Show that the put prices (European and American) are convex functions of the asset price, that is, 

where S₁ and S₂ denote the asset prices and X denotes the strike price.

Let S₁ = h₁X and S₂ = h₂X, and note that the put price function is homogeneous of degree one in the asset price and the strike price, the above inequality can be expressed as

Apply the property that the put prices are convex functions of the strike price.

Transcribed Image Text:

p(λS₁ + (12)S2, X) ≤ p(S₁, X) + (1-2) p(S2, X), 0≤ ≤ 1,