Question 5. (This question has three parts: I, II and III)

The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29. The term structure is flat, with all risk-free interest rates being 10% per annum continuous compounding.

Part I.

What is the price of a European put option that expires in six months and has a strike price of $30?

Part II.

If the observed European put price is $3, is there any arbitrage opportunity? Give your reasoning.

Part III.

If there is no arbitrage opportunity in Part II, what would be the price range of the European put option which will trigger the arbitrage opportunity? If there is an arbitrage opportunity in Part II, provide a specific strategy to take this opportunity and show your profit.