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