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solution

Consider an American call option with time to expiry 2 years, and a strike of 100. The
current price of the underlying is 100. Divide the time to expiry into two 1-year intervals.
Assume that in each 1-year interval, the price can either rise by 15, or fall by 15, with equal
probability. The risk-free (continuously compounding) rate is 0.06.
(a) Using a binomial tree, identify the circumstances under which early exercise would be
rational for the holder of this option.
(b) What is the value of the option?
(c) Now assume that a dividend of 10 is paid on each unit of the underlying, 13 months in
the life of the option. Would early exercise still be rational? Explain your answer. What is the
value of the option in the presence of the dividend?

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