Why an Equally Spaced Call Butterfly Has Nonnegative Value

Summary

The document asks for a detailed proof that the value of a call butterfly is nonnegative when its three strikes are equally spaced. Its expression combines a long call at the lower strike, two short calls at the middle strike, and a long call at the upper strike. The question points to an earlier proof but says that explanation omits steps.

No proof, derivation, market data, or empirical evidence is provided in the document; it is a request for one. The claimed inequality is commonly connected to the convexity of call prices as a function of strike under standard no-arbitrage assumptions. The document does not state those assumptions, specify whether prices are discounted, or discuss early exercise or market frictions, so it cannot establish the claim on its own.

Key ideas

• The question concerns the value of a call butterfly built from three equally spaced strikes.
• It asks for a complete derivation of a nonnegative-value inequality.
• The document supplies no proof or supporting evidence.

Tags

# Proving that the return from the butterfly spread is nonnegative


# Proving that the return from the butterfly spread is nonnegative












The butterfly spread satisfies the inequality

c(X1) - 2c(X2) + c(X3) >= 0

Where call strikes satisfy X1<X2<X3 and X2 - X1 = X3 - X2.

There is a “proof” that was provided here https://quant.stackexchange.com/a/32609/66878. However the proof is missing many steps and serves more as an outline.

Could anyone elaborate on the proof or provide their own in full detail?

Thanks so much, Jordan

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.