An Empirical Research Of Option Pricing With Autoregressivw Conditional Heteroskedasticity Model

The volatility of stock price is a decisive factor in derivatives Pricing. Black &Scholes given European option pricing formula price,whose important assumptions is that stock price obeying geometry Brownian motion in a non-arbitrage analysis and the volatility is a constant.However, more and more empirical results show that the stock yield exist significantly high kurtosis and fat-tailer.generally difficult to describe the normal distribution,and the volatility marked variability characteristics.Therefore,the relaxation of stock price volatility constant is significance for the study of the option pricing.Literary grace this estimate the volatility with conditional heteroskedasticity serial models ( mainly use GARCH (1, 1),EGARCH, TGARCH three models),And introduce it to the option pircing.In empirical research, we selected the Cheung Kong stock and warrants for study. Through analysis the underling securitier-- Cheung Kong shares yield,we found its yield exist marked variability characteristics and non-normality, its features do not meet the condition of the Black &Scholes model assumptions.So Cheung Kong warrant can not be applied directly to the Black &Scholes formula.We estimate the Cheung Kong stock volatility with GARCH (1, 1) model, EGARCH model and TGARCH model,then calculate the theoretical price of warrants.Meanwhile compared to the B-S pricing formula for the price of warrants and the market price.Through visual data and the average tracking different from the analysis,We found: First of all, Look from coming up wholly, The pricing performance of the GARCH (1, 1) model is only better than traditional B-S model slightly, the superior performance is relatively small and not statistically significant. EGARCH model and TGARCH model outperform other modles and statistically significant. Use EGARCH model and TGARCH model go on pricing to be most effective, the result obtained is close to the market price most. Secondly, Subdividing the whole sample into In-the–Money Option, at-the–Money Option and Out-of-the-money option,We found:In the Out-of-the-money option sample, the traditional B-S model outperform other modles,but the superior performance to EGARCH model and TGARCH model is not statistically significant. And the pricing performance of the GARCH (1, 1) model is not so good as other models. In the at-of-the-money option and In-the–Money Option sample, the pricing performance of traditional B-S model is not so good as other models,and statistically significant.THE other models all improve the pricing performance of traditional B-S model.