No-arbitrage pricing with $α$-DS mixtures in a market with bid-ask spreads

Davide Petturiti, Barbara Vantaggi
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:401-411, 2023.

Abstract

This paper introduces $\alpha$-DS mixtures, which are normalized capacities that can be represented (generally not in a unique way) as the $\alpha$-mixture of a belief function and its dual plausibility function. Assuming a finite state space, such capacities extend to a Choquet expectation functional that can be given a Hurwicz-like expression. In turn, $\alpha$-DS mixtures and their Choquet expectations appear to be particularly suitable to model prices in a market with frictions, where bid-ask prices are usually averaged taking $\alpha = \frac{1}{2}$. For this, we formulate a no-arbitrage one-period pricing problem in the framework of $\alpha$-DS mixtures and prove the analogues of the first and second fundamental theorems of asset pricing. Finally, we perform a calibration on market data to derive a market consistent no-arbitrage $\alpha$-DS mixture pricing rule.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-petturiti23a, title = {No-arbitrage pricing with $α$-{DS} mixtures in a market with bid-ask spreads}, author = {Petturiti, Davide and Vantaggi, Barbara}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {401--411}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/petturiti23a/petturiti23a.pdf}, url = {https://proceedings.mlr.press/v215/petturiti23a.html}, abstract = {This paper introduces $\alpha$-DS mixtures, which are normalized capacities that can be represented (generally not in a unique way) as the $\alpha$-mixture of a belief function and its dual plausibility function. Assuming a finite state space, such capacities extend to a Choquet expectation functional that can be given a Hurwicz-like expression. In turn, $\alpha$-DS mixtures and their Choquet expectations appear to be particularly suitable to model prices in a market with frictions, where bid-ask prices are usually averaged taking $\alpha = \frac{1}{2}$. For this, we formulate a no-arbitrage one-period pricing problem in the framework of $\alpha$-DS mixtures and prove the analogues of the first and second fundamental theorems of asset pricing. Finally, we perform a calibration on market data to derive a market consistent no-arbitrage $\alpha$-DS mixture pricing rule.} }
Endnote
%0 Conference Paper %T No-arbitrage pricing with $α$-DS mixtures in a market with bid-ask spreads %A Davide Petturiti %A Barbara Vantaggi %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-petturiti23a %I PMLR %P 401--411 %U https://proceedings.mlr.press/v215/petturiti23a.html %V 215 %X This paper introduces $\alpha$-DS mixtures, which are normalized capacities that can be represented (generally not in a unique way) as the $\alpha$-mixture of a belief function and its dual plausibility function. Assuming a finite state space, such capacities extend to a Choquet expectation functional that can be given a Hurwicz-like expression. In turn, $\alpha$-DS mixtures and their Choquet expectations appear to be particularly suitable to model prices in a market with frictions, where bid-ask prices are usually averaged taking $\alpha = \frac{1}{2}$. For this, we formulate a no-arbitrage one-period pricing problem in the framework of $\alpha$-DS mixtures and prove the analogues of the first and second fundamental theorems of asset pricing. Finally, we perform a calibration on market data to derive a market consistent no-arbitrage $\alpha$-DS mixture pricing rule.
APA
Petturiti, D. & Vantaggi, B.. (2023). No-arbitrage pricing with $α$-DS mixtures in a market with bid-ask spreads. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:401-411 Available from https://proceedings.mlr.press/v215/petturiti23a.html.

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