A non-dividend-paying stock is currently priced at $45 and the risk-free rate with continuous compounding is 5% per annum. Consider options on this stock that have a strike price of $40 and maturity of 1 year.

a) Compute the lower and upper bounds for a European call option on the stock (round to the nearest cent).

Lower bound is: $ _____

Upper bound is: $ _____

b) If the current market price of an American call option on the stock is $5.5, what positions do you need to take today to take advantage of the arbitrage opportunity?

Positions for arbitrage profit (for each asset enter either "long" or "short"):______ the call; _____ the stock

c) If the current market price of an American put option on the stock is $41.5, what positions do you need to take today to take advantage of the arbitrage opportunity?

Positions for arbitrage profit (for each asset enter either "long" or "short"): _____ the put

d) Compute the lower and upper bounds for a European put option on the stock (round to the nearest cent).

Lower bound is: $ _____

Upper bound is: $_____