Research On The Asymptotic Option Pricing Under The Pure Jump Levy Process

On February 9,2015,the Shanghai 50ETF option has officially traded.It means Chinese stock market ushered in the "option era".The breaking news will enrich Chinese financial market,it means that Chinese financial market has been closer to the international market.At the same time,the theory of research in option pricing is experiencing constant innovation.The option pricing model under pure Levy process attracts widely reviews by scholars.In this context,citing new methods for option pricing and Simulation is very important in Chinese specific environment.It can not only give us some theory methods to perceive Chinese derivatives trading operation criterion and degrees of supervision,so that we can get some advice and assistance for Standardized operation of the market,but also it can help us to find the option pricing model in theory in Chinese special environment.Option pricing model has always been a hot issue in financial field.The traditional pricing model represented by Black-Scholes created a new chapter in the theory of financial assets,and it is the cornerstone of derivatives pricing.It based on the assumptions that the logarithmic return rate obeys the normal distribution and some other assumptions.But market research has proved that financial data shows strong non-normality.And the market is not as perfect as it assumes.The Levy process is a stochastic process with independent increment,steady increment and random continuous distribution function.It is widely used in medical and financial aspects.The pure jump Levy process is assumed that the financial asset price process has an infinite number of jumps at any finite time,including the frequent occurrence of small jumps and very few leaps.Pure jump Levy process can describe the characteristics of logarithmic yield better,compared with the B-S model it has a higher accuracy.But a lot of problems occur:Levy process of pricing model structure is complex,parameter estimation and random number simulation have also a little difficulty.At the same time,the efficiency of generation algorithm of Levy random number is low.In consideration of these problems,this paper uses the asymptotic model to analyze the characteristics of Chinese options market.By using the martingale central limit theorem,it can connect the pure Levy process pricing model with the B-S model.Meanwhile,we can obtain the asymptotic model by using the Taylor expansion.The main study of this paper is concluded as follows:1.In this paper,we give some deduced formula of the B-S model and the pure Levy process pricing model,so that we can make it clear in theory.The study of B-S model is from two aspects:in terms of differentials and the risk neutral point.We apply varying-time Brownian motion to solve the problem of option pricing model under the pure Levy process.It is helpful to apply the models into the practice by understanding and explaining the theory.Meanwhile,it laid the foundation of the empirical analysis.2.In the framework of Monte Carlo simulation,we established two typical models of pure jump Levy process:the VG process option pricing model and NIG process option pricing model.We use the generalized moment estimation to estimate the parameter and discuss the risk-neutral adjustment method.Finally,we analyze the price of the Shanghai Stock Exchange 50ETF with these models,and compare the result with the B-S model theory value.The empirical results show that the pure jump Levy process can fit the characteristics of the logarithmic rate of return better.It fully illustrated the Shanghai 50ETF market is imperfect.At the same time,VG process model and NIG process model are better than the B-S model.3.We use nonlinear least squares estimation to evaluate asymptotic model and get regression model for pricing.So,we can do some research with each model.Finally,we find that the asymptotic model is simple and convenient.In this paper,we use the asymptotic model to do forecast analysis,and gain the feasibility and simplicity from asymptotic model.In the empirical part,we use MATLAB software to compute the parameters by nonlinear least squares estimation method.Next,we process the data and predict the market.The results show that the fitting results are better than the B-S model,and the forecasting results are better than B-S model in a certain range.Although there is some distance between the pricing model and the pure jump Levy process option pricing,the asymptotic model is simple and easy to implement.