3. Include the option implied volatility V IX series from the Chicago Board Options Exchange (CBOE) as an explanatory variable in the GARCH equation.

Use MLE to estimate

σ2 t+1

= ω + α (Rt − θσt )2 + βσ2 t

+ γV IX2 t /252, with Rt = σt zt , and zt ∼ N(0, 1)

Set starting values to α = 0.04, β = 0.5, ω = 0.000005, θ = 2, and γ = 0.07.