Empirical Research on the Asymmetric Multifractal Properties in Financial Market Data

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 산업공학과, 2018. 2. 장우진.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 scaleit 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.Chapter 1 Introduction 1 1.1 Resarch motivation and purpose 1 1.2 Theoretical background 5 1.3 Organiation of the research 9 Chapter 2 Asymmetric multi-fractality in the U.S. stock indices using the price-based model of A-MFDFA 10 2.1 Introduction 10 2.2 Price-based A-MFDFA method 13 2.3 Data description 16 2.4 Empirical results of asymmetric scaling behavior 18 2.4.1 Asymmetric fluctuation functions and their dynamics 18 2.4.2 Estimating the generalized Hurst exponent 22 2.4.3 Source of multi-fractality 24 2.4.4 Source of asymmetry 28 2.4.5 Time-varying multi-fractal asymmetry 29 2.5 Conclusion 33 Chapter 3 Study of asymmetric multifractal characteristics through various time series simulations 34 3.1 Introduction 34 3.2 Various probability distribution and time series model 36 3.2.1 Normal distribution 36 3.2.2 Skewed distribution 37 3.2.3 Students t-distribution 37 3.2.4 Autoregressive model 38 3.2.5 Autoregressive conditional heteroscedasticity model 38 3.2.6 Gereralized autoregressive conditional heteroscedasticity model 39 3.3 Method to generate time series using Monte-Carlo simulation 41 3.3.1 Homogeneous time series generating 41 3.3.2 Heterogeneous time series with previous datas sign 41 3.3.3 Heterogeneous time series with precious datas trend 41 3.4 Simulation results 43 3.4.1 Homogeneous time series simulation results 43 3.4.2 Heterogeneous time series with previous datas sign simulation results 50 3.4.3 Heterogeneous time series with precious datas trend simulation results 60 3.5 Conclusion 70 Chapter 4 Evaluating the asymmetric long-range dependence and multifractality of financial markets 72 4.1 Introduction 72 4.2 Methodology 76 4.2.1 Price-based A-MFDFA 76 4.2.2 Evaluating the existence of asymmetric long-range dependence and multifractality 78 4.3 Data description 81 4.4 Results and Discussion 84 4.4.1 Monte Carlo Simulation 84 4.4.2 The results for testing the existence of asymmetric long-range dependence and multifractality in each period 89 4.4.3 Time-varying asymmetric Hurst exponent and multifractality 95 4.5 Conclusion 99 Chapter 5 Concluding Remarks 102 5.1 Summary and contributions 102 5.2 Limitations and future work 106 References 108 Appendix 116 Abstract (in Korean) 149Docto

Market Imitation and Win-Stay Lose-Shift Strategies Emerge as Unintended Patterns in Market Direction Guesses.

Decisions made in our everyday lives are based on a wide variety of information so it is generally very difficult to assess what are the strategies that guide us. Stock market provides a rich environment to study how people make decisions since responding to market uncertainty needs a constant update of these strategies. For this purpose, we run a lab-in-the-field experiment where volunteers are given a controlled set of financial information -based on real data from worldwide financial indices- and they are required to guess whether the market price would go "up" or "down" in each situation. From the data collected we explore basic statistical traits, behavioural biases and emerging strategies. In particular, we detect unintended patterns of behavior through consistent actions, which can be interpreted as Market Imitation and Win-Stay Lose-Shift emerging strategies, with Market Imitation being the most dominant. We also observe that these strategies are affected by external factors: the expert advice, the lack of information or an information overload reinforce the use of these intuitive strategies, while the probability to follow them significantly decreases when subjects spends more time to make a decision. The cohort analysis shows that women and children are more prone to use such strategies although their performance is not undermined. Our results are of interest for better handling clients expectations of trading companies, to avoid behavioural anomalies in financial analysts decisions and to improve not only the design of markets but also the trading digital interfaces where information is set down. Strategies and behavioural biases observed can also be translated into new agent based modelling or stochastic price dynamics to better understand financial bubbles or the effects of asymmetric risk perception to price drops

Intraday Analysis of the Malaysian Stock Index Futures Market

The use of any aggregate financial data to examine the relationship between information and prices using daily, weekly and monthly data leads to loss of information. The problem with such studies that employ time aggregated data is that it ignores the real time price dynamics and intraday interaction of the markets. Generally, most Malaysian financial economists have employed such inadequate methods. Specifically, for the Malaysian futures market, the intraday properties of the Kuala Lumpur Stock Exchange Composite Index (KLCI) futures contracts (FKLI) have not thoroughly examined, and hence, not well understood. Intraday analyses are crucial for investors and policy makers since many of the price adjustments could have taken place during the trading hours. Such real time adjustments can only be captured effectively by the intraday price analysis. In this study, the intraday data of 5-minute and 15-minute intervals of KLCI and FKLI is used to investigate the intraday price discovery mechanism, trading activity, volatility characteristics and spillover effects which has not been examined before by proir studies. The causal effect of both markets is measured by the computation of the bivariate Granger causality. The intraday lead and lag relationships between the KLCI and FKLI were examined under the orientation of multiple regression analysis. The short run dynamics of the volatility movement of the two markets is studied by the impulse response functions. In addition, in order to study the intraday volatility spillover between the cash and futures markets, the Bivariate Error Correction- Exponential Generalised Autoregressive Conditional Heteroscedasticity (ECMEGARCH) model is employed to capture the long-run equilibrium relationship, shortrun causality effect and the nature of the time varying variance in the series. Besides, this model is also used to investigate the asymmetric impact of shocks on stock and futures markets volatility, known as the leverage effect. The empirical evidence obtained from this study indicates that the intraday price volatility of FKLI does not exhibit a convex U-shaped pattern but instead a ‘reverse Jshaped’ pattern. However, the conventional U-shaped curve exists in the tick volume analyses. The results from the bivariate cointegration analysis are in line with those found in the developed markets. The futures prices appear to react more rapidly to new information as compared to the cash prices. The study of lead and lag relationships between the futures and cash markets revealed a bi-directional relationship. The futures returns tends to lead strongly the cash returns, in the time period up to 20 minutes; while the cash returns leads weakly the futures returns, in the time period between 5 to 10 minutes. Generally, the futures index consistently indicates a stronger degree of price discovery and price leadership over the cash index.The bivariate EGARCH analysis of volatility spillover found that there is a persistent bi-directional information flow between the futures and cash markets. It implies that innovations in the futures market could predict the future volatility of the cash market, or vice versa. However, the futures index has a higher degree of volatility spillover as compared with the cash index. Thus, it can be used by market participants to anticipate the future performance of the cash index. Finally, both markets exhibit the asymmetric volatility effects as predicted. In other words, any bad news tends to create greater impact on volatility, than the good news, for both markets. In conclusion, the interesting microstructure discoveries with a reverse J-shape for volatility and a U-shape for tick volume is definitely important for all market participants. As a result, investors with different risk appetite should be able to time their trades in accordance with the volatility and trading activity patterns of FKLI revealed in this study. In terms of price leadership and price discovery, the futures index seems to play a more dominant role in the information transmission mechanism of the two markets, as it possesses a stronger degree of price leadership over the cash index. Hence, the futures index can be perceived as a vehicle for price discovery and the performance of the intraday futures prices can be used by traders to predict the future movements of the cash prices. Finally, emphasizing that volatility is a proxy for information flow, the bivariate ECM-EGARCH analysis indicates that a bi-directional volatility spillover exits between the KLCI and the FKLI markets. However, the spillovers from the futures market to the cash market are more significant and prominent than the reverse. These results are consistent with the evidence supporting the dominant role of FKLI in price discovery. Therefore, it is proven that the futures market is more informationally efficient than the cash market

Agent-based model with asymmetric trading and herding for complex financial systems

Background: For complex financial systems, the negative and positive return-volatility correlations, i.e., the so-called leverage and anti-leverage effects, are particularly important for the understanding of the price dynamics. However, the microscopic origination of the leverage and anti-leverage effects is still not understood, and how to produce these effects in agent-based modeling remains open. On the other hand, in constructing microscopic models, it is a promising conception to determine model parameters from empirical data rather than from statistical fitting of the results. Methods: To study the microscopic origination of the return-volatility correlation in financial systems, we take into account the individual and collective behaviors of investors in real markets, and construct an agent-based model. The agents are linked with each other and trade in groups, and particularly, two novel microscopic mechanisms, i.e., investors' asymmetric trading and herding in bull and bear markets, are introduced. Further, we propose effective methods to determine the key parameters in our model from historical market data. Results: With the model parameters determined for six representative stock-market indices in the world respectively, we obtain the corresponding leverage or anti-leverage effect from the simulation, and the effect is in agreement with the empirical one on amplitude and duration. At the same time, our model produces other features of the real markets, such as the fat-tail distribution of returns and the long-term correlation of volatilities. Conclusions: We reveal that for the leverage and anti-leverage effects, both the investors' asymmetric trading and herding are essential generation mechanisms. These two microscopic mechanisms and the methods for the determination of the key parameters can be applied to other complex systems with similar asymmetries.Comment: 17 pages, 6 figure

How volatilities nonlocal in time affect the price dynamics in complex financial systems

What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made, it remains challenging. Physicists usually apply the concepts and methods in statistical physics, such as temporal correlation functions, to study financial dynamics. However, the usual volatility-return correlation function, which is local in time, typically fluctuates around zero. Here we construct dynamic observables nonlocal in time to explore the volatility-return correlation, based on the empirical data of hundreds of individual stocks and 25 stock market indices in different countries. Strikingly, the correlation is discovered to be non-zero, with an amplitude of a few percent and a duration of over two weeks. This result provides compelling evidence that past volatilities nonlocal in time affect future returns. Further, we introduce an agent-based model with a novel mechanism, that is, the asymmetric trading preference in volatile and stable markets, to understand the microscopic origin of the volatility-return correlation nonlocal in time.Comment: 16 pages, 7 figure

Asymmetric connectedness of stocks: How does bad and good volatility spill over the U.S. stock market?

Asymmetries in volatility spillovers are highly relevant to risk valuation and portfolio diversification strategies in financial markets. Yet, the large literature studying information transmission mechanisms ignores the fact that bad and good volatility may spill over at different magnitudes. This paper fills this gap with two contributions. One, we suggest how to quantify asymmetries in volatility spillovers due to bad and good volatility. Two, using high frequency data covering most liquid U.S. stocks in seven sectors, we provide ample evidence of the asymmetric connectedness of stocks. We universally reject the hypothesis of symmetric connectedness at the disaggregate level but in contrast, we document the symmetric transmission of information in an aggregated portfolio. We show that bad and good volatility is transmitted at different magnitudes in different sectors, and the asymmetries sizably change over time. While negative spillovers are often of substantial magnitudes, they do not strictly dominate positive spillovers. We find that the overall intra-market connectedness of U.S. stocks increased substantially with the increased uncertainty of stock market participants during the financial crisis.Comment: arXiv admin note: text overlap with arXiv:1405.244