A stock is priced at 125.37, the continuously compounded risk-free rate is 4.4 percent, and the volatility is 21 percent. There are no dividends. Answer the following questions.
a. Determine a fair price for a two-year asset-or-nothing option with exercise price of 120.
b. Assuming you purchased the asset-or-nothing option at the price you determined in part a, calculate your profit if the asset price at expiration is (1) 138 and (2) 114.
c. Determine a fair price for a two-year cash-or-nothing option with exercise price of 120 that pays 120 if it expires in-the-money.
d. Assuming you purchased the cash or nothing option at the price you determined in part c, calculate your profit if the asset price at expiration is (1) 138 and (2) 114.