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Accessing your inbox, you find an unsolicited e-mail from Shadyside Stock Brokers offering to sell you “bargain shares”. For example, one bargain share of Amalgamated Consolidated Enterprises is offered for $41.50 even though ACE is now trading at $42. Reading more closely you learn that if you buy and pay for a bargain share today, the stock itself will not be delivered until July 27 (.25 – one quarter - year from today) and even then, if ACE is trading above $45 per share on July 27, you will not receive the stock, but rather a payment of $45.
a) Diagram the payoff function for a bargain share, that is the value you will receive for a bargain share on July 27 as a function of value of ACE stock on that date. Doing further research you learn that ACE pays no dividend, the 90 day (annualized, continuously compounded) risk-free rate is 7% and that European put options on ACE stock (expiring July 27 with a $45 strike price) now trade at $3.15.
b) What is the fair-market (no arbitrage) price of a bargain share and would you be willing to buy one from Shadyside for $41.50?
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