Assume that each week a stock either increases or decreases $1.00 in price with probability 1/2,
and that different weeks are independent. The current price of the stock is $100.00. I agree to buy
a "call option" that lets me buy the stock for $105.00 after 10 weeks if the price is above $105.00
(if I wish). If the price is below $105.00, the option is not exercised. Assuming no transaction fees
and an interest rate of 0%, what is the "fair" price to pay per share for the option?