Empirical Research on the Asymmetric Multifractal Properties in Financial Market Data

Abstract

After the recent financial crisis, the importance of financial market analysis for financial risk management has been emphasized. Financial markets have diverse characteristics that are difficult to explain from the traditional models. Therefore, the effort on describing such characteristics is required. Specifically, many researches are actively conducted on the features of multifractal and asymmetric correlation in financial markets. Multifractal features can be characterized by various fractal features with self-similarity that does not change with scale

it is difficult to represent in a single fractal dimension. This feature can explain the complexity of stock market. The asymmetric correlation, depending on the market trend, represents the asymmetric structure of the financial market. In this context, this dissertation focuses on the asymmetric correlation of multifractal characteristics in the financial market data where the asymmetric market efficiency is measured using asymmetric multifractal property. At first, Price-based Asymmetric Multifractal Detrended Fluctuation Analysis (Price-based A-MFDFA) model is proposed to measure multifractal characteristics which asymmetrically follow the trend of market price. Given that previous models measure the multifractal characteristics based on the entire market, the price-based A-MFDFA model has its advantage by considering the asymmetrical characteristics according to different market conditions. Furthermore, the methods to investigate the cause of multifractal features and the asymmetry are also suggested based on the proposed model. The empirical results in the U.S. financial market data confirms the presence of asymmetric multifractal characteristic and the autocorrelation of the variance in uptrend market and fat-tailed distribution in downtrend market as the cause of multifractality. The results of time-varying asymmetric multifractality show that the difference between the degree of uptrend and downtrend multifractality increases during the financial crisis period. Secondly, a simulation method is applied to prove the ability of capturing the asymmetric multifractal features of the Price-based A-MFDFA model by examining the factors affecting the asymmetric multifractality. In order to mimic the stock market data, an artificial time series with asymmetric features are constructed using the Monte-Carlo simulation. Then, the asymmetric multifractality is observed for each time series using the proposed model. The results show that the proposed model can detect the artificial asymmetric characteristics. In addition, the effects of autocorrelation of time series, autocorrelation of volatility, the skewness and fat-tailed of distribution on the asymmetric long-range dependence and multifractal features are studied. Lastly, a framework for testing the existence of asymmetric long-range dependence and multifractality is proposed. The source of market inefficiency, which has not been identified in previous models, is examined through the uptrend and downtrend multifractal features. The result of thirty four countries suggests that, in the financial crisis period, the difference in the long-range dependence measure and degree of multifractality between uptrend and downtrend increases, whereas the uptrend degree of multifractality has a strong negative correlation with the stock price in financial crisis period. In addition, the relationship between asymmetric long-range dependence and rate of return is tested. In conclusion, the contribution of this dissertation is to further refine the ability of multifractal analysis on asymmetric characteristics in accordance with market conditions as well as the overall market. While past analysis of the overall market focuses on only the downtrend, it is possible to analyze both uptrend and downtrend market through the segmented asymmetric multifractal characteristics. Hence, the proposed model can provide much useful information to various market participants in the perspective of financial risk management.