The Multi-fractal Spectrum Model for the Measurement of Random Behaviour of Asset Price Returns

To forecast the market risk, assessing the stock price indices is the foundation. Multi-fractal has lots of advantage when explaining the volatility of the stock prices. The asset price returns is a multi-period (multi-fractal dimension) market depending on market scenarios which are the measure points. This paper considers the multi-fractal spectrum model (MSM) to measure the random character of asset price returns, aimed at deriving the MSM version of the random behaviour of equity returns of the existing ones in literature. We investigate the rate of returns prior to market signals corresponding to the value for packing dimension in fractal dispersion of Hausdorff measure. Furthermore, we give some conditions which determine the equilibrium price, the future market price and the optimal trading strategy.