Research On Implied Volatility Based On Neural Network Under Leverage Effect

Among many derivatives,options are known as the most shining pearl on the crown of modern finance.Option is not only favored by speculators because of its low cost,high return and high volatility,but also a very high-quality hedging tool,which is widely used in hedging.Option as a right,how to determine its price has always been an interesting and meaningful problem.In the 1970 s,Black-Scholes option pricing model completely changed the problem from a financial problem to a mathematical problem.Today,it is still the most important tool for option traders.In many years of application,we find that although this model is called pricing model,it has never been used to calculate the price,but through the existing market price to calculate various parameters,such as implied volatility.Such calculation of implied volatility and other related parameters will have a large error.In this paper,machine learning method is used to solve the problem of implied volatility.We assume that implied volatility is not a strictly stochastic process,but is highly correlated with stock price,stock return and past implied volatility.This assumption is inspired by leverage effect.Although there is no analytical model for this relationship,We can use deep neural network(DNN)and recurrent neural network(LSTM)to calculate the implied volatility,verify the hypothesis which based on leverage effect and solve the problem of volatility distortion in derivatives trading.We use the SSE50 index price and the SSE50 index option implied volatility as the training and testing data.The deep neural network only performs well in a short term,while the recurrent neural network LSTM can reproduce the implied volatility pattern in a long term,Considering that the error of the non iterative model is larger than that of the iterative model,the actual rolling calculation results should be better and more stable.The results show that the implied volatility can be obtained without using the option price.We use the double layer LSTM to compare with DNN.There are great improvements in the type and structure,so that it still achieves excellent performance in testing set without much samples and rolling training.