Term Structure Levy Model

Financial practitioners tend to get rid of financial risk and make money by future and option trade.Keeping a good knowledge of option pricing can help practitioners make a right decision.As computer technique develops and finan-cial practitioners gradually think highly of quantitative research,more and more financial practitioners put high weight on option pricing with mathematical mod-el.This article develops a new option pricing model-Term Structure Levy model base on Variance Gamma Model.Firstly,this article introduces the knowledge base and develops method on Term Structure Levy model,then uses the options based on GLD ETF with different strikes and different expiration date recorded on 1/27/2017 as data for empirical analysis.Before the analysis,the article does some preprocessing on the data and the put them into the parameters optimiza-tion.After parameters optimization,the article uses the new model to make a prediction on option prices.By comparing the model price and the market price,this article makes an assessment on the pricing ability of the model.At the same time,this article also introduces Variance Gamma Model with Stochastic Arrival Model,which is used to make a comparison with Term Structure Levy model.By comparison between their design intention and their performance in prediction,the article will make a future expectation on the application of this model.Firstly,the article introduces the research background of the model and then introduces the knowledge related with option pricing and method on several typ-ical pricing models.Then the article uses option prices based GLD ETF to make an empirical analysis.The analysis includes data preprocessing,parameters op-timization,price prediction,model comparison and model assessment.In data preprocessing part,the article uses Expectation Maximization algorithm to au-tomatically fix data to guarantee that the optimization will proceed well.As for the method for parameter optimization,the article uses the non-linear optimiza-tion algorithm which is Nelder-Mead algorithm.Because of the complexity of the model,it is not efficient to directly apply this algorithm.So the article makes an adjustment on the algorithm.Then the article uses the model which has been optimized to make a prediction on option price.In addition,in order to get the implied volatility surface and option pricing surface,a lot of options prices are needed so the article chooses fast Fourier transform to do option pricing to im-prove the efficiency.In model comparison,the article focuses on comparing Term Structure Levy model and VGSA model in option price prediction.The result shows that Term Structure Levy model and VGSA model have almost the same ability in data fitting and price prediction,however,Term Structure Levy model has the ability to quantify the change of parameters with respect to time.The content and methods in this article can deep financial practitioners' awareness in option investment and Term Structure Levy model can provide good data for machine learning.Firstly,this article introduces the research background and significance on Ter-m Structure Levy Model,then the related method and knowledge background for the new model are introduced,including concept and application,which is the basis for this article.Then the research design is introduced showing how the re-search proceeds.The most important part is the empirical analysis including data manipulation,parameter estimation and model assessment.The last thing is the expectation and conclusion which summarizes the disadvantages and advantages of the new model and make a prediction on the model's development.