Problem 2: Properties of Options

The price of a European put that expires in six months and has a strike price of $100 is $2.35. The underlying stock price is $104, and a dividend of $2 is expected in two months. The term structure is flat, with all risk-free interest rates being 5% (cont. comp.).

a. What is the price of a European call option on the same stock that expires in six months and has a strike price of $100? [1 mark]

b. Explain in detail the arbitrage opportunities if the European call price is $4.1. How much will the arbitrage profit be? [2.5 marks]

c. Explain in detail the arbitrage opportunities if the European call price is $7.5. How much will the arbitrage profit be? [2.5 marks]