A Nonparametric Approach To Test The Effectiveness Of The Option Market

The financial market of China started late and was not well developed.There is only one option,50 ETF option with 50 ETF fund as its underlying asset,listed on the Shanghai Stock Exchange at present.While it is very important to carry out research on the option products when the China Securities Regulatory Commission is going to approve 300 ETF option to be listed on SSE and SZSE,300 index option to be listed on CICC.As an important financial derivative instrument,option is of great significance to promote the healthy development of capital market.It can help investors to hedge their risks with lower cost,and it can also help different investors to make different investment choices according to their own risk preference.However,the performance of these functions are significantly affected by market efficiency,so how to reasonably test the effectiveness of option pricing means a lot.Most of the existing methods used to verify the validity of the current option market are using ex post facto inspection to verify whether the call-put parity is established or whether the initial option fee and the final income of the box spread model meet the non-arbitrage relationship.It is noted that derivatives,such as option,it's prices can be obtained indirectly by estimating the state price density function,meanwhile,the due non-arbitrage profit of butterfly spread is related to the state price density function.Although by parametric method,the closed form solution of the state price density function can indeed be deduced under the strong assumption that the stock price obeys the geometric Brownian motion,this strong assumption condition is obviously too harsh in reality.There are many nonparametric estimation methods such as nonparametric N-W kernel estimation,semi-parametric N-W kernel estimation,local polynomial estimation and so on.Based on the above,this thesis is divided into two empirical parts.First of all,using all the closing price data of 50 ETF European put options,which have been delisted from SSE,from January to July 2019,the time span is from 2018-07-26 to 2019-07-24,to compare the estimation effect of option price and SPD between nonparametric N-W kernel density estimation,semi-parameter N-W kernel density estimation,local polynomial estimation and the single factor model method(which can reduce the multiple influencing factors of option price to 1,thus solving the problem of dimensionality disaster).The result shows that the local polynomial estimation should be used at where the data is dense,and the single factor method should be used when data is sparsity.Then selecting all 50 ETF European put options that expire in June and July 2019 and also have been delisted from SSE,using 1-tick trading data from 2019-04-01 09:30:00 to 2019-05-31 15:00,on which to build butterfly combinations and test the non-arbitrage relationship between theoretically maturity profit and practically maturity profit of butterfly spread.The testing method including: regression analysis,the relationship between arbitrage opportunity,arbitrage income and option value status,butterfly spread's strike price interval,underlying asset price volatility,the distribution of the number arbitrage opportunity and arbitrage duration within the day are also concerned.Finally the empirical research concluded that though the current SSE 50 ETF option market is not fully effective,it is very close.