| In 1973,Black,Scholes and Merton proposed the B-S-M option pricing model,and the research on option pricing entered a new stage.On the one hand,the everincreasing variety of options brings a variety of available financial tools to traders and institutional investors,and on the other hand,it also challenges their risk management capabilities.And risk management is the most important content in option research and application.Many option traders choose delta neutral strategies for risk hedging when holding options.The implied volatility is calculated through the B-S-M model and market data,and then the delta hedging ratio is calculated based on the implied volatility,and the corresponding assets are allocated to make the investment portfolio reach delta neutral,thereby reducing risk exposure.However,because the theoretical world of the BSM model assumes that the implied volatility is a constant,and in the real world due to the fluctuation of the underlying asset,the influence of option supply and demand,etc.,the option volatility smile and the implied volatility are negatively correlated with the price of the underlying asset.Therefore,it is not the best choice to use the BSM model to introduce delta(hereinafter referred to as BS delta)for risk hedging in the real world.This paper draws on the minimum variance delta model used by Hull and White(2017)and tries to use data-driven methods to give a better minimum variance delta hedging ratio and provide a risk hedging reference for option market traders.This article selects the daily market data of SSE 50 ETF options,and uses machine learning algorithms such as ridge regression,random forest regression and gradient boosting regression tree to train and learn on the basis of the minimum variance delta of the Hull and White(2017)quadratic model.Grid search and cross-validation are optimized,and the minimum variance delta is predicted by rolling window,and the evaluation index constructed by Hull and White(2017)is used for comparison.The conclusion shows that the ridge regression algorithm can improve the effect of call option delta hedging,while the improvement effect of the two integrated learning algorithms of random forest regression and gradient boosting regression tree is not satisfactory.Then this paper compares the actual price of options,BS theoretical price(calculated by BS model)and MV theoretical price(calculated by ridge regression algorithm),and finds that the pricing efficiency of options in the Chinese options market is relatively low,and the actual price of call options is slightly lower than the theoretical price.The actual price of the put option is higher than the theoretical price;and it is concluded that the minimum variance delta hedging is effective for the call option.Finally,this article backtests the trading strategy of call options with negative time value in the market,and uses the minimum variance delta predicted by the BS delta and ridge regression algorithm to dynamically hedge the strategy.The conclusion is that the minimum variance delta is used to dynamically hedge the strategy.Both the rate of return and the maximum retracement have an improvement effect. |
