Option Pricing under Unknown Volatility: An Agent-Based Modeling and Simulation Approach

We modeled an artificial European option market with unknown volatility using an agent-based modeling and simulation approach. Contrary to the standard Black and Scholes model with "known" volatility, there is significant pricing bias (market price/theoretical price) in the presence of unknown volatility. Moreover, the unknown drift has a significant nonlinear effect in the pricing bias. Finally, pricing bias tends to decrease as the drift increasing in the case of low volatility. Our approach may serve as a first step towards the goal of option pricing in disequilibrium with unknown volatility.