So when I studied my bachelor in economics I didn't pay attention to statistics, the way it was explained, it seemed more like an academic exercise than a useful tool.

Now wiser, and soon to begin my master, I am beginning to really regret not knowing statistics and since I only really feel i have learned something is when I have done it, I have made it a personal project to model European style options. I expect there isn't any very reliable formula that can do it, but the exercise is worth the try.

So when you buy a (call) option, you get the right to purchase a stock at a later date at a now determined price. So lets say Company X trades at 100 and you buy 1 option for 10 with an expiration date in one month. At expiration date you can now buy the stock at 100, no matter what everyone else is trading it at. So if everyone else is trading at 120 you can buy the stock for 100, sell it and profit 20 minus the initial 10. If the stock trades at 80 on expiration date, you would be better of not buying it for 100 and you have lost your initial 10. In practice, you just get paid whatever you could have earned based on the current stock price, at expiration date (no need to buy and sell).

Anyway you can of course sell your option to others, and the price of your option is determined by the chance of being profitable at expiration date. It is these fluctuations I would like to try to model. I just realized that I might need another model since the price will move more and more towards one of two extremes, either 0 when the option looks to be worthless or towards the share price - minus the exercise price when profit looks to be made.

Did it make any sense?