Assume the Black-Scholes frame-work. For t ≥ 0, let S(t) be the time-t price of a stock.

You are given:

(i) S(0) = 20.

(ii) The stock’s volatility is 25%.

(iii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 1.5%.

(iv) The continuously compounded risk-free interest rate is 4%.

(v) The payoff of a 3-year European contingent claim is min(S(2), S(3)).

Calculate the time-0 price of the contingent claim.