The spot price of a dividend paying stock is $60. The price of an American call option that expires in 15 months is $4.35 with a strike price of $65. The underlying stock is expected to pay a dividend of $1.50 in 5 months and again $1.50 in 10 months. The term structure is flat and continuously compounded risk-free interest rate is 6% for all maturities.
a. What should be the price of a American put option on the same underlying stock with the same strike price and same maturity?
b. Assume that the American put option described in part (a) is selling for $7.00. Is there any arbitrage opportunity? If yes, then describe the set of transactions that will enable the investor to lock-in the arbitrage profits?