But why shall it be convex? To say that the price is convex in the strike means that. Let's assume that the opposite is true, i.

So I have the possibility of making a profit, but no possibility of making a loss - which is an arbitrage. Since no arbitrages exist, the option price must be convex in the strike price.

Convexity (finance) - Wikipedia

There is a much simpler solution to the question regarding the convexity of the call option function. Therefore we have shown that the call option price function is convex. By posting your answer, you agree to the privacy policy and terms of service.

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Price of a European Call option is a convex function of strike price K. Why this definition of convexity is equivalent to the std definition: Quant Finance 11 4.

Your answer concerns the expected pay-out instead of the price. The latter includes a risk premium. The expected pay-out under the risk-neutral measure is the call option price. What if no risk neutral measure exists? By the Fundamental Theorem of Asset Pricing it's known that the market is arbitrage-free if there exists at least one risk-neutral probability measure.

finance - Price of a European Call option is a convex function of strike price K - Mathematics Stack Exchange

The market is even complete if there exists only one risk-neutral probability measure. Therefore, if there is no risk-neutral measure, the market is not arbitrage-free.

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