Estimation Of Time-varying Coefficient Diffusion Model And Its Option Pricing

Option pricing theory is one of the most important theories in modern finance,and its development has promoted the prosperity of financial markets.This paper studies the option pricing and parameter estimation of the time-varying coefficient diffusion model.To a certain extent,it enriches the estimation problem of the diffusion model.And it also expands the research of option pricing under the diffusion model.At first,this paper introduces the parameter estimation of the jump-diffusion model.It introduces the semi-parametric jump-diffusion model,and obtains the approximate expression of the transition probability density by the closed-expansion method.And,the parameters in the model are estimated by the method of approximate maximum likelihood estimation.For the time-varying parameters and non-time-varying parameters,it obtains the approximate maximum likelihood estimation of the model parameters by using local constant fitting and maximum likelihood estimation methods respectively.At the same time,it proves the asymptotic properties of the obtained estimators.Secondly,this paper introduces the foreign equity option pricing under bivariate time-varying coefficient jump-diffusion model.Since the economic variables change with time,the equity price and foreign exchange rate in the text follow the time-varying coefficient diffusion model.In this paper,the bivariate Bernoulli distribution and the bivariate Laplace distribution are used to simulate the jump indicators and jump sizes,respectively.The distribution of return is analyzed by the It(?) formula and the normal asymmetric Laplace distribution.The pricing formula of foreign equity call option is proposed under the risk-neutral measure.Finally,this paper mainly studies the European option and geometric average Asian option pricing under the time-varying coefficient diffusion model which is based on Tsallis entropy distribution.In this paper,it uses the Tsallis entropy distribution which can describe the distribution of leptokurtosis and fat-tail features to model the motion of the underlying asset.Then it uses the It(?) formula,Feynman–Kac formula and Padé approximation to obtain the closed-form solution of the European option and geometric average Asian option which based on the Tsallis entropy distribution.The simulation results show that the results obtained by the method in this paper are more suitable for the simulation data.According to the analysis of real data,it obtains the value which fits the real data.And it is found that investors using the Black-Scholes model will underestimate the risk than the model in this paper.