The Application Of Information From Option Implied Risk Neutral Density

Breeden and Litzenberger(1978)proved that the probability distribution of the asset’s price(or yield)can be obtained from its corresponding option price by some mathematical computations.Canina and Figlewski(1993)proposed that the information contained in the implied volatility caused a strong interest in studying the implied parameters of the options.For a long time,the research of extracting implied moments from option price is mainly for US market and emerging markets,such as Taiwan and Hongkong.We use the Shanghai 50ETF option price data to extract the risk neutral probability density function,then get the moments under the two measures.On the one hand,the volatility under two measures has a good explanatory for the future volatility,while the future kurtosis is more difficult to predict.We also found the effect of incremental information is obvious.Besides,skewness and kurtosis under the two measures contain little information of the volatility risk.Therefore,it is necessary to include skewness and kurtosis risk factors in the analysis of Chinese market risk.On the other hand,by analyzing the information of the risk premium,we find investors in the pursuit of market excess returns,pay less attention to information of kurtosis risk premium.Relative to volatility risk premium,skewness risk premium can explain more about the market excess returns.When volatility of skewness is low,investors will demand higher excess returns.It also find that the skewness risk premium and kurtosis risk premium have a significant explanatory power for each other,but compared with skewness and kurtosis risk,volatility risk still has its own independent driving factors.Finally,the two indicators representing the liquidity of the market are introduced,and it is found that the investors in the Chinese market are less aware of the market volatility through market liquidity.But market liquidity can provide the expected information of kurtosis.When the transaction is not active,the market expects the future kurtosis will increase,and investors will ask for a positive compensation.