The Study of Analytical Technique under Fractal Market Hypothesis
Date Issued
2009
Date
2009
Author(s)
Ma, Hui-Chun
Abstract
This paper analyzes the daily returns of Taiwan Weight Stock Index over the 10-yr period 1999-2008, by applying the analytical technique under Fractal Market Hypothesis (FMH) -- power coefficient (α) and Hurst exponent (H). The purpose of FHM is to remove the unrealistic assumptions under Efficient Market Hypothesis (EMH). FMH tries to develop some robust analytical tools to catch the two characteristics in financial markets – large price fluctuation and the long-memory effect. Besides calculating the two statistics, I establish a simulation model with fractional Brownian Motion (FBM), and examine it from two aspects:) compare the 1000 routes simulated by FBM and GBM (Geometric Brownian Motion) respectively to the real index at the specific dates, and calculate the probabilities if the simulated outputs contain the down-side risk of real index;) calculate the α coefficients of the two simulation models, and test whether they are different from the real world α significantly or not. The empirical results show that the simulations with FBM dominate the ones with GBM using the four-year historical data, because the FBM simulation models take the long-memory effect into account. Furthermore, the fluctuation of the simulations with FBM is closer to the real index. That is to say, the FBM models could simulate the index efficiently and realistically better than GBM models in both price fluctuation and long-memory effect aspects.
Subjects
Fractal
Power Law
Hurst Exponent
R/S Analysis
Fractional Brownian Motion
Type
thesis
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