Assume the Black-Scholes framework. Let S(t) be the time-t price of a stock. Consider a special 3-year European contingent claim which pays a certain amount three years from now, provided that S(3) is higher than S(1); otherwise, the contingent claim will pay nothing.

You are given:

(i) S(0) = 100.

(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2%.

(iii) The stock’s volatility is 30%.

(iv) The continuously compounded risk-free interest rate is 8%.

Determine the price today of the contingent claim if it pays, at time 3:

(a) S(1)

(b) S(3)