You are asked to price options on KYC stock. KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. KYC does not pay dividend. The risk-free rate is 5% (EAR), and the current stock price of KYC is $100.

a. Price a European put option on KYC with maturity of 2 years and a strike price of 100.

b. Price an American put option on KYC with the same characteristics. Is the price different? Why or why not?

c. Given the price of the put option that you calculated in a), specify the ranges of KYC share price at the option's maturity date for which you will be making a net profit.

d. Suppose you expect the price of KYC stock to have little variance in the future. How would you design a strategy (using options) to take advantage of this?