Empirical Analysis Of European Option Pricing Model With Asymmetric Ambiguous Coefficients

An option is a good tool for hedging,speculative arbitrage and asset allocation.In recent years,China options market has developed rapidly with the support of national policies.The types of options are gradually enriched;the market maker system is constantly improved;the market elements are increasingly complete and the entry barries for options trading are gradually lowered.The rapid devel-opment of the options market attracts many scholars to the research of options.One of the most important research directions is option pricing.According to the development status of China options market,looking for a pricing method that is suitable for options will be helpful to maintain the long-term stabilization and healthy development of China options market.In the classic Black-Scholes-Merton pricing model,the ideal assumptions are quite different from the real financial market,so the model cannot describe the uncertainty in the market.This paper introduces the theoretical results of Zhang and Li(2013)[1].They introduced asymmetric ambiguous coefficients which rep-resent market uncertainty into the classic option pricing model.The specific approach is to define asymmetric ambiguous coefficients through set-valued dif-ferential inclusion and extend the existing and unique risk neutral measure which in the complete market condition to a family of measures.As a result,the value of contingent claim is expanded to a price range.Based on the knowledge of Cho-quet expectation,minimax expectation,g-expectation and backward stochastic differential equation,European call option pricing formulas with asymmetric am-biguous coefficients are obtained.Compared with the classic model,this model aims to describe the existence range of real price by pricing interval.In order to observe the performance of the pricing model in practical applica-tion,this paper makes an empirical analysis on the pricing issue of CSI 300 ETF Options and copper options,which are outstanding in the options trading market.Firstly,the expected return rate and volatility of the underlying are calculated ac-cording to the historical closing price data.Next,the lower and upper ambiguous coefficients are selected according to the sample option contract.Two methods are used to select the ambiguous coefficients:"95%" method and mean square error&ambiguity method,and two groups of ambiguous coefficients:{k1,k2}and {k1,k2} are obtained.Then,the two sets of ambiguous coefficients are taken into the pricing formulas,the fitting price of option contracts outside the sample are calculated and the curve of fitting price and real price of the option are drawn.We analyze the fitting effect of fitting price qualitatively and judge the accuracy of the pricing model quantitatively according to the number of real option prices that fall into the pricing range.It can be found that the fitting price calculated by the ambiguous coefficients which are selected according to the sample option can properly describe the rise and fall trend of the real option price,and the pricing range determined by the ambiguous coefficients selected by the "95%" method is more accurate to describe the change range of the real price.Finally,the two models are compared.The result shows that compared with the European call option pricing model with symmetric ambiguous coefficients,the one with asym-metric ambiguous coefficients can guarantee good description accuracy of the real price and has small model ambiguity.In the further discussion of the selection of ambiguous coefficients,we find that the fitting accuracy of the pricing model to the real price can be significantly improved if the data in the duration of the option contract are grouped according to the time period and the appropriate ambiguous coefficients are selected for each group of data.In summary,the European option pricing model with asymmetric ambiguous coefficients not only can be strictly proved in theory,but also has excellent per-formance in practical application.It can be used as a powerful tool for European option pricing.