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, :35 am
End: Jan 5, :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: 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