The continuously compounded risk-free rate is 12% per annum and interest rates are constant. Shares in Uni Corp are listed and actively traded. The shares are currently trading at $65. You own a four-month American-style over-the-counter call option on a share of Uni Corp with an exercise price of $50. There is no liquid secondary market in which these options can be sold. Uni Corp will not pay any dividends during the next four months.

After a careful analysis of the industry and the firm you are convinced that Uni Corp is considerably overvalued and is likely to soon decrease in price. Your new colleague suggests that since you cannot easily sell the option, you should realize $15 now by exercising the option and then immediately selling the share.

Explain clearly and completely why your colleague is wrong. Show that if you do not exercise immediately you can lock-in a current payoff of at least $16.96053 irrespective of what subsequently happens to Uni Corp's share price.

Your answer to this question should be no more than a half page.