The price of a European call that expires in six months and has a strike price of $82.50 is $5.5. The underlying stock price is $79.75. The interest rates are 10% per annum for all maturities.

(a) What is the price of a European put option that expires in six months and has a strike price of $82.50?

(b) Explain carefully the arbitrage opportunities if the European put price is $4. Describe the arbitrage strategies. (How to proceed with the arbitrage transaction?)

(c) Show the payoff table for the arbitrage strategies if ST < K or ST > K.

(d) Calculate the arbitrage profit now (at t=0). (Please calculate the answer accurate to the fourth decimal place.)