An Empirical Research Of Warrant Pricing Theory With GARCH(1,1) Volatility 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-tailed , 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 warrants pricingIn this paper, a more practical application value of the GARCH (1,1) model to estimate volatility, The model was introduced to warrant pricing theory, use of the risk-neutral pricing principles and Monte Carlo simulation method given the pricing model. In empirical research, we selected Yangtze Power warrant for study. Through analysis the underling securities--Yangtze Power shares (long G) yield, we found its yield exist marked "clusters" and non-normality, so Yangtze Power warrant can not be applied directly to the Black-Scholes pricing formula because its features do not meet the condition of the Black-Scholes model assumptions. We use Eviews econometric software to estimate the Yangtze Power stock volatility of the GARCH (1, 1) model, using Matlab mathematical software pricing model for programming, and calculating the theoretical price. Meanwhile compared to the Black-Scholes pricing formula for the price of warrant and the market price, through visual data and the average tracking difference from the analysis, we found that use the volatility GARCH (1, 1) model calculation of the theoretical price of warrant is better than historical volatility under the Black-Scholes pricing formula. We also found that the two methods of calculating prices significantly lower than theoretical market price, It shows that the market price of warrant significantly overestimate, the main reason for this phenomenon is the stock market does not allow short selling and lack of arbitrage mechanism...