Problem:
You are observing the following prices. A put option that expires in six months has an exercise price of $45 and it sells for $5.80. The stock is currently priced at $40, and the risk-free rate is 3.6% per year, compounded continuously.
Required:
Question 1: What is the price of a call option with the same exercise prices and maturity?
Question 2: In the above example, suppose you form a portfolio consisting of buying a call and a put option on the same stock having the same maturity (known in the market as a "long straddle"). Is this portfolio risk free (perfectly hedged)?
Note: Explain all steps comprehensively.