# Tag Info

Accepted

### Is it possible to deal with non-normal distribution in Black-Litterman model?

Well there are two main things to consider here. Many implementation of Black-Litterman use the market portfolio and the ex post volatility and correlation structure to back out implied returns to ...
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### Reconciling Two Claims About Volatility Under Fat Tails

I don't think the claim that "Lévy alpha-stable distributions are better descriptors of returns" is universally accepted. While Mandelbrot (and others before him) has correctly identified ...
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### Quantile normal and lognormal

Quantiles are preserved under monotonic transformations, hence the quantile for $Y$ is simply the exponential of the quantile of $X$, no need for corrections whatsoever (see here for instance). Put ...
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### Density plot of the skew-t distribution

The rsgt is a skewed generalized t distribution, whereas your picture is a skewed student-t distribution. Try using fGarch ...
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### Normal Inverse Gaussian distribution - any consensus on an accurate quantile function?

When possible, I look at implementations in IMSL and the GSL for really good accuracy. Neither one appears to implement the Wald (inverse gaussian) or its quantile function. Matlab does have the ...
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### Problem with obtaining densities

You know that : $X \sim N(\mu,\sigma^2)$. $Z = \large\frac{X-\mu}{\sigma}$. $\text{Var}(Z) = \large\frac{1}{\sigma^2}\text{Var}(X) = \large\frac{1}{\sigma^2}\sigma^2 = 1$. So that $Z \sim N(0,1)$. ...

### How to derive the implied probability distribution from B-S volatilities?

Brian B gives the overall idea. But the use of a simple polynomial will not be appropriate in general. The paper Model-free stochastic collocation for an arbitrage-free implied volatility: Part I ...
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### Verifying that the extreme value copula is indeed a copula

Note that, you only need to show that \begin{align*} A\left(\frac{\log(u_2)}{\log(u_1u_2)}\right)-\frac{\log(u_2)}{\log(u_1u_2)}A'\left(\frac{\log(u_2)}{\log(u_1u_2)}\right) \ge 0, \end{align*} or, ...

### Compare two distributions for forecasting returns

Your feeling that there is more to the problem than adding up probabilities is very justified. To give you the bad news first: Your problem as stated has no solution. Since probability distributions ...