Suppose that C₁, C₂ and C₃ are the prices of European calls on the same underlying asset maturing at time T and struck at K₁ 2 3 respectively, with K₃ K₂ = K₂ K₁.

Graph the payoff of the corresponding butterfly spread strategy: a portfolio long one call struck at K1, short two calls struck at K2 and long one call struck at K3.

Using algebra prove that the payoff of the butterfly spread is always non-negative.

Argue that C2 (C1 + C3)/2.