Analysis Of The Effect On Index Options’ Market Price Of Index Futures Backwardation And Contango

According to the no-arbitrage theory,there are lower boundary and upper boundary of options’ value.In general,the price of option falls between the lower and upper bound.In fact,it is not surprising that option’s price falls below the lower boundary in Chinese capital market.Focusing on CSI 300 stock index options,this article analyzed the effect of future backwardation or contango on the option price.All of the option sample are classified into eighteen groups according to the attribute of option(“call”、”put”),the term of option(“Long”,”Medium”,”Short”),and the strike price of option(“ATM”,“ITM”,”Deep ITM”).After data analysis,firstly it is found that the percentage of option contracts which have a close price lower than the theoretic lower bound is 28.45%.Secondly,the phenomena of falling below the lower bound is unusual for ATM options and more frequent for call options than put options.In terms of the relationship between futures’ backwardation or contango and option price,the descriptive result shows that when the extent of futures’ backwardation(contango)gets bigger,the possibility of falling below the theoretic lower bound for call(put)option price becomes bigger as well.Furthermore,this article sets up XGboost models and time regression models to each of the eighteen option groups.According to the regression result,the extent to which the call(put)option price falls below its lower boundary becomes bigger when futures’ option is in backwardation(contango)and the extent gets bigger as well.As a result of limited liquidity,the relationship in “P-Long” option groups was not clear and the relationship in “Deep ITM” option groups is much stronger than in “ITM” groups.Furthermore,based on the regression model used before,this article uses two methods which are time regression based on alternative emotion group and adding interaction term to the regression model respectively to analyse the role of market emotion plays in the relationship between futures’ backwardation or contango and option price.This article uses the CISI indicator to represent market emotion which is downloaded from website.The results from the two methods are the same.During the time when the market emotion is instinct,the relationship between futures’ backwardation or contango and the extent to which the option price falls below its lower boundary is much more strong.The result shows that market emotion is an important channel through which the future backwardation or contango has effect on option price.In the next step,this article analyses the influence of futures’ backwardation or contango on the process during which the option price moves from down to up of the lower bound.This article sets up logit regression.The dependent variable is a dummy variable the value of which equals 1 means the recover of option price happens.The key independent variable is also a dummy variable the value of which equals 1 means the trading volume of future contract increases compared with last trade day.In all of the option groups,the regression parameter of the key independent variable is positive.While in terms of put options,the result contains little information because the sample of put options the end day close price of which falls below lower bound is limited.In general,it is supported that arbitrage transaction promote the recover of option price.