Transaction Costs, 383</p>
<p>14.2 Review of Functional Analysis, 386</p>
<p>14.3 Solution of the Problem (14.2) and (14.3) in Sobolev Spaces, 391</p>
<p>14.4 Model with Transaction Costs and Stochastic Volatility, 400</p>
<p>14.5 The Analysis of the Resulting Partial Differential Equation, 408</p>
<p>References, 418</p>
<p>Index 421</p>