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

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

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.

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?

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).

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

Data GE Prices- 2 hourly log-returns Start: Jan 21, 2006 9:35 am End: Jan 28, 2008 3:35 pm n: 2000 Iterations: 1000 Burn-in: 100

Results: φ

Results: μ = .0034

Results: V = 1.1950

Results

Results: Residual Plot

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