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!
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!
