Modeling and asset allocation for financial markets based on a discrete time microstructure model

On the basis of the market microstructure theory and the continuous time stochastic volatility-style microstructure model, a discrete time stochastic volatility microstructure model with state-observability is proposed for describing the dynamics of financial markets. From the discrete time microstructure model proposed, estimates of two immeasurable state variables representing the market excess demand and liquidity respectively may be obtained. A simple trading strategy for dynamic asset allocation, based on the indirectly obtained excess demand information instead of the prediction for price, is presented. An approach to the estimation of the discrete time microstructure model using the extended Kalman filter and the maximum likelihood method is also presented. Case studies on financial market modeling and the estimated model-based asset dynamic allocation control for the JPY/USD (Japanese Yen/US Dollar) exchange rate and Japan TOPIX (TOkyo stock Price IndeX) show satisfactory modeling precision and control performance. Received 11 March 2002 / Received in final form 4 November 2002 Published online 4 February 2003 RID="a" ID="a"Currently a visiting researcher at the Institute of Statistical Mathematics, 4-6-7 Minami Azabu, Minato-ku, Tokyo 106-8569, Japan e-mail: peng@ism.ac.jp     

Testing for persistent deviations of stock prices to dividends in the Nasdaq index

In this paper we test for the presence of bubbles in the Nasdaq stock market index over the period 1994–2003 applying fractional integration techniques and allowing for structural breaks and non-linear adjustments of prices to dividends. The results show a significant structural break in 1998 for all model specifications and data periodicity. Furthermore, we do not find evidence of asymmetric adjustment of prices to dividends when using M-TAR and TAR models. The evidence of bubbles varies depending on the data periodicity and model specification used in the analysis. Finally, the results show persistent deviations of stock prices to dividends in all cases considered, though we only find evidence of bubbles in the Nasdaq index when using weekly data for the time period after June 1998.     

Correlations and multi-affinity in high frequency financial datasets

In this paper we perform a quantitative check of long term correlations and multi-affinity in Deutsche Mark/US Dollar exchange rates using high frequency data. We show that the use of business time, i.e., the ranking of the quotes in the sequences, eliminates most of the seasonality in financial-time series, allowing a precise estimation of some return anomalies.     

Multifractal detrended cross-correlations between the Chinese exchange market and stock market

Based on the daily price data of the Chinese Yuan (RMB)/US dollar exchange rate and the Shanghai Stock Composite Index, we conducted an empirical analysis of the cross-correlations between the Chinese exchange market and stock market using the multifractal cross-correlation analysis method. The results demonstrate the overall significance of the cross-correlation based on the analysis of a statistic. Multifractality exists in cross-correlations, and the cross-correlated behavior of small fluctuations is more persistent than that of large fluctuations. Moreover, using the rolling windows method, we find that the cross-correlations between the Chinese exchange market and stock market vary with time and are especially sensitive to the reform of the RMB exchange rate regime. The previous reduction in the flexibility of the RMB exchange rate in July 2008 strengthened the persistence of cross-correlations and decreased the degree of multifractality, whereas the enhancement of the flexibility of the RMB exchange rate in June 2010 weakened the persistence of cross-correlations and increased the multifractality. Finally, several relevant discussions are provided to verify the robustness of our empirical analysis.     

The relationships between Shanghai stock market and CNY/USD exchange rate: New evidence based on cross-correlation analysis,structural cointegration and nonlinear causality test

This paper explores the co-movement of Shanghai stock market and China Yuan (CNY) exchange rates. First, we find that stock price and exchange rate are significantly cross-correlated. Second, employing a cointegration test allowing for a structural break, we find that the Shanghai Composite Index (SCI) is not cointegrated with the exchange rate of CNY/USD. The so-called “cointegration” found in previous studies is just caused by the shock of the recent financial crisis. Third, using linear and nonlinear Granger causality tests, we find no causality between stock prices and exchange rates during the period before the recent financial crisis. After the financial crisis, a unidirectional causality behavior running from exchange rates to stock index is present.     

How to Measure a Two-Sided Market

Applying the theories of complex network and entropy measurement to the market, the two-sided market structure is analyzed in constructing the O2O platform transaction on the entropy measurement of the nodes and links. Market structure entropy (MSE) is initially introduced to measure the consistency degree of the individuals and the groups in the O2O market, according to the interaction in the profits, the time/space, and the information relationship. Considering that the market structure entropies are changing upward or downward, MSE is used to judge the consistency degree between the individuals and the groups. Respectively, considering the scale, the cost and the value dimensions, MSE is expanded to explain the market quality entropy, the market time-effect entropy, and the market capacity entropy.MSE provides a methodology in studying the O2O platform transaction and gives the quantitative index in the evaluation of the O2O market state.     

Multifractal analysis of the Korean agricultural market

We have studied the long-term memory effects of the Korean agricultural market using the detrended fluctuation analysis (DFA) method. In general, the return time series of various financial data, including stock indices, foreign exchange rates, and commodity prices, are uncorrelated in time, while the volatility time series are strongly correlated. However, we found that the return time series of Korean agricultural commodity prices are anti-correlated in time, while the volatility time series are correlated. The $n$-point correlations of time series were also examined, and it was found that a multifractal structure exists in Korean agricultural market prices.     

The prediction of periods of high volatility in exchange markets

A statistical connection is identified between the current spread in a market over a given time period and the drift of the market during previous time periods. It is shown that periods of high spread are likely to be preceded by periods with relatively large market drifts. Several markets, including the UK pound per US Dollar, US Dollar per Yen, UK pound per Euro, and the UK FT100 index have been analysed from 1991 to 2000 over variable periods of weeks, months and quarters. Within each period, i the natural logarithm of the daily end-of-trade market value has been least squares fitted to a linear regression line, and evaluations made of the regression line slope μ _i, the direct spread s_i with respect to the mean value, and the regression spread r_i of the deviations from the regression line. Significant correlations have been observed between the current monthly direct spread s_i for each period i and the absolute value of the drifts |μ _i-j| evaluated j periods earlier. This correlation coefficient is as high as 0.746 for a period of one quarter (j = 1) and appears to die away after around 9 months for quarterly averages, after around 4 months for monthly averages and after around 2 months for weekly averages. Received 11 October 2000     

Low q-moment multifractal analysis of Gold price, Dow Jones Industrial Average and BGL-USD exchange rate

An estimate of the low q-moment values of the assumed multifractal spectrum of Gold price, Dow Jones Industrial Average (DJIA) and Bulgarian Lev - USA Dollar (BGL-USD) exchange rate over a 6 1/2 year time span has been made. The findings can be compared to the analysis made on 23 foreign currency exchange rates by Vandewalle and Ausloos but there is a clear indication of some differences. Comparison to fractional Brownian motion is made. The analysis shows that these three financial data are not likely fractal but rather multifractal indeed. Received 17 October 1998 and Received in final form 2 November 1998     

Entropy-Based Behavioural Efficiency of the Financial Market

The most known and used abstract model of the financial market is based on the concept of the informational efficiency (EMH) of that market. The paper proposes an alternative which could be named the behavioural efficiency of the financial market, which is based on the behavioural entropy instead of the informational entropy. More specifically, the paper supports the idea that, in the financial market, the only measure (if any) of the entropy is the available behaviours indicated by the implicit information. Therefore, the behavioural entropy is linked to the concept of behavioural efficiency. The paper argues that, in fact, in the financial markets, there is not a (real) informational efficiency, but there exists a behavioural efficiency instead. The proposal is based both on a new typology of information in the financial market (which provides the concept of implicit information—that is, that information ”translated” by the economic agents from observing the actual behaviours) and on a non-linear (more exactly, a logistic) curve linking the behavioural entropy to the behavioural efficiency of the financial markets. Finally, the paper proposes a synergic overcoming of both EMH and AMH based on the new concept of behavioural entropy in the financial market.     

Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis

In this paper, we investigate the efficiency and multifractality of a gold market based on multifractal detrended fluctuation analysis. Our evidence shows that the gold return series are multifractal both for time scales smaller than a month and for time scales larger than a month. For time scales smaller than a month, the main contribution of multifractality is fat-tail distribution. For time scales larger than a month, both long-range correlations and fat-tail distribution play important roles in the contribution of multifractality. Using the method of rolling windows, we find that the gold market became more and more efficient over time, especially after 2001. The abnormal points of scaling exponents can also be related to some occasional events. By defining a new inefficiency measure related to the multifractality, we find that the gold market is more efficient during the upward periods than during the downward periods.     

Contagion effects in a chartist-fundamentalist model with time delays

In this paper two models of speculative markets are developed to study the effects of feedback mechanisms in financial markets. In the first model, a crash market model couples a linear chartist-fundamentalist model with time delays with a log-periodic market index I(t) through direct coupling. Numerical solutions to the model show that asset prices exhibit significant persistence as a result of the coupling to the log-periodic market index. An extension to include endogenous wealth dynamics shows that the chartists benefit from the persistent dynamics induced by the coupling. The second model is a two-asset model represented by a 2-dimensional delay-differential equation. Asset one price exhibits limit cycle dynamics while in the second market asset prices follow stable damped oscillations. The markets are coupled through a diffusive coupling term. Solutions to the coupled model show that the dynamics of asset two changes fundamentally with the price now exhibiting a limit cycle. The stable converging dynamics is replaced with limit cycle oscillations around the fundamental.     

Cross-sample entropy of foreign exchange time series

The correlation of foreign exchange rates in currency markets is investigated based on the empirical data of DKK/USD, NOK/USD, CAD/USD, JPY/USD, KRW/USD, SGD/USD, THB/USD and TWD/USD for a period from 1995 to 2002. Cross-SampEn (cross-sample entropy) method is used to compare the returns of every two exchange rate time series to assess their degree of asynchrony. The calculation method of confidence interval of SampEn is extended and applied to cross-SampEn. The cross-SampEn and its confidence interval for every two of the exchange rate time series in periods 1995-1998 (before the Asian currency crisis) and 1999-2002 (after the Asian currency crisis) are calculated. The results show that the cross-SampEn of every two of these exchange rates becomes higher after the Asian currency crisis, indicating a higher asynchrony between the exchange rates. Especially for Singapore, Thailand and Taiwan, the cross-SampEn values after the Asian currency crisis are significantly higher than those before the Asian currency crisis. Comparison with the correlation coefficient shows that cross-SampEn is superior to describe the correlation between time series.     

Market efficiency in foreign exchange markets

We investigate the relative market efficiency in financial market data, using the approximate entropy(ApEn) method for a quantification of randomness in time series. We used the global foreign exchange market indices for 17 countries during two periods from 1984 to 1998 and from 1999 to 2004 in order to study the efficiency of various foreign exchange markets around the market crisis. We found that on average, the ApEn values for European and North American foreign exchange markets are larger than those for African and Asian ones except Japan. We also found that the ApEn for Asian markets increased significantly after the Asian currency crisis. Our results suggest that the markets with a larger liquidity such as European and North American foreign exchange markets have a higher market efficiency than those with a smaller liquidity such as the African and Asian markets except Japan.     

Commodity predictability analysis with a permutation information theory approach

It is widely known that commodity markets are not totally efficient. Long-range dependence is present, and thus the celebrated Brownian motion of prices can be considered only as a first approximation. In this work we analyzed the predictability in commodity markets by using a novel approach derived from Information Theory. The complexity-entropy causality plane has been recently shown to be a useful statistical tool to distinguish the stage of stock market development because differences between emergent and developed stock markets can be easily discriminated and visualized with this representation space [L. Zunino, M. Zanin, B.M. Tabak, D.G. Pérez, O.A. Rosso, Complexity-entropy causality plane: a useful approach to quantify the stock market inefficiency, Physica A 389 (2010) 1891-1901]. By estimating the permutation entropy and permutation statistical complexity of twenty basic commodity future markets over a period of around 20 years (1991.01.02-2009.09.01), we can define an associated ranking of efficiency. This ranking is quantifying the presence of patterns and hidden structures in these prime markets. Moreover, the temporal evolution of the commodities in the complexity-entropy causality plane allows us to identify periods of time where the underlying dynamics is more or less predictable.     

A study of the interplay between the structure variation and fluctuations of the Shanghai stock market

The intricate interplay between the variation of the stock network structure and fluctuations of that stock market is increasingly becoming a hot topic. In this work, employing a moving window to scan through every stock price time series over a period from 2 January 2001 to 7 December 2010, we use mutual information to measure the statistical interdependence between stock prices, and we construct a corresponding network for 501 Shanghai stocks in every given window. Then we address the time-varying relationships between the structure variation and fluctuations for the Shanghai stock market. All the results obtained here indicate that at turning points the growing independence of stocks causes the scalefreeness of the degree distribution to be disrupted, and that the Shanghai stock index has little volatility clustering. In contrast, under normality of the market, the stock networks have characteristics of scalefree degree distribution. Furthermore, the degree of volatility clustering is a little higher.     

Martingales, detrending data, and the efficient market hypothesis

We discuss martingales, detrending data, and the efficient market hypothesis (EMH) for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that martingale stochastic processes generate uncorrelated, generally non-stationary increments. Generally, a test for a martingale is therefore a test for uncorrelated increments. A detrended process with an x-dependent drift coefficient is generally not a martingale, and so we extend our analysis to include the class of (x,t)-dependent drift coefficients of interest in finance. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. And while a Markovian market has no memory to exploit and presumably cannot be beaten systematically, it has never been shown that martingale memory cannot be exploited in 3-point or higher correlations to beat the market. We generalize our Markov scaling solutions presented earlier, and also generalize the martingale formulation of the EMH to include (x,t)-dependent drift in log returns. We also use the analysis of this paper to correct a misstatement of the ‘fair game’ condition in terms of serial correlations in Fama's paper on the EMH. We end with a discussion of Levy's characterization of Brownian motion and prove that an arbitrary martingale is topologically inequivalent to a Wiener process.     

基于上证指数高频数据的中国资本市场微观特性研究

以上证指数高频数据为研究对象,基于上涨、平缓和下跌三个市场状态分析我国金融市场的微观特性.通过分析上证指数在不同时间间隔下的概率分布、自相关性和多分形三个特性,发现上证指数对数增量序列存在厚尾、列维非高斯分布特征,且随着时间间隔的增大,收益序列愈收敛于正态分布,其中,下降趋势收敛于正态分布的速度更快,拟合于列维分布的效果更好.最为突出的是,在自相关函数分析中,上证指数的收益率无长期记忆性,而波动率则具有较强的记忆性.同时,波动率的自相关性存在明显的周期性特征,即T=240 min,且在下降趋势时其相关性最高.在以时间增量刻画的多重分形结构中,对于不同的时间序列、时间间隔,由于受投资期限和流动性的影响,三种股市状态的收益率波动存在着短期和长期性的差异.上证指数的总体宏观行为与国际成熟股市较为一致,但在微观特性上仍存在显著差异,其所特有的周期性是投资者的惯性反冲所致,而自相关性函数较之成熟股市衰减较慢,则表明投资者的投资行为更多地受历史信息的影响.     

Convergence of fundamentalists and chartists’ expectations: An alarm for stock market crash

We construct a network of the Tehran stock market based on the cross-correlation of trading volume of stocks both for fundamentalists and chartists. In order to investigate the dynamics of expectations of fundamentalists and chartists over time we introduced a homogeneity coefficient. Our results show that in the Tehran Stock Exchange (TSE) which is an emerging market, chartists in comparison with fundamentalists more strongly believe the stocks’ co-movements. We also found that in a bull market (booming period), the optimism of fundamentalists and chartists about the similarity of stocks’ performance diverge from each other while in a bear market (recession period) both groups of traders have approximately same level of pessimism about the simultaneous collapse of stock prices.     

Assessing market uncertainty by means of a time-varying intermittency parameter for asset price fluctuations

Maximum likelihood estimation techniques for multifractal processes are applied to high-frequency data in order to quantify intermittency in the fluctuations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency parameter λ$\lambda$ characterising the degree of volatility clustering. We can therefore study the time evolution of volatility clustering and test the statistical significance of this variability. By analysing data from the Oslo Stock Exchange, and comparing the results with the investment grade spread, we find that the estimates of λ$\lambda$ are lower at times of high market uncertainty.