Assume the Black-Scholes framework. Let S(t) denote the price at time t of a stock, which will pay a dividend of $1 after 3 months.

Consider a European gap option which matures in 9 months. If the 9-month stock price is less than $28, the payoff is 30 − S(9/12); otherwise, the payoff is zero.

You are given:

(i) S(0) = $30.

(ii) Var[ln F^P_t,9/12(S)] = 0.1225t, for 0 ≤ t ≤ 9/12.

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

Calculate the price of the gap option.