Bid-ask bounds for option prices: the two-tail distortion model

Umberto Cherubini and Sabrina Mulinacci

Quantitative Finance, 2025, vol. 25, issue 4, 527-542

Abstract: We model the bid-ask spreads of call and put options by a two-tail distortion (2TD) of a reference probability distribution. The model applies the Choquet pricing approach with no-arbitrage restrictions, requiring a duality relationship between the capacities pricing long and short positions of call and put options. Moreover, the put-call parity relationship requires that the sum of bid-ask spreads of call and put options with the same strike be invariant across the strikes. We calibrate the 2TD model with a simple Sugeno distortion on a sample of two months daily data for three stock indexes and three different reference models and show that the 2TD generally provides a better fit to the data than the standard distortion of one tail only. Moreover, the estimate of the distortion parameter happens to be very similar across the different models.

Date: 2025
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DOI: 10.1080/14697688.2025.2475087

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