You have been asked to determine the prices of the options on ABX stock, currently trading at $22.50 a share. You estimate the continuously compounded ABX stock return volatility () to be 0.20 (20%) and the risk-free rate to be 2.25 percent. These options have 108 days left to expiration.

a. Determine the equilibrium prices, time and intrinsic values of the following:

1.ABX 20 options

2.ABX at-the-money options

b.Suppose you purchase 800 shares of ABX stock and simultaneously purchase 12 ABX 20 put optioncontracts. 1 contract = 100

1. Is your portfolio delta neutral? Explain.
2. What would you do to achieve delta neutrality?

c.Suppose you own 800 shares and wish to be fully hedged using ABX 22.50 calls

1. Show how you achieve such delta neutrality.
2. Exactly 30 days have expired since you fully hedged your long ABX stocks using ABX 22.5 calls. ABX stock has risen to 24.75, the risk-free rate has declined to 2 percent. 

Discuss your position delta and demonstrate how you can maintain delta neutrality.