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# garch

1. ### YouTube T2-26: Maximum likelihood estimation of GARCH parameters

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...
2. ### YouTube T2-25: Comparing volatility approaches: MA versus EWMA versus GARCH

The general form for all three is: σ^2(n) = γ*V(L) + α*u^2(n-1) + σ^2(n-1).
3. ### YouTube T2-24: Forecast volatility with GARCH(1,1)

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
4. ### YouTube T2-23: Volatility: GARCH 1,1

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...
5. ### P1.T2.706. Bivariate normal distribution (Hull)

Learning objectives: Calculate covariance using the EWMA and GARCH(1,1) models. Apply the consistency condition to covariance. Describe the procedure of generating samples from a bivariate normal distribution. Describe properties of correlations between normally distributed variables when using...
6. ### P1.T2.704. Forecasting volatility with GARCH (Hull)

Learning objectives: Explain mean reversion and how it is captured in the GARCH(1,1) model. Explain the weights in the EWMA and GARCH(1,1) models. Explain how GARCH models perform in volatility forecasting. Describe the volatility term structure and the impact of volatility changes. Questions...
7. ### P1.T2.703. EWMA versus GARCH volatility (Hull)

Learning objectives: Apply the exponentially weighted moving average (EWMA) model to estimate volatility. Describe the generalized autoregressive conditional heteroskedasticity (GARCH(p,q)) model for estimating volatility and its properties. Calculate volatility using the GARCH(1,1) model...
8. ### R16.P1.T2. Hull - expected value of u(n+t-1)^2

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!
9. ### GARCH(1,1) vs EWMA for Forecasting Volatility

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...
10. ### P1.T2.502. Covariance updates with EWMA and GARCH(1,1) models

Learning outcomes: Define correlation and covariance, differentiate between correlation and dependence. Calculate covariance using the EWMA and GARCH (1,1) models. Apply the consistency condition to covariance. Questions: 502.1. About the consistency condition, each of the following is true...
11. ### P1.T2.409 Volatility, GARCH(1,1) and EWMA

Concept: These on-line quiz questions are not specifically linked to AIMs, but are instead based on recent sample questions. The difficulty level is a notch, or two notches, easier than bionicturtle.com's typical AIM-by-AIM question such that the intended difficulty level is nearer to an actual...