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5

These are 2 completely different ways of estimating volatility. GARCH models are calibrated on historical time series i.e. information provided under the real-world measure $\mathbb{P}$. Although you can obviously use them for forecasting, the core information which is used to build the model is backward-looking in nature (historical behaviour of the stock)....


3

If your question is: "Given all the information available up to time $t$, if I compute the 1 period ahead forecast $r_{t+1}$, is the conditional volatility over $[t,t+1[$ given by $\sqrt{r_{t+1}}$?", the answer is NO. To compute the 1 period ahead conditional variance, you should use your model equations (see this post which might help you better understand ...


3

Let's assume T=1 and let S be a geometric gaussian process with zero drift, i.e. $\ln(S_1/S_0)$ is normally distributed with mean $-1/2\times\mathrm{VEV}^2$ and volatility VEV. Then $$\ln(\mathrm{VaR}/S_0) = -1/2\mathrm{VEV}^2 - \mathrm{VEV} \times 1.96$$ with the VAR at $0.975$ quantile. This is a quadratic equation in VEV, with solutions $$\mathrm{VEV}...


2

Volatility (often defined in terms of standard deviation of returns, or in terms of implied volatility from option markets) is indeed one measure of risk, but like any single measure of risk, it is incomplete. Part of the reason for this is that in financial markets, the returns are not normally distributed but rather have "fat tails." This means that ...


1

If you have options data with long enough history you could always construct a comparable index by computing the implied volatilities and using a similar weighting methodology to VIX or looking at the implied volatility of the 1 month call/put with strike closest to the price at the observation date (i.e. one closest to 100% moneyness). If you want an ...


1

let' s define a ARMA-GARCH model: $y_{t} = \mu_{t} + \epsilon_{t}$ where $\mu_{t} $ is the conditional mean process (ARMA(p,q) part, $\mu_{t} = E(y_{t}|\mathcal{F}_{t-1})$) . The errors (or mean residuals) re defined by: $\epsilon_{t} = \sigma_{t} \eta_{t}$ where $\eta_{t}$ is a white noise (0,1) Then : $Var[\epsilon_{t}]= \sigma_{t}^{2}$. next see ...


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It isn't strictly speaking possible to convert a log vol to a normal vol, although it may be possible to get a rough idea. I am assuming you only have the vol of log returns but not the actual time series here. If you had the original time series, then you would just calculate the standard deviation of the prices to get the normal vol. I assume this is ...



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