Adaptive Option Implied Volatility:Construction And Market Tests

As we all know,Breeden&Litzenberger(1978)had laid the foundation for subsequent research on extracting risk-neutral distributions and model-free implied variance from option prices.After that,since the insurance features of options and the S&P500 options volume had been increasing explosively,the research on model-free option implied volatility had been deeply done,such as Britten-Jones&Neuberger(2000),Jiang&Tian(2005),Carr&Wu(2009).So,our article extends the research of Jiang&Tian(2005),Carr&Wu(2009)by relaxing interest rates being stochastic,and takes account of the dividend-protection mechanism of options;we also continue to extend previous and traditional option model-free implied volatility,by incorporating the consideration of the distinguishing features of SSE 50ETF options,in order to make the model-free option implied volatility in our article to be more adaptive and general,which can be suitable for S&P500 options,but also SSE 50ETF options.To summarize our improving work,our article call the final model-free option implied volatility as the adaptive option implied volatility,the improvement is called as the adaptive mechanism.Compared with the traditional VIX,Firstly,our implied volatility allows stochastic interest rate,which means research can be started on the most general hypothesis that there is no arbitrage in the market,so implied volatility can be derived under a more general semi-martingale process,the theoretical framework is extended to most general level.Secondly,takes the effect of dividend protection into account,we find that only adjustment is making dividend-adjustment to forward price.More importantly,small number and wide increments of strike prices of 50ETF options in trading still make many situations worse,transaction costs and trans-position costs in this option market are very large,and hardness to short any underlying asset also makes research more different.All these distinguishing features would make traditional construction of model free implied volatility unsuitable to 50ETF options market.In order to handle it,an adaptive option screening mechanism is proposed.The option screening mechanism is able to choose the most informative option data automatically to calculate our model-free implied volatility index,the following interpolations and extrapolations are conducted on the basis of these filtered option prices,thus calculated option implied volatility will make the most use of the best information content contained in option market.Hence,the Adaptive Mechanism contains stochastic interest rate effect,dividend protection effect and options screening mechanism.This article proposes an adaptive mechanism to extract the implied information from options,based on this adaptive mechanism proposed by this article,we can obtain an improved and better VIX-AVIX,and Adaptive forward volatility.Our empirical study based on China SSE 50ETF options market demonstrates that compared with the iVIX,a traditional VIX in 50ETF option market,AVIX is a more efficient forecast for future realized volatility,and AVIX is a better reflection of implied volatility and market sentiment,as a more accurate,sensitive and forward-looking market volatility index.Hence,the proposed Adaptive option mechanism is more suitable to China 50ETF option market,its improved ability is very significant.And these conclusions are robust.Due to the good nature of Adaptive option mechanism,generality and automatic adaptive quality,this article continues to construct the option forward volatility,applied to test whether investor expectation in 50ETF option market is rational.If result behaves irrational,is the performance in option market overreaction or underreaction?Empirical studies show that overreaction do exist in 50ETF option market,investors always overestimate the short-term information of volatility and ignore the long-term discipline of option market.Hence our article continue to explore the latent reasons,we find that the most possible interpretation of this irrational expectation can be the investor sentiment,but the traditional liquidity effects only can afford a little explanation.This can show that now 50ETF option market is most influenced by market investor sentiment.It can be predicted that,when the number of strike prices traded in option market can be increasing and the cost of market transaction can gradually decline,the expectation in 50ETF option market will tend to be rational.