  Our goal here is to discuss the pricing problem of European and American
options in discrete time using elementary calculus so as to be an easy
reference for first year undergraduate students. Using the binomial model we
compute the fair price of European and American options. We explain the notion
of Arbitrage and the notion of the fair price of an option using common sense.
We give a criterion that the holder can use to decide when it is appropriate to
exercise the option. We prove the put-call parity formulas for both European
and American options and we discuss the relation between American and European
options. We give also the bounds for European and American options. We also
discuss the portfolio's optimization problem and the fair value in the case
where the holder can not produce the opposite portfolio.
