A nine-month European put option's underlyingstock 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 is8% per annum with continuous compounding for all maturities.

1)What should be thelowest boundprice for asix-month European put option on a dividend-paying stockfor 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. 1)theoretical price=5.80
2. 1)theoretical price=6.30
3. 1)theoretical price=7.10
4. 1)theoretical price=7.90
5. 2)arbitrage strategy:shortthe putandbuy the stock
6. 2)arbitrage strategy:buy the putandshortthe stock
7. 2)arbitrage strategy:buy the putandbuy the stock
8. 2)arbitrage strategy:shortthe putandshortthe stock
9. 3)arbitrageur gain=1.30in present value terms
10. 3)arbitrageur gain=1.80in present value terms
11. 3)arbitrageur gain=2.30in present value terms
12. 3)arbitrageur gain=2.80in present value terms