"close a deal" is more often used by salespeople to describe the end of a negotiation process when they completed the deal i.e. the customer was finally persuaded said "yes, I will buy this from you".
In your case, you could say this though it could sound a bit pretentious to some people.
You could just say : "I am now buying / I have just bought 100 shares in XYZ Inc" or "I have just done a deal to buy 100 shares in XYZ Inc"
or to be more precise about the last stage : "I am finalising / completing a deal...."