garch

GARCH(1,1) is the popular approach to estimating volatility, but its disadvantage (compared to STDDEV or EWMA) is that you need to fit three parameters. Maximum likelihood estimation, MLE, is an immensely useful statistical approach that can be used to find "best fit" parameters. In this video...

The general form for all three is: σ^2(n) = γ*V(L) + α*u^2(n-1) + σ^2(n-1).

The GARCH(1,1) volatility forecast is largely a function of the first term omega, ω = γ*V(L), which itself is the product of a rate of reversion, γ, and a reversion level, V(L); aka, long-run or unconditional variance David's XLS is here: https://trtl.bz/2yGdnjv

The GARCH(1,1) volatility estimate shares a similarity to EWMA volatility: both assign greater (lesser) weight to recent (distant) returns. But the GARCH(1,1) has an additional feature: it models a long-run (aka, unconditional) variance toward which the volatility series is pulled. David's XLS...

In Hull - Risk Management and Financial Institutions, it is stated, in page 222 (10.10 using GARCH(1,1) to forecase future volatility), that: "the expected value of u(n+t−1)^2 is σ(n+t−1)^2". Is this something obvious? Can anybody explain why this should be the case? Thanks!

So I link this video which explains GARCH(1,1) as a measure to forecast future volatility. Now we know EWMA is a special case of GARCH which sums alpha and beta equal to 1 and therefore ignores any impact on long run variance, implying that variance is not mean reverting.. Again when we...