What open source or commercial .NET statistical package would you guys recommend? I am doing statistical arbitrage in options. The functions I need mainly are regressions, optimizations..etc. It would be better if the package has some built-in functions specifically for options, but it's fine if it doesn't. Quality, speed, easy-to-do of statistical analysis, good compatibility with C++/C# are my priorities.
Python is really a good idea. You could even optimize it with PyPy for better performance.
But it is just my opinion.
Not sure why Python is recommended when you clearly ask for a .Net solution (well you may look at IronPython but I do not recommend it given there are much better options, see below), aside the fact that Python is horribly slow even when performing non-mission-critical data analysis and research. Even C# easily runs circles around most python scripts, given your coding skills are average or better. I understand its the language of choice aside Matlab and R by most quants, mostly because they have a standardized approach in terms of access to data sets, and anyway the language is most often dictated by the trading desk or head quant which means its not necessarily the most optimal choice.
I would recommend you to look at the following for managed C# or otherwise C++ implementation. You can run both in .Net and if not directly you could wrap C++ code in order to have access through a library (following is not in the order of significance):
And here you get another host of packages: http://en.wikipedia.org/wiki/List_of_numerical_libraries#C.2B.2B (not all come with statistical tools and may focus on math, but I included the link as its a comprehensive source of packages)
You can also directly link to Matlab or R out of .Net but again I would argue it will be at the expense of speed given how you implement the link. A raw library will always serve you the best in terms of performance given it offers the algorithms you look for.
Good luck. Hope this helps.