The Study On European Option Pricing Problem Based On Levy Process

With the rapid development in recent decades option pricing theory, the classic Black-Scholes option pricing theory is already not a good description of the market in its assumptions are too harsh. Under the option pricing model based on Levy process with respect to the BS model will be able to better characterize the market characteristics. Levy model not only to overcome the underlying assets must be subject to the harsh conditions of geometric Brownian motion, but also to describe the process of continuous and jump through the market peak, thick tail distribution characteristics for modeling, to better reflect the description of the market process superiority.In this paper, some common model (VG model, NIG model, CGMY model) of Levy process under based on different performance on the European option pricing process described, and a comparative study with the BS model, which is selected European options for the Hong Kong Hang Seng Index Options. Firstly, the subject of the option-Hang Seng Index logarithmic returns distribution fitting, fitting results of three studies of randomly distributed and its corresponding statistical test. Secondly, the use of Monte Carlo simulation to generate several models under the Hang Seng Index’s price. Risk neutral path through the model to obtain the desired value of the option, and then get its risk-discounted prices. After the results obtained under different models of different methods, and then were the real market price of a comparative analysis of statistics, and then come in different manifestations of the Hong Kong market in the Levy process model. For several types of parameters Levy process model, we use the moment estimation method and the least square approximation correction, the use of simulation technology, and then to study the parameters of the above model, while comparison between models. Through empirical research results:(1) the Hang Seng Index in the goodness of fit logarithmic returns distribution, the distribution of Levy processes have excelled compared to the normal distribution, and the Hang Seng Index to better describe imperfect markets; (2) Monte Carlo moment estimation parameters by nonlinear least squares approximation corrected simulation, simulation results show that the accuracy of the new model parameters greatly increased, while the analog Levy model is still superior to analog BS model; (3) In sample forecasting ability, Levy model accurately than the BS model, the Levy model with the option price jump closer.