You invested in 1,000 shares of stock ABC. Current stock price is $35; there is no dividend; interest rate is 5%. You are planning to buy a house in one year, which will require a down payment of $36,000. And you will need to sell the shares in one year and use the proceeds as down payment. In order to be able to sell your shares in one year for at least $36/share, you are considering 2 alternative strategies:

(1) Use 1-year forward contract on 1000 shares

(2) Use 1-year European options on 1000 shares

a). If you use strategy (2) and choose one of the four available options on the stock: call with strike $33; call with strike $38; put with strike $33; and put with strike $38. Which option and what option position would you use?

b) Given your choice in a) and your estimation for stock volatility 0.2. What is the total option premium using Black-Scholes-Merton model?

c). Suppose options' market prices are: (call, $33): $4.29; (call, $38): 1.60; (put, $33): 0.68; (put, $38): 2.75. Is implied volatility higher or lower than your estimation?

d) Given your choice in a) and option market price in c), would you be able to make the down payment in one year? For simplicity, assume option premium is received or paid in one year.