Learning agents in Black-Scholes financial markets

Tushar Vaidya (Corresponding author), Carlos Murguia, Georgios Piliouras

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number201188
Number of pages14
JournalRoyal Society Open Science
Issue number10
Publication statusPublished - 21 Oct 2020

Bibliographical note

© 2020 The Authors.


  • Black-Scholes and social learning
  • agent-based learning
  • trading
  • volatility smiles


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