A nonparametric approach for European option valuation

A nonparametric approach for European option valuation is proposed in this paper, which adopts a purely jump model to describe the price dynamics of the underlying asset, and the minimal entropy martingale measure for those jumps is used as the pricing measure of this market. A simple Monte Carlo simulation method is proposed to calculate the price of derivatives under this risk neural measure. And the volatility of the spot market can be renewed automatically without particular specification in the proposed method. The performances of the proposed method are compared to that of the Black–Scholes formula in an artificial world and the real world. The results of our investigations suggest that the proposed method is a valuable method.