1. A stock trades at $20. Its annual volatility is 18%. The risk-free rate is 3%.

a. Calculate the price of a European call option and put option with strike K = 20 and T equal to 4 months.

b. Calculate the of a portfolio consisting of 2 long calls and 1 short put from the previous problem. How many shares of the stock would you short in order to build a new portfolio that is delta-neutral?

c. If the stock moves down 15 cents, what is the exact change in price of the delta-neutral portfolio from the previous problem? What is the of one of these calls? of one of the puts?

Please explain how you got the answers! Thank you!