Learning agents in Black–Scholes financial markets

Author:

Vaidya Tushar1ORCID,Murguia Carlos2ORCID,Piliouras Georgios1ORCID

Affiliation:

1. Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore

2. Eindhoven University of Technology, Department of Mechanical Engineering, 5612 AZ Eindhoven, Netherlands

Abstract

Black–Scholes (BS) is a remarkable quotation model for European option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS framework assumes that volatility remains constant across all strikes; however, in practice, it varies. How do traders come to learn these parameters? We introduce natural agent-based models, in which traders update their beliefs about the true implied volatility based on the opinions of other agents. We prove exponentially fast convergence of these opinion dynamics, using techniques from control theory and leader-follower models, thus providing a resolution between theory and market practices. We allow for two different models, one with feedback and one with an unknown leader.

Funder

Singapore University of Technology and Design

National Research Foundation Singapore

MOE AcRF Tier 2 Grant

Publisher

The Royal Society

Subject

Multidisciplinary

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Averaging plus learning models and their asymptotics;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2023-07

2. PRICING CARBON CREDITS BASED ON MODIFIED BLACK-SCHOLES;Environmental Engineering and Management Journal;2023

3. A bibliometric analysis and basic model introduction of opinion dynamics;Applied Intelligence;2022-12-10

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