The Strike Quietly Absorbed a Square Root
A call whose payoff is the square of the stock minus 100 does not start paying at 100, it starts paying at 10, because the square clears the strike exactly when the stock clears its square root. Placing the kink at the written strike prices the option at essentially zero on a stock at 12, when its real value is 53.8168. The closed form is ordinary Black-Scholes on the transformed asset with a growth term of 4 percent and a strike leg that still discounts at the riskless rate, and the value curve sits above intrinsic everywhere while being shallower than it at the spot in question.