Learning Agents in Financial Markets: Consensus Dynamics on Volatility

Tushar Vaidya, Carlos Murguia, Georgios Piliouras

Abstract: Black-Scholes (BS) is the standard mathematical 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 and analyze the convergence properties of natural models of learning agents, in which they update their beliefs about the true implied volatility based on the opinions of other traders.