Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock. You are given:

(i) S(0) = $48.

(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3%.

(iii) Var[ln S(t)] = 0.04t for all t ≥ 0.

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

Consider a 3-month European gap option. If the 3-month stock price is less than $48, the payoff of the option is K − S(0.25); otherwise, the payoff is zero.

The value of K is set so that the gap option is free (i.e., its price is zero).

Calculate the current delta of the gap option.