Expansion Of SV Model And Stock Index Future Pricing

Stock Index Future is the future whose target is stock index. People buy and sell futures and hedge the stock portfolios with the difference of prices in the transaction because the stock index can represent the trend and magnitude of the whole stock market. Then the futures can be used to avoid the risk of system or take an arbitrage. The Stock Index Future has been developed quickly in the developed countries, and prepared in China. The pricing of Stock Index Future has become the focus in research.In this thesis, we are concerned with the problem of pricing of Stock Index Future using Stochastic Volatility (SV) model. The previous methods of pricing are mainly based on the Non-Arbitrage Pricing Model using risk-free interest rate. These methods have some disadvantages: They can't explain the "heavy-tail" of Stock Index Future's distribution very well, and price the Future without considering the stochastic process of the index, and they can't predict the Stock Index Future's price effectively and reasonably in the future. We introduce the SV model as another method to model the Stock Index Future, catch the behavior of "Volatility Clustering" and "heavy-tail" of index distribution.The primary task of this thesis is as follows: Firstly, we give an introduction of stock index future pricing, and the general formulae of future pricing using SV model. Secondly, we discuss the estimation of parameters in SV model by the Empirical Characteristic Function method with Normal-Tail and Heavy-Tail SV model. Thirdly, we model the KOSPI and KOSPI200 Index of Korea Stock Exchange using Heavy-Tail SV model and estimate the parameters with Gauss-Hermite Numerical Integral and Nelder-Mead Optimization Algorithm, and analyze the price of KOSPI200 index future. Finally, the conclusion is given.