American Option Pricing And Risk Measurement Under The Mixed Gaussian Model

With the development of financial markets,options with huge leverage and hedging function,so it is favored by the majority of investors.How to price has become a widespread concern of scholars? Scholars use the classical Brownian motion model and fractional Brownian motion model to study the pricing of options.But the empirical study of the financial market shows that the classical Brownian motion model and fractional Brownian motion model can’t describe the price change of financial assets perfectly.It is necessary to find a suitable stochastic model to describe the changes of financial asset prices.In this paper,the pricing and risk measurement of American options under the mixed Gaussian model are studied.This paper is mainly divided into three parts.In the first part,using the mixed Gaussian model to characterize the underlying price changes,the pricing formula of American options under this model are deduced.Firstly,the option price satisfying stochastic differential equations is established.Secondly,by solving the stochastic differential equations to obtain a partial differential equation.Finally,using the boundary conditions of American option get the pricing formula of American option under the mixed Gaussian model.In the second part,Firstly,the logarithmic distribution of the underlying asset price is obtained by using the stochastic differential equation satisfied with the underlying price of the option.Secondly,measure the risk of American options by the return mapping valuation method and Monte Carlo simulation method.Finally,several specific examples of risk measurement of four American options are given,such as China International Trade etc.In the third part,we examines the validity of the proposed model by using the historical data of ten American stock options listed on the Hong Kong stock exchange.Firstly,the statistical characteristics of the historical data of the option label are tested.Secondly,the change path of the option price and the price of options under different models are simulated.Finally,the simulation results are analyzed.The results show that the option pricing under mixed Gaussian model is closer to the real value of the option than the classical B-S,so it is reasonable and effective to use the mixed-Gaussian model to price the option.The study not only provides new theoretical basis for the research of option pricing,but also takes a step in practice.At the same time,it also provides a theoretical basis for the application of option pricing in risk management.