Let S(t) denote the price at time t of a stock that pays dividends continuously at a rate proportional to its price. Consider a European gap option with expiration date T, T > 0.

If the stock price at time T is greater than $100, the payoff is S(T) − 90; otherwise, the payoff is zero.

You are given:

(i) S(0) = $80.

(ii) The price of a European call option with expiration date T and strike price $100 is $4.

(iii) The delta of the call option in (ii) is 0.2.

Calculate the price of the gap option.

(A) $3.60

(B) $5.20

(C) $6.40

(D) $10.80

(E) There is not enough information to solve the problem.