Assume the Black-Scholes framework. For a European put option and a European gap call option on a stock, you are given:

(i) The expiry date for both options is T.

(ii) The put option has a strike price of 40.

(iii) The gap call option has strike price 45 and payment trigger 40.

(iv) The time-0 gamma of the put option is 0.07.

(v) The time-0 gamma of the gap call option is 0.08.

Consider a European cash-or-nothing call option that pays 1000 at time T if the stock price at that time is higher than 40.

Find the time-0 gamma of the cash-or-nothing call option.

(A) −5

(B) −2

(C) 2

(D) 5

(E) 8