Show that the second derivative with respect to strike of the call payoff f(ST ,K) = (ST

Question:

Show that the second derivative with respect to strike of the call payoff f(ST ,K) = (ST − K, 0)+, at expiry T is given by:

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where δ(ST −K) denotes the Dirac delta function, satisfying the property;

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for a function f of a real variable x. Use this property to show that, for the undiscounted call price

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