No-Arbitrage Pricing with $α$-DS Mixtures in a Market with Bid-Ask Spreads
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
Text
Petturiti and Vantaggi. "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, 2023.Markdown
[Petturiti and Vantaggi. "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, 2023.](https://mlanthology.org/isipta/2023/petturiti2023isipta-noarbitrage/)BibTeX
@inproceedings{petturiti2023isipta-noarbitrage,
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},
year = {2023},
pages = {401-411},
volume = {215},
url = {https://mlanthology.org/isipta/2023/petturiti2023isipta-noarbitrage/}
}