Learning agents in Black–Scholes financial markets. Issue 10 (21st October 2020)

• Record Type: Journal Article
• Authors: Vaidya, Tushar; Murguia, Carlos; Piliouras, Georgios
• Is Part Of: Royal Society open science. Volume 7:Issue 10(2020)
• Publication Date: 2020-10-21
• Subjects: agent-based learning -- volatility smiles -- trading -- Black–Scholes and social learning; Science -- Periodicals; 500
• DOI: 10.1098/rsos.201188
• Languages: English
• ISSNs: 2054-5703

Abstract

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.