Patriot Corp. compensates executives with 10-year European call options which is granted at-the-money. If there is a signi?cant drop in the share price, the company's board will reset the strike price of the options to equal the new share price. Then, the maturity of the repriced option will equal the remaining maturity of the original option. Suppose σ = 30%, r = 6%, δ = 0, and the original share price is $100. Calculate the following:
a. The value at grant of an option that will not be repriced
b. The value at grant of an option that is repriced when the share price reaches $60
c. The repricing trigger that maximizes the initial value of the option