基于多标度分形理论的金融风险测度指标研究

Study on financial risk measure based on multifractal theory

多标度分形(multifractal)理论是一种刻画金融市场波动复杂性特征的有力工具,而金融价格时间序列的多标度分形谱(multifractal spectrum)则是对测度对象复杂性特征的一种具体和全面的描述.以上海证券交易所综合股价指数高频价格时间序列的多标度分形谱计算为例,建立了基于多标度分形谱两个主要参数的市场风险测度指标Rf,弥补了传统风险测度指标在非有效市场条件下的不足.通过对上证综指的实证研究验证了这一指标的有效性,并对其在价格波动预测方面的作用进行了初步的探讨和理论解释.

Multifractal is a powerful tool to describe the complexity of fluctuations in financial markets, and the muhifractal spectrum of financial price time series is a concrete and complete description of its complex characteristics. Take the multifractal spectrum of high frequency price time series of Shanghai Stock Exchange Composite index as example, a new market risk measure based on two main parameters of multifractal spectrum is constructed, which may make up for the shortcomings of traditional risk measure in inefficient markets. Empirical study is carried out to test the efficientcy of the new risk measure, and its ability of predicting price movements is also studied.