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How to Price an Option?

 

In the last pages we have looked at the PAYOFF of an option. To estimate whether in the end at expiration day the stock is higher or lower than the strike price - the guaranteed price for buying (call option) or selling (put option) one has to model the changing price of the stock over time.

The MODELING of Price Changes is at the heart of the OPTION game!

 

   Standard assumption  

The stock changes percentagewise at some rate (i.e. an increase of 6 % per 6 months) like the interest you get on your savings account. In addition, there is uncertainty in the market, prices fluctuate back and forth all the time. This unpredictable fluctuation is described by the term RANDOM WALK. Prices "walk" around the mean value in a random fashion. 

THE CHANGE OF STOCK PRICE: average percentage rise/fall in time and average fluctuation (e.g. +-3% every month) of the price

 

 

Let us understand the stock movement with a game of Pachinko!