Question

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.

   1.What is the price of a call option with the same exercise prices and maturity?

   2.Suppose you form a portfolio consisting of buying the call and the put options above (Note, they are written on the same stock having the same maturity). The resulting portfolio is known in the market as a “long straddle”. Is this portfolio risk free (perfectly hedged)? NEED DETAILED EXPLANATION AND CALCULATION

Answer 1

Working

b).When the market price>excercise price, investor exercise the call option

When the market price<strike price, investor excerise the put option.

When the market price>excercise price, portfolio said to be risk free.

The long straddle strategy is risk free when the maximum loss will be whne excercising the put option but the gain is unlimited by exercising the call option