Dynamic $α$-DS Mixture Pricing in a Market with Bid-Ask Spreads
Abstract
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 non-dividend paying stock. Next, by taking $\alpha$-mixtures of bid-ask prices, where $\alpha \in [0,1]$ acts like a pessimism index, we propose a dynamic pricing rule consisting in the recursive one-step $\alpha$-mixture of upper and lower conditional Choquet expectations. We provide a dynamic pricing rule that has a closed-form for monotonic contract functions. Finally, we perform a calibration procedure on market data, complying with the tuning of $\alpha$.
Cite
Text
Petturiti and Vantaggi. "Dynamic $α$-DS Mixture Pricing in a Market with Bid-Ask Spreads." Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, 2025.Markdown
[Petturiti and Vantaggi. "Dynamic $α$-DS Mixture Pricing in a Market with Bid-Ask Spreads." Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, 2025.](https://mlanthology.org/isipta/2025/petturiti2025isipta-dynamic/)BibTeX
@inproceedings{petturiti2025isipta-dynamic,
title = {{Dynamic $α$-DS Mixture Pricing in a Market with Bid-Ask Spreads}},
author = {Petturiti, Davide and Vantaggi, Barbara},
booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications},
year = {2025},
pages = {218-230},
volume = {290},
url = {https://mlanthology.org/isipta/2025/petturiti2025isipta-dynamic/}
}