上证指数收益率的长相依性分析及其欧式期权定价

对上证指数对数收益率的长相依性进行了统计检验并完成了相应的统计建模以及参数估计.完成了在此模型下的欧式期权定价设计,比较了具有长相依性质的模型下期权定价与经典的Black-Scholes模型下期权定价的不同点,分析了长相依性质对于期权定价的影响.统计检验采用的是经典的R/S分析法和修正R/S分析法,通过对上证指数收益率的时间序列进行了实证分析,发现上证指数体现出长相依性质.数值分析的结果显示分数布朗运动模型下欧式期权定价与经典Black-Scholes期权定价有很大的不同点,主要表现在分数布朗运动模型下的定价从时间的角度来看表现得更为平稳.

Long range dependence of Shanghai stock market and pricing of European option

This paper aims at the empirical statistical test of the long range dependence of Shanghai Composite Index and finishes statistical modeling for corresponding financial data and derives the valuation formula for European call option under the model we proposed. Theoretical analysis and numerical examples are given to illustrate the impact of the long range dependence on the option pricing by comparing the option valuation formula under fractional Brownian motion (fBm for short) model and the one under Black-Scholes model. The main statistics we adopted are R/S and modified R/S statistics. Numerical results show that the valuation formula under fBm are much more stable than the one under Black-Scholes model due to the former one has the long range dependence property.