A purely data driven method for European option valuation

An alternative option pricing method is proposed based on a random walk market model. The minimal entropy martingale measure which adopts no arbitrage opportunity in the market, is deduced for this market model and is used as the pricing measure to evaluate European call options by a Monte Carlo simulation method. The proposed method is a purely data driven valuation method without any distributional assumption about the price process of underlying asset. The performance of the proposed method is compared with the canonical valuation method and the historical volatility-based Black-Scholes method in an artificial Black-Scholes world. The simulation results show that the proposed method has merits, and is valuable to financial engineering.