Prediction Of Implied Volatility Based On No Arbitrage Constrained Neural Network

In the financial derivatives market,option pricing plays an important role in improving the financial market system.If we can accurately predict the options price,investors and financial institutions can establish trading strategies according to them,and carry out accurate asset management to disperse risks.However,due to the complexity of options,it is very difficult to price them directly,so we can further determine the price of options by studying the implied volatility corresponding to the option price.Therefore,it is of great significance for financial institutions to accurately predict the implied volatility.In this paper,a no arbitrage constrained neural network is proposed to predict the implied volatility.It imposes constraints to punish the loss function of the neural network to ensure that the implied volatility meets the no arbitrage condition.It innovatively combines data-driven deep learning technology with financial prior knowledge,which greatly improves the generalization ability of the neural network model.Compared with other nonparametric models whose inputs only include the underlying asset price,strike price and time to maturity,this paper also adds the volatility index as a new input information to avoid the model falling into over fitting,and effectively improves the prediction ability of the model.In the empirical analysis of TXO call options,we design two training methods:training one day before,forecasting one day after,and forecasting one day after training seven days before.From the results of average absolute percentage error and root mean square error on the test set,the learning method of one day after forecasting seven days before training is slightly better than that of one day after forecasting seven days before training.We also compare the constrained neural network model with the traditional AHBS model.In the test set,the prediction ability of our model is significantly better than that of AHBS model.The experiment proves the accuracy of our model.In order to verify the effectiveness of our model constraint improvement,we also set two groups of models without no arbitrage constraint and without volatility index as the input as the control model.In the test set,the average absolute percentage error and root mean square error of the improved model are significantly lower than those of the control model.The empirical results show that the generalization ability of our improved model is better.Generally speaking,this paper has two main contributions.First of all,the research of this paper is helpful to the application of machine learning method in the financial field,which obtains an accurate implied volatility model based on constraint neural network.Secondly,this study provides a method to combine data-driven model with financial knowledge,which has a certain reference value for the follow-up research.