A Neural Network Approach To Calculate Minimum Variance Delta

Derivatives are a time-honoured financial contract that has always played an important role in the financial sector.Option is the most prevailing one.As China continues to open up in the financial sector,the issuance of corresponding option contracts has also been put on the agenda.Although China’s options and market size are constantly expanding,compared to foreign countries,our market is still very immature.Due to the lack of actual transaction data,domestic scholars’ research on options mainly focuses on pricing,and few of them can provide actionable ideas and methods for option traders.As has been pointed out by a number of reasearchers,the normally calculated delta does not minimize the variance of changes in the value of a trader’s position.This is because there is a non-zero correlation between movements in the price of the underlying asset and movements in the asset’s volatility.The minimum variance delta takes account of both price changes and the expected change in volatility conditional on a price change.We first use daily data on the SSE 50 ETF options to drive a relationship between the expected change in implied volatility and three variables: the return on the SSE 50 ETF,the moneyness of the option,and the remaining life of the option.The minimum variance delta calculated based on this model(hereinafter collectively referred to as the three-factor model)reduces the hedging errors by 5.93% and 1.73% for call and put options,respectively.We then enhance the model with an additional feature: the level of the SSE 50 ETF volatility index prior to the change being observed.The minimum variance delta calculated based on this model(hereinafter collectively referred to as the four-factor model)reduces the hedging errors by 14.03% and 8.83% for call and put options,respectively.