Dynamic α-DS mixture pricing in a market with bid-ask spreads

This paper faces the problem of pricing a European derivative contract inside a discrete-time market with frictions in the form of bid-ask spreads. To this aim, we use a Markov and time-homogeneous multiplicative binomial process under Dempster-Shafer uncertainty for modeling the bid price of a nondividend paying stock. Next, by taking α-mixtures of bid-ask prices, where α ∈ [0, 1] acts like a pessimism index, we propose a dynamic pricing rule consisting in the recursive one-step α-mixture of upper and lower conditional Choquet expectations. We provide a dynamic pricing rule that has a closedform for monotonic contract functions. Finally, we perform a calibration procedure on market data, complying with the tuning of α.