Learning Agents in Black-Scholes Financial Markets: Consensus Dynamics and Volatility Smiles
arXiv:1704.07597
Abstract
Black-Scholes (BS) is the standard mathematical model for 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 models of learning agents, in which they update their beliefs about the true implied volatility based on the opinions of other traders. We prove 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.
19 pages, 3 figures
References in corpus (7)
- Statistical physics of social dynamics
- Agent-based Models of Financial Markets
- Reasoning in Bayesian Opinion Exchange Networks Is PSPACE-Hard
- Opinion Dynamics in Networks: Convergence, Stability and Lack of Explosion
- Idiosyncrasies and challenges of data driven learning in electronic trading
- Volatility Smile as Relativistic Effect
- Regrets, learning and wisdom