1. Stochastic Volatility Models: High Frequency Data & Large Volatilities
Haolan Cai

2. Previously Introduction to Stochastic Volatility Models
Was suggested to use higher than daily frequency returns
Stuck phi (persistence) parameter in autoregressive process
Underpredicted volatility by a factor of 2

3. Theoretical vs. Practical
Historically:
choose large initial values for φ (close to 1)
use mixture of 7 normals to approximate the log chi-squared distribution.

4. Original Initials Parameters of approximation of log chi-squared
c = .95 C = .2 a = 1000
Theoretically makes sense. Why does it not work in practice?

5. Issues
Trade off between high phi (persistence) and accuracy of error term
Large volatility
Originally we restrict the phi parameter to high values and impose the original variance structure with high degree of freedom (a = 1000, has more influence).

6. Quick Fix
Increase the left tail size of the approximation for the error term
Multiply ω1, ω2, & ω3 each by 9
Decrease the Degrees of Freedom for variance structure in AR process
a = 10
Change parameterization for Phi
c = 0 C = .4

7. Data GE Prices- 2 hourly log-returns Start: Jan 21, 2006 9:35 am
End: Jan 28, :35 pm
n: 2000
Iterations: 1000
Burn-in: 100

8. Results: φ

9. Results: μ = .0034

10. Results: V =

11. Results

12. Results: Residual Plot

13. Further Analysis More exploration Deeper theoretical problem
What are the best initial values?
What is the optimal sampling frequency?
How does this model behave with higher volatility data (i.e. last 6 months)?
Deeper theoretical problem
Inadequate error term approximation
Interpretation of phi