Research On Pricing Method Of Stock Index Options Based On GARCH Model

Option is one of the most important trading tools in financial market, it has the function of price discovery, hedging, speculation and interest arbitrage. The problem of option pricing can be considered as the most important part in option theory. All the factors that affect option pricing, volatility is regarded as one of the most significant. The traditional Black-Scholes option pricing model assumes that the volatility of the underlying asset is a constant figure. However, recent research reveals that the volatility is time-varied.The first part of this article is about the research on the underlying asset of The Shanghai 50 ETF Option which is Shanghai 50 ETF. In this part, it can be concluded that the volatility of SSE 50 ETF is not a constant figure. The volatility figure of logarithm of SSE 50 ETF shows that there exist volatility cluster, i.e. big fluctuations always follow big fluctuations, and small fluctuations follow small fluctuations. This paper principally aims to present a new method of option pricing of the SSE 50 ETF Option. By this character, the model of Generalized Autoregressive Conditional Heteroskedastic, namely GARCH model, Exponential Generalized Autoregressive Conditional Heteroskedastic (EGARCH) model and Threshold Auto-Regressive Conditional Heteroskedastic(TARCH) model are put into use in order to estimate the character of underlying asset of SSE 50 ETF Option. In order to build a model more in line with the characteristic of real financial market, investor sentiment is added to volatility model. It can be ascertained that SSE 50 ETF have a leverage effect which have different performance to positive information and negative information. Of all the different volatility models, the GARCH(1,1) model addd with investor sentiment can explain the volatility characteristic of 50ETF better.Based on GARCH model, EGARCH model and TARCH model, the improved Black-Scholes option pricing formula which volatility varies with time can be proposed. The effectiveness of four different model can be compared by the degree of deviation. It is shown thatGARCH (1,1) is the most effective one. So it can be determined that by changing the assumption of volatility is a constant figure to volatility changes with time, the result of option pricing can be more effective. By observing the result, it is easy to find the price derived by both Black-Scholes option pricing model and the improved model, are lower than the real. So it can be inferred that option pricing formula only contain some of the factors that affect the price of option. At the last part of this paper, statistical analysis was proposed in order to examine how the investor sentiment factors affect the SSE 50 ETF option pricing, all the data was gathered from Shanghai Stock Exchange. It can be concluded:the data of volume have no significant influence on SSE 50 ETF option pricing, open interest have significant positive influence on SSE 50ETF option pricing, and the turnover rate have significant positive influence on SSE 50ETF option pricing.