For a two-period binomial model for stock prices, you are given:

(i) The length of each period is one year.

(ii) The current price of a nondividend-paying stock is $40.

(iii) u = 1.05, where u is one plus the percentage change in the stock price per period if the price goes up.

(iv) d = 0.9, where d is one plus the percentage change in the stock price per period if the price goes down.

(v) The continuously compounded risk-free interest rate is 3%.

Consider Derivative X, which gives its holder the right, but not the obligation, to buy a $38-strike European put option at the end of the first year for $0.5. This put option is written on the stock and will mature at the end of the second year.

(a) Calculate the current price of Derivative X.

(b) Using the result of part (a), calculate the current price of Derivative Y, which is identical to Derivative X, except that it gives its holder the right to sell the same put option for $0.5 at the end of the first year.