Detecting Arbitrage in Call Prices Across Strikes

Summary

The document asks how to detect arbitrage in a series of call option prices with a common maturity and different strikes. It proposes checking familiar static relationships, including butterfly arbitrage and monotonicity of call prices with respect to strike, and asks whether other straightforward violations should be tested. It also raises the possibility of a more efficient general method than enumerating arbitrage patterns one at a time.

No solution, algorithm, data, or test results are provided. The material is therefore a framing of an options validation problem rather than a complete arbitrage detector. Any practical screening method would need to account for the assumptions behind static option bounds and relationships, as well as data quality and market frictions; these issues are not developed in the document.

Key ideas

• The problem concerns arbitrage detection across call options sharing a maturity.
• Monotonicity in strike and butterfly relationships are proposed as basic checks.
• The author asks whether additional simple static arbitrage conditions are needed.
• The document does not provide an algorithm, proof, data, or empirical results.

Tags

# Arbitrage opportunities


# Arbitrage opportunities












I want to write a program that can find arbitrage in the curve of call prices for different strike K. So if I have a time serie with the price of call prices for different strikes and same time to maturity I want to find if there's is an arbitrage opportunity. Is there a simple way of doing so?

I was thinking about listing all the type of known simple arbitrage that exists: butterfly arbitrage, curve should be strictly increasing in the strike price and basically just manually check for these two (are there other simple arbitrage that are easy to spot from the time serie that I am missing here?)

Otherwise are there more efficient way than just listing all arbitrage that exists and check for each of them one by one?

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