Assume the Black-Scholes framework. For t ≥ 0, let S(t) denote the time-t price of a stock. Consider a 1-year European contingent claim. If the 1-year stock price is less than $60, the payoff of the contingent claim is S(1) − 40; otherwise, the payoff is zero.

You are given:

(i) S(0) = 50.

(ii) The only dividend is 2 to be paid in eight months.

(iii) Var[ln F^P_t,1(S)] = 0.04t, for 0 ≤ t ≤ 1.

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

Calculate the current price of the contingent claim.