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

Davide Petturiti, Barbara Vantaggi
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:218-230, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v290-petturiti25a, 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}, pages = {218--230}, year = {2025}, editor = {Destercke, Sébastien and Erreygers, Alexander and Nendel, Max and Riedel, Frank and Troffaes, Matthias C. M.}, volume = {290}, series = {Proceedings of Machine Learning Research}, month = {15--18 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v290/main/assets/petturiti25a/petturiti25a.pdf}, url = {https://proceedings.mlr.press/v290/petturiti25a.html}, 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 $\alpha$.} }
Endnote
%0 Conference Paper %T Dynamic $α$-DS mixture pricing in a market with bid-ask spreads %A Davide Petturiti %A Barbara Vantaggi %B Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2025 %E Sébastien Destercke %E Alexander Erreygers %E Max Nendel %E Frank Riedel %E Matthias C. M. Troffaes %F pmlr-v290-petturiti25a %I PMLR %P 218--230 %U https://proceedings.mlr.press/v290/petturiti25a.html %V 290 %X 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 $\alpha$.
APA
Petturiti, D. & Vantaggi, B.. (2025). Dynamic $α$-DS mixture pricing in a market with bid-ask spreads. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:218-230 Available from https://proceedings.mlr.press/v290/petturiti25a.html.

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