Stochastic Volatility Deep Dive
Unlike GARCH where σₜ is deterministic given the past, SV models treat log-volatility hₜ as a latent AR(1) process with its own noise — making the model fundamentally unobserved.
Uncond. Vol (ann.)
1359.8%
Vol half-life
22.8 d
Persistence φ
0.97
Leverage ρ
Strong ✓
Returns rₜ with Instantaneous Volatility σₜ = exp(hₜ/2)
Latent Log-Volatility Path hₜ (AR process)
ACF Comparison — hₜ (true) vs log|rₜ| (proxy)
μ (mean log-vol)-0.5
φ (persistence)0.970
σ_h (vol-of-vol)0.15
ρ (leverage)-0.40
Observations1000
Seed3
σ_h controls the variability of volatility itself. High φ (near 1) gives long-memory clustering. Negative ρ produces the leverage effect: falling prices → higher volatility. Unlike GARCH, hₜ is never directly observed — estimation requires MCMC or particle filters.