Master Volatility with ARCH & GARCH Models
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TL;DW Executive Summary
Volatility is an unobservable measure of variability in the return space
We can proxy for volatility in a backward looking sense (historic or realized volatility) or in a forward looking sense (implied volatility)
There are many stylized facts about volatility including the leverage effect, volatility clustering, excess kurtosis (fat tails, leptokurtic return distributions)
Naïve parametric models fail to capture these dynamics and severely underestimate tail risk - a big problem!
Engle proposed ARCH, an autoregressive conditionally heteroskedastic model capable of modeling these dynamics improving forecasts!
Bollerslev proposed a generalized ARCH model (GARCH) which is an infinite order ARCH model, thus a more parsimonious version
GARCH can capture richer dynamics with fewer lags, impressive!
These volatility models outperform other models that do not account for dynamics especially in the context of risk modelling as we saw in our VaR example in this video
I hope you enjoyed!
Roman
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📖 Chapters:
00:00 - Introduction
04:00 - What is Volatility?
05:17 - Realized or Historic Volatility
09:07 - Implied Volatility
12:05 - Volatility Risk Premium
15:01 - Which Volatility Does ARCH/GARCH Model?
16:38 - Kurtosis and Excess Kurtosis in Returns
21:23 - Stylized Facts of Volatility to Model
25:38 - Modeling Volatility in a Pre-ARCH World
26:16 - ARCH Models
30:15 - Example: EWMA vs. ARCH for Volatility Forecasting
32:35 - Dynamics of Volatility the ARCH Model Captures
36:01 - GARCH Models
40:52 - Applications of ARCH/GARCH Models
43:43 - TL;DW Executive Summary
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🗣️ Shout Outs
A special thank you to my members on YouTube for supporting my channel and enabling me to continue to create videos just like this one!
⭐ Quant Guild Directors
Dr. Jason Pirozzolo
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