New answers tagged volatility
1
you need to use the forecast for both the mean and sigma. It should look something like this:
forecast = ugarchforecast(modelfit, n.ahead = 1, data = mydata);
sigma(forecast);
fitted(forecast)
Then plug these values into the equation:
\begin{align}
\hat{VaR}_{0.99,T|T-1}&=\hat{\mu}_{T|T-1} + \hat{\sigma}_{T|T-1} * q_{0.99}
\end{align}
where $T$ is ...
1
So to expand a bit further on what Brian had mentioned, you're going to get a different vol surface given american vs european. So this is something Brian already pointed out, but one very simple and practical way that you can prove this to yourself is just to think about how the implied forwards are generated.
In the European case we use the entire strip ...
3
For a standard American exercise option expiring at $T>0$, price is still monotically increasing in volatility under the Black-Scholes model (though obviously it is not strictly monotonic, due to early exercise rendering price insensitive to volatility in some regions of parameter space).
To see this, you can use one of three techniques:
Investigate ...
0
The first and the second moment are independent, so even if returns
are not autocorrelated the size of returns can be.
of course. Example: generate path of variable with binomial distribution that takes value of 1 or -1, that is
$\sum_{i=1}^n{} x_i,x_i=\{1,-1\}$
now you can generate another path $\sum_{i=1}^n{} x'_i,x'_i=\{1,-1\}$ choosing values of ...
2
To your first question: The first and the second moment are independent, so even if returns are not autocorrelated the size of returns can be.
To your second question: Autocorrelated volatility implies volatility not being constant but varying, which is heteroscedasticity or volatility clustering.
1
As Quartz says it is possible to make non-linear transformations taking into account skew and kurtosis, but this is mostly is limited to univariate processes (one approach for a t distribution is to match moments). For multivariate processes, it is considerably more difficult. A more general solution is to rely on Entropy Pooling. You could take views on ...
3
It's not possible with a simple linear transformation like the one you mentioned: since scale and thus the distance between mean and median are required to change, either the mean or the median will not be preserved.
Therefore you must use nonlinear transformations, which will complicate quite a bit mantaining skew and kurtosis and imho will not be ...
1
The standard answer to your question would be to do the maximum likelihood estimation. When you say "plug in $\sigma$" you can show that the sample estimate of $\sigma$ is actually the maximum likelihood estimate of $\sigma$ for the normal distribution.
If I can assume that your data are IID then what you do is use your distribution with parameters ...
Top 50 recent answers are included
