Robust Cos Method For Option Pricing In Affine Jump Diffusion Models

Recently,in addition to meet the daily consumption,how to accumulate funds for effective value-added,is appealing to more and more attention.Among them,options have gradually attracted people’s attention by virtue of their risk aversion,strong professionalism and flexible ways.Their position in the financial derivatives market is increasing day by day,and they are also a hot research topic in modern financial theory.Option pricing has always been an indispensable part of modern financial theory research.With the development of China’s financial market,the need for this kind of research is becoming very strong.Therefore,the study of option pricing affects the investment strategies of various investors from the micro perspective and the financial development of the whole country from the macro perspective.More importantly,the successful listing of 50 ETF option shows that China’s financial market is moving towards a stage of gradual improvement,which makes the community to increase expectations for the accuracy of option pricing.Therefore,the establishment of a more mature option pricing model is imminent,for the promotion of the development of the entire financial market is also extremely important.Firstly,this paper introduces the general affine jump diffusion model,including Merton jump diffusion model,Bates stochastic interest rate jump diffusion model,Kou double exponential jump diffusion model and CGMY model.Then,based on the robust Fourier-cos method,we use these models to price options.From the CPU calculation time of several pricing methods,we known that compared with other methods,the fast FourierCos method is faster in calculation time.Comparing the absolute error of the option price calculated by the robust Cos method of these models,we can see that the option price calculated by the robust Cos method of Merton model,Kou model and CGMY model has higher accuracy,especially the CGMY model has the best effect.Numerical tests show that the robust Cos method is stable for all cases when α ∈1.0001,1.2 and ∈ 6,18 is reasonable in most cases except when the probability density function of the underlying asset has a heavy tail.In the case of thick tail,the option price is stable when ∈ 17,25.With different T values the above results are robust.The numerical strength test shows that the robust Cos method has high accuracy and robustness.For efficiency comparison,four Cos methods are used to price options for several types of models.The error convergence of the robust Cos method is better than that of the option parity formula Cos method,and the error convergence results will not change with the change of T.Considering the robustness of robust Cos method,it is found that several Cos methods have better robustness.Finally,the implicit parameter method is used to estimate the parameters of Heston stochastic volatility model,Kou jump diffusion model and CGMY model with Markov chain.Comparing the fitting error results,we find that the implicit parameter method has good stability for parameter estimation of several models.