1. A stock trades at $20. Its annual volatility is 18%. The risk-free rate is 3%. Calculate the price of a European call option and put option with strike K = 20 and T equal to 4 months.

2. (Continued) 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?

3. (Continued) If the stock moves down 15 cents, what is the exact change in price of the delta-neutral portfolio from the previous problem?

4. (Continued) What is the of one of these calls? of one of the puts?

5. (Continued) Calculate the and the of a straddle built from one of the calls and one of the puts. This example illustrates why a straddle built from at-the-money options is close to being delta-neutral and is a bet on volatility.

Please solve 2 and 5 as soon as possible. 1,3,4 are for reference