garch

Learning Objectives: Apply the GARCH (1,1) model to estimate volatility. Explain and apply approaches to estimate long horizon volatility/VaR and describe the process of mean reversion according to a GARCH (1,1) model. Evaluate implied volatility as a predictor of future volatility and its...

Learning Objectives: Explain how asset return distributions tend to deviate from the normal distribution. Explain reasons for fat tails in a return distribution and describe their implications. Distinguish between conditional and unconditional distributions and describe regime switching. Compare...

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...

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...

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...

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...

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...

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...

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...