Bid-Ask Bounds for Option Prices: The Two-Tail Distortion Model

Mulinacci Sabrina, University of Bologna

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 option 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. The talk is based on joint work with Umberto Cherubini.

Area: CS44 - Algebraic option pricing and probability: in honor of Peter Carr (Umberto Cherubini and Sabrina Mulinacci)

Keywords: Fuzzy measures, Choquet pricing, Bid-ask spreads, Option pricing

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