Consider an American Call with K=50, with current stock price S=60, T-t=12 months r=6% p.a. w monthly compounding, and a dividend of $1 anticipated in 1 month.

a) Ellie is debating exercising the call immediately... if the call's market price was greater than $10 - say it was $10.05 - she says she would sell it rather than exercise it, as long as the incremental transaction cost to selling was greater than 5c. Is her statement right?

b) Karl says, you're missing something... you should ALSO ask if the call is UNDERPRICED at SAY $10.01, right? In that case you should NOT sell it, you might want to buy more of it? In order to answer his Q, use the lower boundary for American Calls: A call's price (Ct) must never fall below the maximum of zero, its immediate exercise value (St - K), or the value dictated by present value boundary, which is St - (PV (K) + D+). Algebraically Ct max [0, St - K, St - (PV(K) + D+)]

Here D+ is the PV of the max anticipated dividend over the option's life.

[Hint: Assume the call is priced at $10.01 today and that there are NO trans costs. Then: BUY the Call Now, Short the Stock at $60, Lend the difference at market rates for 1 month. Close the portfolio just a day before the dividend is paid, taking the OPTIMAL ACTION w respect to the call at that time - justify your actions! You should discover an arbitrage recipe that prohibits the Amcall from being priced at market for its immediate exercise value at any date prior to a dividends, with r>0.]