1. (15 points) The current price of stock X is $100. Stock X pays $5 dividend in 2 months and $10 in 5 months. The 2-month spot rate is 6%, the 5-month spot rate is 4%, and the 6- month spot rate is 3% continuously compounding. There are 6-month at-the-money European call and put options written on stock X. The call options are traded at $2, and the put options are traded at $15.

   1. (8 points) Is there an arbitrage? If yes, describe an arbitrage strategy. If no, explain why not.

   2. (7 points) Suppose that when you lend money you earn the interest rates as specified above. However, when you borrow you pay 2% in addition to the current spot rates. That is, if you borrow money for 2 months your annualized interest rate is 8%, for 5 months 6%, and for 6 months 5% continuously compounding. Further assume that you cannot enter any forward rate agreements to lock in forward rates. Finally, suppose that if you short sell stock X for 6-months, then you have to post $150 collateral, and the collateral earns the 6-month spot rate as interest. Is there an arbitrage? If yes, describe an arbitrage strategy. If no, explain why not.