We consider the randomness of market trade as the origin of price and return stochasticity. We look at time series of trade values and volumes as random variables during the averaging interval Δ and describe the dependences of market-based volatilities of price and return on the volatilities and correlations of market trade values and volumes. We describe the market-based origin of the lower boundaries of the accuracy of macroeconomic variables and consider, as an example, the accuracy of macroeconomic investments. We highlight that current macroeconomic models describe relations between the 1st order variables determined by sums of trade values or volumes. To predict market-based volatilities of price, return, and volatilities of macroeconomic variables, one should develop econometric methodologies, collect data, and elaborate macroeconomic theories of the 2nd order that model the mutual dependence of the 1st and 2nd order economic variables. The absence of macroeconomic theories of the 2nd order means no economic basis for predictions of market-based volatilities of price and return, as well as volatilities of any macroeconomic variables. In turn, that limits the accuracy of forecasting probabilities of price, return, and the accuracy of macroeconomic variables in the best case by Gaussian distributions.
Selecting stock portfolios and assessing their relative volatility risk compared to the market as a whole, market indices, or other portfolios is of great importance to professional fund managers and individual investors alike. Our research uses the cross-sectional intrinsic entropy (CSIE) model to estimate the cross-sectional volatility of the stock groups that can be considered together as portfolio constituents. In our study, we benchmark portfolio volatility risks against the volatility of the entire market provided by the CSIE and the volatility of market indices computed using longitudin…
We propose a novel method to quantify the clustering behavior in a complex time series and apply it to a high-frequency data of the financial markets. We find that regardless of used data sets, all data exhibits the volatility clustering properties, whereas those which filtered the volatility clustering effect by using the GARCH model reduce volatility clustering significantly. The result confirms that our method can measure the volatility clustering effect in financial market.
Asymmetric relationship between price and volatility is a prominent feature of the financial market time series. This paper explores the price-volatility nexus in cryptocurrency markets and investigates the presence of asymmetric volatility effect between uptrend (bull) and downtrend (bear) regimes. The conventional GARCH-class models have shown that in cryptocurrency markets, asymmetric reactions of volatility to returns differ from those of other traditional financial assets. We address this issue from a viewpoint of fractal analysis, which can cover the nonlinear interactions and the self-s…
This paper examines quantile dependence between international stock markets and evaluates its use for improving volatility forecasting. First, we analyze quantile dependence and directional predictability between the US stock market and stock markets in the UK, Germany, France and Japan. We use the cross-quantilogram, which is a correlation statistic of quantile hit processes. The detailed dependence between stock markets depends on specific quantile ranges and this dependence is generally asymmetric; the negative spillover effect is stronger than the positive spillover effect and there exists…
We exploit a continuous time random walk description of stock prices to obtain a fast and accurate evaluation of their volatility from intraday data. We show that financial markets are usefully described as open physical systems. Indeed we find that the process determining market volatility is not stationary while the market response to external volatility shocks stays constant over the time period of more than two years covered by our experimental data. Furthermore the autocorrelation function of volatility increments yields a value of about -0.4 at one-day time lag that is nearly equal for a…
We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $σ(t)$ which is directly observable from data. This quantity is usually indirectly defined by $r(t)=σ(t) ω(t)$ where the $r(t)$ are the daily returns of the market index and the $ω(t)$ are i.i.d. random variables with vanishing average and unitary variance. The relation $r(t)=σ(t) ω(t)$ alone is unable to give an operative definition of the index volatility, which remains unobservable. On the contrary, we show that using the whole i…
We study the relation between serial correlation of financial returns and volatility at intraday level for the S&P500 stock index. At daily and weekly level, serial correlation and volatility are known to be negatively correlated (LeBaron effect). While confirming that the LeBaron effect holds also at intraday level, we go beyond it and, complementing the efficient market hyphotesis (for returns) with the heterogenous market hyphotesis (for volatility), we test the impact of unexpected volatility, defined as the part of volatility which cannot be forecasted, on the presence of serial correlati…
This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in markets. We support our methodology by simulations where we also discuss the importance of stochastic noise and volatility in deterministic cusp catastrophe model. The m…
This study investigates the volatility of daily Bitcoin returns and multifractal properties of the Bitcoin market by employing the rolling window method and examines relationships between the volatility asymmetry and market efficiency. Whilst we find an inverted asymmetry in the volatility of Bitcoin, its magnitude changes over time, and recently, it has become small. This asymmetric pattern of volatility also exists in higher frequency returns. Other measurements, such as kurtosis, skewness, average, serial correlation, and multifractal degree, also change over time. Thus, we argue that prope…
We show how bad and good volatility propagate through forex markets, i.e., we provide evidence for asymmetric volatility connectedness on forex markets. Using high-frequency, intra-day data of the most actively traded currencies over 2007 - 2015 we document the dominating asymmetries in spillovers that are due to bad rather than good volatility. We also show that negative spillovers are chiefly tied to the dragging sovereign debt crisis in Europe while positive spillovers are correlated with the subprime crisis, different monetary policies among key world central banks, and developments on com…
We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pdf in the region of low values of volatility whereas the Hull and White model better approximates the empirical pdf for large values of volatility. Both models fails in describing the empirical pdf over a moderately large volatility range.
Using high frequency data, we have studied empirically the change of volatility, also called volatility derivative, for various time horizons. In particular, the correlation between the volatility derivative and the volatility realized in the next time period is a measure of the response function of the market participants. This correlation shows explicitly the heterogeneous structure of the market according to the characteristic time horizons of the differents agents. It reveals a volatility cascade from long to short time horizons, with a structure different from the one observed in turbulen…
We test various volatility models using the Bitcoin spot price series. Our models include HIST, EMA ARCH, GARCH, and EGARCH, models. Both of our in-sample-fit and out-of-sample-forecast results suggest that GARCH and EGARCH models perform much better than other models. Moreover, the EGARCH model's asymmetric term is positive and insignificant, which suggests that Bitcoin prices lack the asymmetric volatility response to past returns. Finally, we formulate an option trading strategy by exploiting the volatility spread between the GARCH volatility forecast and the option's implied volatility. We…
Impact of the COVID-19 pandemic on the financial market efficiency of price returns, absolute returns, and volatility increment: Evidence from stock and cryptocurrency markets
We perform a scaling analysis on NYSE daily returns. We show that volatility correlations are power-laws on a time range from one day to one year and, more important, that they exhibit a multiscale behaviour.
We apply the formalism of the continuous time random walk (CTRW) theory to financial tick data of the bond futures transacted in Korean Futures Exchange (KOFEX) market. For our case, the tick dynamical behaviors of the returns and volatility for bond futures are treated particularly at the long-time limit. The volatility for the price of our bond futures shows a power-law with anomalous scaling exponent, similar to other options. Our result presented will be compared with that of recent numerical calculations.
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility would indicate market inefficiency. Using minute-by-minute data on S&P 500 index options, we provide evidence regarding delayed and gradual movements in implied volatility after the arrival of return jumps. These movements are directed and persistent, especially in the case of negative return jumps. Our results are significant when the implied volatilities …
We shortly 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…
To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices: open, high, low, and close prices (OHLC), along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a compa…
Taking the European Central Bank unconventional policies as a reference, we suggest a class of Multiplicative Error Models (MEM) taylored to analyze the impact such policies have on stock market volatility. The new set of models, called MEM with Asymmetry and Policy effects (MAP), keeps the base volatility dynamics separate from a component reproducing policy effects, with an increase in volatility on announcement days and a decrease unfolding implementation effects. When applied to four Eurozone markets, a Model Confidence Set approach finds a significant improvement of the forecasting power …
Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that under no-arbitrage assumption, the market impact function can only be of power-law type. Furthermore, we prove that this implies that the macroscopic price is diffusive with rough volatility, with a one-to-one correspondence between the exponent of the impact function and the Hurst parameter of the volatility. Hence we simply explain the universal rough behavior of the volatility as a consequence of the no-arbitrage property. From a mathematical viewpoin…
This paper introduces new methods to study behaviours among the 52 largest cryptocurrencies between 01-01-2019 and 30-06-2021. First, we explore evolutionary correlation behaviours and apply a recently proposed turning point algorithm to identify regimes in market correlation. Next, we inspect the relationship between collective dynamics and the cryptocurrency market size - revealing an inverse relationship between the size of the market and the strength of collective dynamics. We then explore the time-varying consistency of the relationships between cryptocurrencies' size and their returns an…
Recently, to account for low-frequency market dynamics, several volatility models, employing high-frequency financial data, have been developed. However, in financial markets, we often observe that financial volatility processes depend on economic states, so they have a state heterogeneous structure. In this paper, to study state heterogeneous market dynamics based on high-frequency data, we introduce a novel volatility model based on a continuous Ito diffusion process whose intraday instantaneous volatility process evolves depending on the exogenous state variable, as well as its integrated v…
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a power law, and the exponents $p_\pm$ usually vary with the strength of the large volatilities. The large-volatility dynamics is time-reversal symmetric at the time scale in minutes, while asymmetric at the daily time scale. Careful analysis reveals that the time-reversal asymmetry is mainly induced by exogenous events. It is also the exogenous events which driv…
In financial markets, greater volatility is usually considered synonym of greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To investigate this surprising feature, here we propose using the mean first hitting time, i.e. the average time a stock return takes to undergo for the first time a large negative or positive variation, as an indicator of price stability, and relate this to a standard measure of volatility. In an empirical analysis of daily returns for $1071$ stocks traded in t…
This study investigates the impacts of asymmetry on the modeling and forecasting of realized volatility in the Japanese futures and spot stock markets. We employ heterogeneous autoregressive (HAR) models allowing for three types of asymmetry: positive and negative realized semivariance (RSV), asymmetric jumps, and leverage effects. The estimation results show that leverage effects clearly influence the modeling of realized volatility models. Leverage effects exist for both the spot and futures markets in the Nikkei 225. Although realized semivariance aids better modeling, the estimations of RS…
We detect and quantify asymmetries in volatility spillovers using the realized semivariances of petroleum commodities: crude oil, gasoline, and heating oil. During the 1987--2014 period we document increasing spillovers from volatility among petroleum commodities that substantially change after the 2008 financial crisis. The increase in volatility spillovers correlates with the progressive financialization of the commodities. In terms of asymmetries in spillovers we show that periods of increasing crude oil prices strongly correlate with dominating spillovers due to bad volatility. Overall, ba…
We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology), and realized volatility. We compare visually and statistically distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. We find that the ratio is best fitted by heavy-tailed -- lognormal and fat-tailed (power-law) -- distributions, depending on whether preceding or concurrent month of realized variance is used. We do not find substantial difference in accuracy between VIX and VXO. Additionally, we study the var…
We examine volatility of an Indian stock market in terms of aspects like participation, synchronization of stocks and quantification of volatility using the random matrix approach. Volatility pattern of the market is found using the BSE index for the three-year period 2000-2002. Random matrix analysis is carried out using daily returns of 70 stocks for several time windows of 85 days in 2001 to (i) do a brief comparative analysis with statistics of eigenvalues and eigenvectors of the matrix C of correlations between price fluctuations, in time regimes of different volatilities. While a bulk of…
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 …
Bid-ask spread is taken as an important measure of the financial market liquidity. In this article, we study the dynamics of the spread return and the spread volatility of four liquid stocks in the Chinese stock market, including the memory effect and the multifractal nature. By investigating the autocorrelation function and the Detrended Fluctuation Analysis (DFA), we find that the spread return is lack of long-range memory, while the spread volatility is long-range time correlated. Moreover, by applying the Multifractal Detrended Fluctuation Analysis (MF-DFA), the spread return is observed t…
ARCH and GARCH models assume either i.i.d. or (what economists lable as) white noise as is usual in regression analysis while assuming memory in a conditional mean square fluctuation with stationary increments. We will show that ARCH/GARCH is inconsistent with uncorrelated increments, violating the i.i.d. and white assumptions and finance data and the efficient market hypothesis as well.
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynamics. Another interesting manner to study the volatility phenomena is by using measures based on the concept of entropy. In this paper we investigate the long memory and volatility clustering for the SP 500, NASDAQ 100 and Stoxx 50 indexes in order to compare the US and European M…
Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and volume interact, particularly when the levels of both are high. We find that the distribution of the volume-conditional volatility is well fit by a power-law function with an exponential cutoff. We find that the volume-conditional volatility distribution scales with volume, and collapses these distributions to a single curve. We exploit the characteristics o…
We study the volatility of the MIB30-stock-index high-frequency data from November 28, 1994 through September 15, 1995. Our aim is to empirically characterize the volatility random walk in the framework of continuous-time finance. To this end, we compute the index volatility by means of the log-return standard deviation. We choose an hourly time window in order to investigate intraday properties of volatility. A periodic component is found for the hourly time window, in agreement with previous observations. Fluctuations are studied by means of detrended fluctuation analysis, and we detect long…
Institute of Data Science and NUS Graduate School for Integrative Sciences & Engineering, National University of Singapore（新加坡国立大学数据科学研究所及综合科学与工程研究生院）；Department of Mathematics and Risk Management Institute, National University of Singapore（新加坡国立大学数学系及风险管理研究所）
Volatility for financial assets returns can be used to gauge the risk for financial market. We propose a deep stochastic volatility model (DSVM) based on the framework of deep latent variable models. It uses flexible deep learning models to automatically detect the dependence of the future volatility on past returns, past volatilities and the stochastic noise, and thus provides a flexible volatility model without the need to manually select features. We develop a scalable inference and learning algorithm based on variational inference. In real data analysis, the DSVM outperforms several popula…
Recent literature seek to forecast implied volatility derived from equity, index, foreign exchange, and interest rate options using latent factor and parametric frameworks. Motivated by increased public attention borne out of the financialization of futures markets in the early 2000s, we investigate if these extant models can uncover predictable patterns in the implied volatility surfaces of the most actively traded commodity options between 2006 and 2016. Adopting a rolling out-of-sample forecasting framework that addresses the common multiple comparisons problem, we establish that, for energ…
This paper analyses the behaviour of volatility for several international stock market indexes, namely the SP 500 (USA), the Nikkei (Japan), the PSI 20 (Portugal), the CAC 40 (France), the DAX 30 (Germany), the FTSE 100 (UK), the IBEX 35 (Spain) and the MIB 30 (Italy), in the context of non-stationarity. Our empirical results point to the evidence of the existence of integrated behaviour among several of those stock market indexes of different dimensions. It seems, therefore, that the behaviour of these markets tends to some uniformity, which can be interpreted as the existence of a similar be…
Using a time-varying approach, this paper examines the dynamics of volatility in the REIT sector. The results highlight the attractiveness and suitability of using GARCH based approaches in the modeling of daily REIT volatility. The paper examines the influencing factors on REIT volatility, documenting the return and volatility linkages between REIT sub-sectors and also examines the influence of other US equity series. The results contrast with previous studies of monthly REIT volatility. Linkages within the REIT sector and with related sectors such as value stocks are diminished, while the ge…
In this paper, we propose and study a novel continuous-time model, based on the well-known constant elasticity of variance (CEV) model, to describe the asset price process. The basic idea is that the volatility elasticity of the CEV model can not be treated as a constant from the perspective of stochastic analysis. To address this issue, we deduce the price process of assets from the perspective of volatility elasticity, propose the constant volatility elasticity (CVE) model, and further derive a more general variable volatility elasticity (VVE) model. Moreover, our model can describe the posi…
We simulate a series of daily returns from intraday price movements initiated by microstructure elements. Significant evidence is found that daily returns and daily return volatility exhibit first order autocorrelation, but trading volume and daily return volatility are not correlated, while intraday volatility is. We also consider GARCH effects in daily return series and show that estimates using daily returns are biased from the influence of the level of prices. Using daily price changes instead, we find evidence of a significant GARCH component. These results suggest that microstructure ele…
We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce various stylized facts of different markets and different assets with the same set of model parameters. We show that the power-law properties and the scaling of return intervals and other financial variables have a similar origin and could be…
In this paper, we analyze the time-series of minute price returns on the Bitcoin market through the statistical models of generalized autoregressive conditional heteroskedasticity (GARCH) family. Several mathematical models have been proposed in finance, to model the dynamics of price returns, each of them introducing a different perspective on the problem, but none without shortcomings. We combine an approach that uses historical values of returns and their volatilities - GARCH family of models, with a so-called "Mixture of Distribution Hypothesis", which states that the dynamics of price ret…
This work is devoted to the study of modeling geophysical and financial time series. A class of volatility models with time-varying parameters is presented to forecast the volatility of time series in a stationary environment. The modeling of stationary time series with consistent properties facilitates prediction with much certainty. Using the GARCH and stochastic volatility model, we forecast one-step-ahead suggested volatility with +/- 2 standard prediction errors, which is enacted via Maximum Likelihood Estimation. We compare the stochastic volatility model relying on the filtering techniq…
Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the S&P 500, FTSE100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TA…
Prediction and quantification of future volatility and returns play an important role in financial modelling, both in portfolio optimization and risk management. Natural language processing today allows to process news and social media comments to detect signals of investors' confidence. We have explored the relationship between sentiment extracted from financial news and tweets and FTSE100 movements. We investigated the strength of the correlation between sentiment measures on a given day and market volatility and returns observed the next day. The findings suggest that there is evidence of c…
In this paper, we analyse the South African implied volatility in various setting. We assess the information content in SAVI implied volatility using daily markets data. Our empirical application is focused on the FTSE/JSE Top 40 index and we emphasize our models performance in distinct sub-periods. Our results are compared with VIX/VXN and S&P 500/NASDAQ 100 data in some points which are taken as our benchmark. We find a significant negative relationship between returns and volatility, in line with the results found in other markets. Finally, the link between SAVI, VIX and VXN are undertaken …
We study historical correlations and lead-lag relationships between individual stock risk (volatility of daily stock returns) and market risk (volatility of daily returns of a market-representative portfolio) in the US stock market. We consider the cross-correlation functions averaged over all stocks, using 71 stock prices from the Standard \& Poor's 500 index for 1994--2013. We focus on the behavior of the cross-correlations at the times of financial crises with significant jumps of market volatility. The observed historical dynamics showed that the dependence between the risks was almost lin…
We develop a new stock market index that captures the chaos existing in the market by measuring the mutual changes of asset prices. This new index relies on a tensor-based embedding of the stock market information, which in turn frees it from the restrictive value- or capitalization-weighting assumptions that commonly underlie other various popular indexes. We show that our index is a robust estimator of the market volatility which enables us to characterize the market by performing the task of segmentation with a high degree of reliability. In addition, we analyze the dynamics and kinematics …
We analyze realized volatilities constructed using high-frequency stock data on the Tokyo Stock Exchange. In order to avoid non-trading hours issue in volatility calculations we define two realized volatilities calculated separately in the two trading sessions of the Tokyo Stock Exchange, i.e. morning and afternoon sessions. After calculating the realized volatilities at various sampling frequencies we evaluate the bias from the microstructure noise as a function of sampling frequency. Taking into account of the bias to realized volatility we examine returns standardized by realized volatiliti…
We analyse high-frequency realised volatility dynamics and spillovers in the bitcoin market, focusing on two pairs: bitcoin against the US dollar (the main fiat-crypto pair) and trading bitcoin against tether (the main crypto-crypto pair). We find that the tether-margined perpetual contract on Binance is clearly the main source of volatility, continuously transmitting strong flows to all other instruments and receiving only a little volatility. Moreover, we find that (i) during US trading hours, traders pay more attention and are more reactive to prevailing market conditions when updating thei…
One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known traditional techniques in the literature to measure stock market volatility, a central point in this debate that constitutes the actual scope of this paper is to compare this common approach in which we discuss such popular techniques as the standard deviation and an innovative methodology based on Econophysics. In our study, we use the concept of Tsallis entropy…
We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period is characterized by the Omori law, which describes the decay in the rate of aftershocks of a given size with time t by a power law with exponent close to 1. A shock followed by such a power law decay in the rate is here called Omori process. Studying several aftercrash time series, we show that the Omori law holds not only after significant market crashes, bu…
