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/}
}