European Option Pricing Formula In Risk-Aversive Markets

Option is one of the important financial derivatives and the study of its pricing formula has received much attention in financial mathematics.Based on the assumption of the risk-neutral financial market,the traditional option pricing theory assumes that the arbitrage opportunity does not exist and the market is balanced and complete.These ideal assumptions do not conform to the real trading market,which leads to the limitations of the traditional option pricing theory.In the paper,under the conditions that the financial market is risk-aversive and the pricing process of the underlying asset follows a geometric Brownian motion,the pricing formulas for European options are obtained by discounting the terminal expectation into its initial value based on risk measures including standard deviation,Va R and TVa R.In particular,owing to the fact that option traders do not need risk compensation in the risk-neutral market,the pricing model degenerates into the traditional Black-Schole pricing model.The pricing model of this paper is still applicable in the unbalanced and incomplete market and largely relaxes the requirements of the traditional pricing model.As a by-product,the results indicate that the value of European option depends on the drift coefficient ? of the underlying asset,which is equal to the risk-free interest rate r in a risk-neutral market and does not display in the Black-Scholes model due to the no-arbitrage opportunity principle.Finally,the empirical analyses on Shanghai 50 ETF options including error index analysis,regression analysis and expiration profit analysis of option sellers show that the fitting effect of obtained pricing formulas is superior to that of the Black–Scholes model,showing higher pricing accuracy and better pricing nature.