The Islamic Fiqh Council issued a statement that Forex trading is not allowed. The so-called Islamic Forex is not free from the reasons for the prohibition of Forex trading, or most of them. For more, see the detailed answer.

Murabahah transactions in which an item is sold to the one who asked for it to be purchased, if a person buys a product after it has come into the possession of the one who was instructed to buy it, and after it was acquired in the manner stipulated in Shari`ah, are permissible transactions, so long as the one who was instructed to buy it is liable for any damage before selling it and handing it over to the one who instructed him to buy it, and provided that the product may be returned if there is a hidden fault and the like, which dictates that it should be returned after being handed over, and provided that the conditions of sale are met and impediments to sale are absent.

The basic principle is that it is permissible to hold shares in any company if it does not deal with haram things such as riba and so on. But if it does deal with haram things such as riba, then it is not permissible to hold shares in it.