Stochastic Volatility Model: High Frequency Data

1. Stochastic Volatility Model: High Frequency Data Haolan Cai Econ201FS Final Presentation

2. Previously • Problems with model specification • AR(1) not the best model for long term persistence • Inadequate error specification • Problems with intra-day volatility • Need to normalize by local realized volatility • No rubric for model comparison • GARCH(1,1) • Only in-sample model fitting

3. Model

4. Data GE Prices Normalized 2 hourly log-returns Start: Jan 1, 2006 9:35 am End: Jan 5, 2008 3:35 pm n: 2000 Iterations: 5000 Burn-in: 500

5. Data

6. Initial c = .95 C = .2 a = 1000 Previously, error term was not sufficient. Allowed error term’s tail size to vary.

7. Results: φ = .95

8. Results: μ = .4561

9. Results: rs = .3342

10. Results

11. In-Sample Fit • Regress real absolute returns on returns as predicted by SV model • Coefficient of Determination is .1039 • R-squared is in the range as expected by Andersen and Bollerslev (1998)

12. Out-of-Sample Prediction SV Model • Built into the Gibbs Sampler • Predicts next 60 two-hourly normalized returns for each iteration GARCH model • GARCH(1,1) using built-in GARCH toolbox in matlab • Predicts next 60 steps of the process, predicts returns and std. dev. of returns Comparison • For each model, plotted volatility as predicted by the model against the absolute returns from data

13. Results: SV model

14. Results: GARCH model

15. Comparison R^2 for SV: .0074 R^2 for GARCH: .0031

16. Summary • R^2 for in-sample SV model fit (on high frequency data) is in the expected range • Fit of predicted values also in the expected range, marginally better than R^2 for GARCH

17. Further Work How to further improve model? • AR structure is not perfect • Try higher order AR process • Try sum of AR(1)s