Narrow Results

We investigate the stochastic resonance of periodic volatility in two financial markets with stock crashes for Dow Jones component stocks and Hang Seng index, based on the modified Heston model with an effective potential to describe the stock crashes. We introduce a cosine term to Heston model and develop a modified Heston model with periodic stochastic volatility for capturing the periodicity of the volatility process or volatility clustering which was observed in historical financial data sets. The proposed model was tested against Dow Jones industrial and Hang Seng index data. The experimental results demonstrate that the proposed model fits the historical data well when compared with the original Heston model. The signal power amplification (SPA) is calculated and studied to investigate the stochastic resonance of the proposed dynamic system. Experimental results suggest that: (i) optimal values of volatility parameters can be identified which maximize the effects of systematic and non-systematic randomness to the market periodicity; (ii) different values of correlation strength between noise sources will cause critical phenomenon and induce single or multiple resonances.

We explore the roles of information time delay and noise correlation on the stability of electricity market by the method of mean first passage time (MFPT) and delayed Heston model. We employ the least square method of probability distribution to estimate the parameters of the proposed model with the closing price data of electricity futures daily of the European Energy Exchange. Then the probability density functions of the price returns are empirically compared between both the simulated data from the delayed Heston model and the electricity futures data, and a good agreement can be found between them. Through the stochastic simulation of the mean first passage time of returns, some results show that: (i) the phenomenon of correlation enhancing stability can be observed in MFPT versus mean reversion of volatility; (ii) we can observe that the delay time and the growth rate can induce the critical phenomenon; (iii) there are optimal values of volatility parameters matching maximum stability of electricity futures price. In addition, the increased growth rate and the delay time enhance the stability of electricity futures price.

General researches show that all kinds of random risk information and periodic information in the financial system are mainly transmitted to the asset price through influencing the volatility, thus impacting the whole market. So can the periodic information and random factors in the price be transmitted to the volatility in reverse and cause volatility changes? Hence, in this paper, we investigate the stochastic resonance of volatility which is influenced by price periodic information in financial market, based on our proposed periodic Brownian Motion model and absolute return volatility. The parameter estimation of the periodic Brownian Motion model is obtained by minimizing the mean square deviation between the theoretical and empirical return distributions for the CSI300 data set. The good agreements of the probability density functions of the price returns, realized volatility (RV) at 5 minutes, RV at 15 minutes and absolute return volatility between theoretical and empirical calculation are found. After simulating the absolute return volatility and signal power amplification (SPA) of volatility via periodic Brownian Motion model, the results indicated that (i) single and double inverse resonance phenomena can be observed in the function of SPA versus random information intensity or economic growth rate; (ii) multiple inverse resonance phenomena can be also observed for SPA versus frequency of periodic information. The results imply that the transmission of stochastic factors and periodic information is not only from the volatility to the price, but also from the price to the volatility.

We briefly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times with that obtained from real market data. Afterwards we analyze in detail the effect both of noise and different initial conditions on the escape time in a market model with stochastic volatility and a cubic nonlinearity. For this model, we compare the PF of the stock price returns, the PF of the volatility and the return correlation with the same statistical characteristics obtained from real market data.

The Theil index is much used in economy and finance; it looks like the Shannon entropy, but pertains to event values rather than to their probabilities. Any time series can be remapped through the Theil index. Correlation coefficients can be evaluated between the new time series, thereby allowing to study their mutual statistical distance — to be contrasted to the usual correlation distance measure for the primary time series. As an example this entropy-like correlation distance method (ECDM) is applied to the Gross Domestic Product of 20 rich countries in order to test some economy globalization process. Hierarchical distances allow to construct (i) a linear network, (ii) a Locally Minimal Spanning Tree. The role of time averaging in finite size windows is illustrated and discussed. It is also shown that the mean distance between the most developed countries, was decreasing since 1960 till 2000, which we consider to be a proof of globalization of the economy for these countries.

The recent turbulence on the world's stock markets has reinvigorated the attack on classical economic models of stock market fluctuations. The key problem is determining a dynamic model, which is consistent with observed fluctuations and which reflects investor behavior. Here, we use a novel equation-free approach developed in nonlinear dynamics literature to identify the salient statistical features of fluctuations of the Dow Jones Industrial Average over the past 80 years. We then develop a minimal dynamical model in the form of a stochastic differential equation involving both additive and multiplicative system-noise couplings, which captures these features and whose parameterization on a time scale of days can be used to capture market distributions up to a time scale of months. The terms in the model can be directly linked to "herding" behavior on the part of traders. However, we show that parameters in this model have changed over a number of decades producing different market regimes. This result partially explains how, during some periods of history, "classic" economic models may work well and at other periods "econo-physics" models prove better.

In this paper, the generalized Hurst exponent is used to investigate multifractal properties of historical volatility (CHV) in stock market price and return series before, during and after 2008 financial crisis. Empirical results from NASDAQ, S&P500, TSE, CAC40, DAX, and FTSE stock market data show that there is strong evidence of multifractal patterns in HV of both price and return series. In addition, financial crisis deeply affected the behavior and degree of multifractality in volatility of Western financial markets at price and return levels.

The diagonal effect of orders is well documented in different markets, which states that the orders are more likely to be followed by the orders of the same aggressiveness and implies the presence of short-term correlations in order flows. Based on the order flow data of 43 Chinese stocks, we investigate if there are long-range correlations in the time series of order aggressiveness. The detrending moving average analysis shows that there are crossovers in the scaling behaviors of overall fluctuations and order aggressiveness exhibits linear long-term correlations. We design an objective procedure to determine the two Hurst indexes delimited by the crossover scale. We find no correlations in the short term and strong correlations in the long term for all stocks except for an outlier stock. The long-term correlation is found to depend on several firm specific characteristics. We also find that there are nonlinear long-term correlations in the order aggressiveness when we perform the multifractal detrending moving average analysis.

Grains account for more than 50% of the calories consumed by people worldwide, and military conflicts, pandemics, climate change, and soaring grain prices all have vital impacts on food security. However, the complex price behavior of the global grain spot markets has not been well understood. A recent study performed multifractal moving average analysis (MF-DMA) of the Grains & Oilseeds Index (GOI) and its sub-indices of wheat, maize, soybeans, rice, and barley and it was found that only the maize and barley sub-indices exhibit an intrinsic multifractal nature with convincing evidence. Here, we utilize multifractal fluctuation analysis (MF-DFA) to investigate the same problem. Extensive statistical tests confirm the presence of intrinsic multifractality in the maize and barley sub-indices and the absence of intrinsic multifractality in the wheat and rice sub-indices. Different from the MF-DMA results, the MF-DFA results suggest that there is also intrinsic multifractality in the GOI and soybeans sub-indices. Our comparative analysis does not provide conclusive information about the GOI and soybeans and highlights the high complexity of the global grain spot markets.

We extend the neural-network approach for the valution of financial derivatives developed by Hutchinson et al. [1] to the case of fat-tailed distributions of the underlying asset returns. We use a two-layer perceptron with three inputs, four hidden neurons, and one output. The input parameters of the network are: the simulated price of the underlying asset F divided by the strike price E, the time-to-maturity T, and the ratio |F-E|/T. The latter takes into account the volatility smile, whereas the price F is generated by the method of Gorenflo et al. [2] based on fractional calculus. The output parameter is the call price C over E. The learning-set option price C is computed by means of a formula given by Bouchaud and Potters [3, 4]. Option prices obtained by means of this learning scheme are compared with LIFFE option prices on German treasury bond (BUND) futures.

An empirical analysis of the Romanian emerging stock market RASDAQ based on the statistical study of the composite index RASDAQ-C reveals the leptokurtic profile of the probability density function (p.d.f.) of the stock index changes, the power law asymptotic behaviour of the p.d.f., the breakdown of scaling at long time scales, the absence of linear correlation in the stock index changes but existence of long-range correlation in nonlinear function such as the absolute value or the square of index changes (implicitly the long-range correlation in the index volatility). These results, consistent with the similar referring to the more liquid markets, suggest the presence of several universal features, in addition to several particularities related to the quickness of assimilation of the new information and its impact over the investors.

Using a relationship between the moments of the probability distribution of times between the two consecutive trades (intertrade time distribution) and the moments of the distribution of a daily number of trades, we show that the underlying point process is essentially non-Markovian. A detailed analysis of all trades in the EESR stock on the Moscow International Currency Exchange in the period January 2003–September 2003, including correlation between intertrade time intervals is presented. A power-law decay of the correlation function provides an additional evidence of the long-memory nature of the series of times of trades. A data set including all trades in Siemens, Commerzbank and Karstadt stocks traded on the Xetra electronic stock exchange of Deutsche Boerse in October 2002 is also considered.

We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the exact expression of the characteristic function associated to the risk neutral probability density. This expression allows us to compute option prices exploiting a formula derived by Lewis and Lipton. We analyze in detail the case of Plain Vanilla calls, being liquid instruments for which reliable implied volatility surfaces are available. We also compute the analytical expressions of the first four cumulants, that are crucial to implement a simple two steps calibration procedure. It has been tested against a data set of options traded on the Milan Stock Exchange. The data analysis that we present reveals a good fit with the market implied surfaces and corroborates the accuracy of the linear approximation.

We focus on the stochastic description of the stock price dynamics. Thereby we concentrate on the Heston model and the Hull–White model. We derive the stationary probability density distribution of the variance of both models in the case of zero correlation coefficient. These distributions are used to calculate solutions for the logarithmic returns of the stock price for short time lags. Furthermore we apply the solutions of both models to the German tick-by-tick Dax data [1]. The data are from May 1996 to December 2001. We use the probability density distributions of the logarithmic returns, calculated out of the data, and fit these distributions to the theoretical distributions.

We study the statistical properties of escape times for stock price returns in the Wall Street market. In particular we get the escape time distribution for real data from daily transactions and for three models: (i) the Wiener process with drift and a constant market volatility, (ii) Heston and (iii) GARCH models, where the volatility is a stochastic process. We find that the first model is unable to catch all the features of the escape time distribution of real data. Moreover, the Heston model describes the probability density function for both return and escape times better than the GARCH model.

Following the victory of the Congress Party, the Indian SENSEX index crashed in May 2004. We present a brief analysis of the crash, showing that very likely the crash was due to the outcome of the Indian elections, but in a situation of very high instability, with the market already past a transition point, well described by the Sornette-Johansen model.

For stock market data, the empirical distribution of the return for stock price and the empirical distribution of the return for stock market index are well known. However, for the detrended data (defined as data divided by trend), which is a different fluctuating quantity compared to the return, only the distribution of detrended daily stock volume is known so far. In this paper, we show that for both stock price and stock market index, the detrended daily data is well fitted by a stable probability density with characteristic exponent parameter less than 2. The trend was modeled using either cubic smoothing spline or principal component analysis. The significance of our results for stock market modeling is discussed.

We use the multifractal detrended cross-correlation analysis (MF-DCCA) method to explore the multifractal behavior of the cross-correlation between exchange rates of onshore RMB (CNY) and offshore RMB (CNH) against US dollar (USD). The empirical data are daily prices of CNY/USD and CNH/USD from May 1, 2012 to February 29, 2016. The results demonstrate that: (i) the cross-correlation between CNY/USD and CNH/USD is persistent and its fluctuation is smaller when the order of fluctuation function is negative than that when the order is positive; (ii) the multifractal behavior of the cross-correlation between CNY/USD and CNH/USD is significant during the sample period; (iii) the dynamic Hurst exponents obtained by the rolling windows analysis show that the cross-correlation is stable when the global economic situation is good and volatile in bad situation; and (iv) the non-normal distribution of original data has a greater effect on the multifractality of the cross-correlation between CNY/USD and CNH/USD than the temporary correlation.

The correlation structure of a stock market contains important financial contents, which may change remarkably due to the occurrence of financial crisis. We perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 Chinese stocks. Both raw correlation matrix and partial correlation matrix with respect to the market index in two time periods of one year are investigated. We find that the Chinese stocks have stronger average correlation and partial correlation in 2008 than in 2007 and the average partial correlation is significantly weaker than the average correlation in each period. Accordingly, the largest eigenvalue of the correlation matrix is remarkably greater than that of the partial correlation matrix in each period. Moreover, each largest eigenvalue and its eigenvector reflect an evident market effect, while other deviating eigenvalues do not. We find no evidence that deviating eigenvalues contain industrial sectorial information. Surprisingly, the eigenvectors of the second largest eigenvalues in 2007 and of the third largest eigenvalues in 2008 are able to distinguish the stocks from the two exchanges. We also find that the component magnitudes of the some largest eigenvectors are proportional to the stocks’ capitalizations.

In this paper, we investigate the dynamics of large-size trades after the recommendation revisions using all A-share stocks data in Chinese stock market. We find the sell-side security analysts’ recommendation revisions (both upgrade and downgrade) do have large-size trades trend effect which means that the large-size trades have persistent change (being larger or smaller) after the recommendation revisions; the downgrade revisions have much greater impacts on large-size trades. We further analyze the large-size trades’ power-law behaviors and the relaxation exponents show that downgrade recommendation revisions have greater impacts on the large-size trade than the upgrade recommendation revisions. The downgrade recommendation revisions have greater impacts on selling order of large-size trades relative to buying orders of large-size trades while the results do not give the consistent evidence that the upgrade recommendation revisions have greater impacts on the buying orders of large-size trades.