Tanker Company stock, which currently sells for 30 per share and has an anticipated volatility (annual return standard deviation) equal to 0.6, also has a three-month (0.25 year) call option with an exercise price equal to 30. The current riskless return rate equals 0.05.

a. Calculate this second call’s value.

b. Calculate this call’s delta, gamma, theta, vega, and rho.

c. What is the Black-Scholes implied probability that the stock price will exceed 30 three months from now?

d. What positions in these calls and the calls from Question 10 should be taken for each long share of stock to maintain a delta-gamma neutral portfolio?

e. What is the theta of the portfolio in part d?