| The Pricing Kernel,also known as the Stochastic Discount Factor(SDF),has been extremely important in asset pricing since its inception and is an integral part of the asset pricing building.Research on pricing kernels can explore the implied market utility function and investor’s risk appetite,and incorporate all asset pricing models into a generalized model to price all financial assets.In the traditional economic theory,pricing kernel should appear as a monotonically decreasing function according to the basic assumption of rational investor risk aversion behavior.However,Ait-Sahalia and Lo(2000)estimate the empirical pricing kernel by dividing the risk-neutral distribution by the physical distribution.Their results show that the pricing kernel has a local increase,which is contrary to the conclusions of traditional financial theory.Thus,the "pricing kernel puzzle" was born.Later,more and more empirical studies have shown that empirical pricing kernel is not a monotonically decreasing function,and investors are not completely risk-averse.Many scholars have used data from financial markets in different countries.Through empirical research,it has been confirmed that the phenomenon of "pricing kernel puzzle" is widespread.According to the standard framework for pricing kernel estimates proposed by Rosenberg and Engle(2002),if the pricing kernel is to be solved,one of the two sets of data necessary is an index that can reflect the total wealth,and the other is the option.Before 2015.although it was possible to find an index that would reflect the overall endowment of society,but limited to options that did not correspond to it,research on pricing kernels could not be carried out.Although China’s financial derivatives market started late,since the launch of the Shanghai and Shenzhen 300 stock index futures on April 16,2010,the China Financial Futures Exchange has achieved rapid development and market functions are increasingly playing,but the development of the derivatives market is still in its infancy.The stage is far behind mature foreign markets.In order to improve China’s capital market,the State Council issued the "Several Opinions on Further Promoting the Healthy Development of the Capital Market" on May 8,2014,stating that it is necessary to gradually enrich the stock index futures,stock index options and stock option varieties,and the launch of stock options is put forward.schedule.On February 9,2015,approved by the China Securities Regulatory Commission,the Shanghai Stock Exchange officially listed and sold 50 ETF options.The listing of options marks China’s entry into a new era of diversified investment and risk management.According to the Shanghai Stock Exchange’s stock options market development report released on February 1,2019,the Shanghai Stock Exchange’s stock option market development report shows that the 2018 SSE 50 ETF option market is running smoothly,the pricing is reasonable,the economic function is gradually exerted,and the overall risk is controllable.After nearly four years of development,the SSE 50 ETF option has become one of the world’s major ETF options.Last year,the cumulative turnover of SSE 50 ETF options was 316 million,an increase of 76%from the 180 million in 2017.The cumulative face value was 8.35 trillion yuan,and the accumulated royalty was 179.76 billion yuan.The average daily turnover was 1,301,300,with an average daily holding of 1,187,700,with a daily average face value of 34.382 billion yuan and a daily average premium of 740 million yuan.It can be seen that both the market size and the activity level are steadily increasing,and the indicators for measuring market quality and risk are at a reasonable level.Based on the steady and rapid development of China’s index option market,research on the pricing kernel of China’s financial market has been carried out.This paper first calculates the monthly objective risk probability density by selecting the SSE 50 ETF index that reflects the overall wealth of society.After processing the data,it is found that the logarithmic yield of the SSE 50ETF has a sharp peak tail and a conditional heteroscedasticity,which satisfies the GARCH process.By comparing the fitting results of the normal distribution and the empirical probability distribution to the time series,it is found that the GARCH model of the empirical probability distribution can better simulate the edge distribution of the time series.Next,construct a risk neutral probability density parameter model of cubic spline interpolation,and use the SSE 50ETF option data(transaction volume.exercise direction,exercise price,closing price)observed in the market to estimate the model parameters and bring them into the market.The original model obtained a monthly risk neutral probability density.In order to verify the accuracy of the risk neutral probability density estimation in this paper,this paper also uses the estimated risk neutral density curve to inversely fit the market price and calculate the degree of deviation between the fitted value and the market price.Sex density can better fit the market price and can extract market information more effectively.Dividing the monthly risk neutral probability density from the objective probability density,we obtained the monthly pricing kernel of the Chinese market.Through the visual observation of the pricing kernel,we find that most of the time pricing kernels show a monotonous decreasing feature.In some special periods.the pricing kernel presents the characteristics of local increment or U-shaped pricing kernel.In order to more accurately describe the monotonicity of the pricing kernel,we constructed a monotonic statistic,and conducted a monotonic test on the pricing kernels of all months.The results show that at the 95%confidence level,we can reject the pricing kernel monotonically decreasing in 18%of the period.For the first time,empirical evidence on the existence of the "principle of pricing nuclear" in the Chinese market is given.Finally,this paper analyzes the relationship between pricing kernel and the trend of the Shanghai Stock Exchange,and finds an interesting phenomenon;the degree of non-monotonic decline in pricing is very large(U-shaped pricing kernel or the local increment is obvious)often indicates that the market will have a larger trend in the next period.The degree of shock or decline.ln order to verify this phenomenon,we use the pricing non-monotonous decreasing statistics to regress the next-term market yield and the volatility.The results show that the non-monotonic statistic is significant,the non-monotonic decline of the pricing kernel is inversely related to the market earnings of the next period and positively related to the market amplitude of the next period.The main contribution is to conduct a comprehensive and systematic study on the pricing kernel in the Chinese market.Using the option market and the underlying index data since February 2015,the monthly pricing kernel of 50 months has been estimated.The empirical evidence of "pricing kernel puzzle" in China’s financial market,and innovatively linking the phenomenon of "pricing kernel puzzle" to the next market trend.After giving theoretical support,it is proved by empirical test that the phenomenon of "pricing kernel puzzle" has a certain predictive effect on future market trends. |
