Research On The Inverse Problem Of Option Pricing

Option is the inevitable outcome of the financial development,which can effectively separate financial asset allocation and financial risks.Reasonable and effective option pricing can benefit the financial market participants to achieve a win-win situation.Option pricing includes forward and inverse problems.Mathematically,the forward problem of option pricing is essentially solving the option price;the inverse problem of option pricing is essentially the study of implied volatility,namely,the valuation of derivatives is consistent with the market price.Implied volatility of options is largely a reflection of market expectations of future price volatility.Option pricing must first predict the future volatility changes to predict option price.Therefore,it is more important to study the inverse problem of option pricing than to solve the direct problem of option pricing.In this paper,the implied volatility of the inverse problem is the main research object.According to the three aspects of the "implied volatility smile" phenomenon,the term structure and implied volatility surface,we can obtain more relevant information and stronger influence factors on implied volatility for further analysis and research.Nowadays,there are many methods to research on implied volatility.In a general sense,the common methods of modeling can be classified into three types:the parametric model,semi-parametric model and non-parametric model.Parametric model is often predisposed to specific relationships between factors,and the model is relatively simple and direct.Part of structure on semi-parametric model is known and this model needs to estimate the parameters.Non-parameter model is well-known in statistics.It can be used in a variety of shapes,but it performs well if there is a substantial amount of data.Based on these characteristics,we propose four new models of the implied volatility:the double-window Nadaraya-Watson Gaussian kernel regression model,Similar semi-parametric Nadaraya-Watson Gaussian kernel regression model,Parzen window uniform kernel regression model and Similar Parzen-window Nadaraya-Watson Gaussian kernel regression model.In this paper,the forecast models are discussed in detail,including model analysis and empirical test.We have done empirical tests on a large body of option data of AAPL option.These tests indicate that our models have higher accuracy and adaptability to the real data than existing models.First we divide the data of AAPL option into two parts.The difference is that one part is large and the other is small.The large data set is used for fitting models,and the other is used for testing the forecasting ability of the models.Through the empirical analysis and test in this paper,we get that our models can be well applied to the market of Apple stock option and have a better forecasting ability,especially when dealing with a large number of datasets.