Question

This is a problem that has THREE questions. Therefore, please choose THREE answers (one choice for each question) to get full credit for this questions, otherwise you will only get partial points.

A nine-month European put option's underlying stock price is $39, while the strike price is $45 and a dividend of $3 is expected in four months. Assume that the risk-free interest rate is 8% per annum with continuous compounding for all maturities.

1)  What should be the lowest bound  price for a six-month European put option on a dividend-paying stock for no arbitrage?

2) If the put option is currently selling for $5, what arbitrage strategy should be implemented?

3) With the above arbitrage strategy, how much profit does the arbitrageur generate?

		1) theoretical price = 5.80
		1) theoretical price = 6.30
		1) theoretical price = 7.10
		1) theoretical price = 7.90
		2) arbitrage strategy: short the put and buy the stock
		2) arbitrage strategy: buy the put and short the stock
		2) arbitrage strategy: buy the put and buy the stock
		2) arbitrage strategy: short the put and short the stock
		3) arbitrageur gain = 1.30 in present value terms
		3) arbitrageur gain = 1.80 in present value terms
		3) arbitrageur gain = 2.30 in present value terms
		3) arbitrageur gain = 2.80 in present value terms

Answer 1

1.
Lower bound for European put=Ke^(-rt)+D-S=45*e^(-8%*9/12)+3*e^(-8%*4/12)-39=6.30

2.
arbitrage strategy: buy the put and buy the stock
As the put is undervalued

3.
arbitrageur gain = 1.30 in present value terms