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

Question:

where S₁and 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

[h + (1 - )h]pX, X h + (1 - )h < X, X whip (x. A) + + (1 - )hp(x, X 12 P(X, Z.).

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

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Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

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Question Posted: Dec 02, 2023 03:00 AM

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

Question:

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

Step by Step Answer:

This concludes the demonstration of the convexity propert...View the full answer

Mathematical Models Of Financial Derivative

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