GARCH Diffusion Option Pricing Theory With Transaction Costs And Its Application

This dissertation is intended to study GARCH diffusion option pricing problems, so as to establish the mathematic models of option pricing with GARCH diffusion process by means of mathematical tools such as martingale methods and stochastic analysis, to deduce the GARCH diffusion option pricing equation, and to make an empirical analysis for the historical data of Shanghai and Shenzhen stock markets by using GARCH diffusion option pricing models.Firstly, we summarize the development of the option pricing theory, and the study situation of the option pricing theory with transaction costs. Secondly, the first four conditional moments of the integrated variance implied by the GARCH diffusion process are derived analytically. Based on these conditional moments and a power series method, an analytical approximation formula to price European options under the GARCH diffusion model is obtained. Thirdly, based on GARCH diffusion process, the canonical Black-Scholes option pricing model is extended a situation with transaction costs. Finally, we made an empirical analysis on volatility of daily returns in the Shanghai and Shenzhen stock markets by using the the GARCH (1,1) model with more practical value. The results show that the Shanghai and Shenzhen stock markets have obvious heteroscedasticity and volatility risk premium and a causal relationship between the two stock markets.