Research On The Index Option Returns Based On Dynamic Delta Hedge Strategy

The Black-Scholes-Merton option pricing model proposed by Black,Scholes,and Merton states that because the price of an option and its underlying stock both depend on the same source of potential uncertainty,thereby a risk-free portfolio can be constructed by holding a certain percentage of option positions and the underlying stock positions.However,existing literature(such as,Bakshi et al.(2000))proves that the average return of a Delta-hedge(buying options and deltahedging their underlying assets)option based on the Black-Scholes-Merton model is not risk-free rate.Broadie et al.(2009)find that the delta hedging strategy significantly reduces the exposure of options to the underlying assets.Using the return of the delta-hedged option as the research object can largely avoid the influence of the premium of the underlying stock on the option return,so that the direct impact of factors of the return of the option beyond its underlying stock price can be more effectively explored.Although the existing literature(such as Cao and Han(2013),and Cao(2017),etc.)has proved that the return of Delta neutral stock options is affected by its underlying stock characteristic variables,but because the stock index is often considered as the approximate measure of performance of the whole stock market,the factors that affect stock index returns are not exactly the same as the factors that explain changes in individual stock prices.Therefore,based on the impact factors of stock index return rates proposed in the existing literature and the dynamic delta hedging strategy,this paper studies the explanatory power and prediction performance of stock characteristic variables,macroeconomic indicators,and market friction for index options during the sample period from January 1996 to June 2019.The research ideas of this paper are shown as follows: First of all,based on the returns of Delta neutral option defined by Bakshi and Kapadia(2003),this paper constructs a dynamic delta hedging strategy to calculate the excess returns of Delta-hedged options.Secondly,the linear model is used to analyze the influence and impact channel of the 11 variables that represent stock characteristic variables,macroeconomic indicators and market friction on the return of Delta-hedged stock index option.Thirdly,referring to the research framework of Dangl and Halling(2012),this paper uses the historical long-term average return of Delta-hedged Options as a benchmark to test the in-sample and out-of-sample prediction performance of the above variables for the Delta-hedged index option return based on the difference of mean square prediction error(MSPE-difference)statistic.Finally,the market timing strategy is used to further analyze the out-of-sample prediction performance of the prediction model from the perspective of investors’ actual trading.The main conclusions of this paper are as follows:(1)Consistent with the conclusions of Bakshi and Kapadia(2003),the excess return rate of the dynamic delta hedging strategy based on the long position of index option and the short position structure its underlying stock index is negative at a significance level of1%(2)Although stock characteristic variables,macroeconomic indicators,and market friction that affect stock index returns can also explain the changes in delta hedge option returns over time series,except for stock index volatility,other variables are likely to have an impact on the returns of Delta-hedged options via volatility risk premium;(3)The volatility risk premium has a significant and dominant influence on the returns of Delta-hedged options,and it is positively related to the returns of Delta-hedged options in time series;with the certain volatility risk premium,the negative value of the return of Delta-hedged options is greater in the period when the stock market is more volatile;(4)the dynamic delta hedging with a higher rebalancing frequency without considering transaction costs is more effective;(5)multivariable predictive model has the best in sample and out of sample prediction.Moreover,under the indicating of the hedged option returns predicted by multivariable predictive model,market timing strategy almost outperformances the benchmark strategy.This multivariable predictive model is able to earn extra returns compared to benchmark strategy.This paper contributes the literature in the following two ways:(1)Compared to the previous study,which mainly focuses on the relationship between the returns of delta-hedged firm options and the firm’s characteristic variables.This paper takes macroeconomic variables into consideration to study what causes the negative excess return of delta-hedged options,which is a reasonable supplement to the existing literature.(2)This paper extends the research method of impact analysis by using the volatility risk premium as a control variable to further explore the influence channel of stock characteristic variables,macroeconomic variables and market friction on stock index returns.(3)Different from the majority of existing literature that use statistic variables to test the prediction power,this paper further tests the prediction performance of impact factors from the perspective of market transactions through market timing strategies.This test of predictability of the returns of delta-hedged options is more intuitive and straightforward for investors.