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Yes there is a method to deal with non-normal market distributions in Black Litterman optimization. It is call Black Litterman Copula Opinion Pooling which uses copulas to model the market returns and therefore solve the non-normality problem. It was propose by Attilio Meucci and it can be implemented in R or Matlab. Never the less there is an other problem ...


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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 use as prior. As far as I know, there is no standard way to reverse-engineer the optimization problem in the presence of nonnormal markets. (the first guess is ...


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The most correct way if you want to do it with log returns is the way you stated on your first edit, but indeed for daily data the approximation error is negligible.


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You might also look at the boost package which should (I'm no expert for this) be usable within C#. It comes with an implementation of the inverse normal distribution which is explained in the online documentation http://www.boost.org/doc/libs/master/libs/math/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html Here they claim quite a high ...


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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 distribution (as inversegaussian) so you could roll your own with fzero() or another root-finder based on that if you are unhappy with the accuracy, or for testing ...



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