Research On VIX Forecast And VIX Futures Pricing From The Perspective Of Stock Market Shock

Volatility is an important attribute of financial assets and a measure of market uncertainty.It plays an important role in portfolio optimization,asset pricing and financial risk management.In the financial market,futures pricing research not only helps to improve the efficiency of resource allocation,but also provides a means for enterprises to avoid risks in order to achieve the purpose of preserving the value of future commodities.This article focuses on the forecast of the VIX index published by the CBOE and the pricing of VIX futures.Since the release of the VIX index,after decades of development,it has been recognized by the financial market,and the trading volume of VIX futures has also continued to rise.The research on them is highly representative and provides effective information for the efficient operation and normal functioning of our country’s derivatives market.The economy and society are random,and the estimation model simply relying on constant parameters cannot capture the changes of the economic market in time.Therefore,many studies have proposed the use of models with state transition probability.In addition,a large number of studies have found that liquidity and leverage effects play a key role in financial markets,and various empirical studies have also shown that the two are effective in forecasting volatility and volatility derivatives.Firstly,based on the HAR model,this paper studies the predictive ability of liquidity and leverage effect on the VIX index: the HAR model is directly modeled on the logarithmic VIX index,and the liquidity and leverage effect are introduced into the HAR model respectively,denoted as HAR-X Then,the Markov transition probability is introduced into the HAR model: the constant transition probability,denoted as MS-HAR model;and the time-varying transition probability(liquidity and leverage effect as driving factors),denoted as MS-TVTP-HAR model.In addition,this paper also selects the widely used HN-GARCH model to compare the prediction effect of the model.The empirical results show that the introduction of liquidity and leverage effects directly into the HAR model improves the predictive ability of the HAR model,and in some sample periods,both the MS-HAR model and the MS-TVTP-HAR model show good predictive effects.Secondly,this paper deduces the linear model futures pricing formula of the HAR-X model under the risk-neutral measure,and empirically compares it with the HN-GARCH model and the HAR model.The empirical results show that the liquidity and leverage effect on the prediction of VIX futures There is a significant improvement: the leverage effect is more effective for the sample period with relatively large fluctuations,and the liquidity is more effective for the relatively stable sample period.Finally,this paper deduces a nonlinear model futures pricing formula with a state transition probability model.Since the modeling form of the logarithmic VIX index cannot deduce a closed pricing formula,the MS-HAR model and MS-TVTP-The HAR model was changed to directly model the VIX index,from which the pricing formula of VIX futures was derived separately.The empirical results show that the in-sample fitting results of the MS-HAR model are better than those of the HAR model;for out-of-sample prediction,the out-of-sample results of the MS-HAR model using the true VIX index are also better than the HAR model.