Trading frequency and volatility clustering

Volatility clustering, with autocorrelations of the hyperbolic decay rate, is unquestionably one of the most important stylized facts of financial time series. This paper presents a market microstructure model that is able to generate volatility clustering with hyperbolically decaying autocorrelations via traders with multiple trading frequencies, using Bayesian information updates in an incomplete market. The model illustrates that signal extraction, which is induced by multiple trading frequencies, can increase the persistence of the volatility of returns. Furthermore, we show that the volatility of the underlying time series of returns varies greatly with the number of traders in the market.     

Volatility spillovers and hedging effectiveness between the oil market and Eurozone sectors: A tale of two crises

This paper aims to analyze the mean and volatility spillovers between oil prices and the Eurozone supersector returns. It uses daily data of the Brent prices and 19 Eurozone supersector indices for the period from August 2004 to August 2015. This area experienced two important instabilities in that period, the global financial crisis (GFC) and the Euro debt crisis (EDC). Because financial turbulences are suspected to induce changes in the volatility dynamics, the full sample is divided into three sub-samples. Empirically, this study employs a bivariate VAR-BEKK-GARCH model that allows for transmission in volatility. The obtained volatilities and covariances are used to compute the optimal weights and hedge ratios for oil–stock portfolio holdings. The findings show that both mean and volatility spillovers between the oil market and the different Eurozone sectors are time-varying and heterogeneous. In the GFC sub-period, there is evidence of contagion effects because there is an intensification of volatility spillovers. The EDC does not seem to have induced any particular change in the spillover effects. The optimal weights, hedge ratios, and correlation analysis results allow an accurate understanding of the time series relationship between the two markets and are useful for financial market participants and policymakers.     

Credit risk modeling with affine processes

This article combines an orientation to credit risk modeling with an introduction to affine Markov processes, which are particularly useful for financial modeling. We emphasize corporate credit risk and the pricing of credit derivatives. Applications of affine processes that are mentioned include survival analysis, dynamic term-structure models, and option pricing with stochastic volatility and jumps. The default-risk applications include default correlation, particularly in first-to-default settings. The reader is assumed to have some background in financial modeling and stochastic calculus.     

Processes for stocks capturing their statistical properties from one day to one year

A realistic ARCH process is set up so as to duplicate, for all practical purposes, the properties of stock time series from 1 day to 1 year. The process includes heteroskedasticity with long memory, leverage, fat-tail innovations, relative return, price granularity, and holidays. Its adequacy to describe empirical data is controlled over a broad panel of statistics, including (robust L-statistics) skew, (robust) kurtosis, shape factor for the volatility distribution, and lagged correlations between combinations of return and volatility. These statistics are computed for returns and volatilities with characteristic time intervals ranging from 1 day to 1 year. This wide cross-check between stock time series and simulations ensures that the most important features of the data are correctly captured by the process up to 1 year. The by-products of the statistical analyses and estimations are (1) a positive skew, (2) a cross-sectional relation between kurtosis and heteroskedasticity, (3) a very similar cross-sectional distribution for the statistics evaluated over the empirical data set or for the process with one set of parameters and (4) the heteroskedasticity is very close to an integrated volatility process.     

Dynamic Relationship among Intraday Realized Volatility,Volume and Number of Trades

In this paper, the vector autoregressive model is fitted to find out the causal relationship among realized volatility, the number of transactions and volume with the intraday time intervals of 10, 20 and 30 min. To understand the impact of shock to the market on specific variables, a multivariate Impulse Response Function analysis is also introduced to visualize the causal relationship among the variables. From the analysis of a stock listed on the Stock Exchange of Hong Kong, we find that realized volatility reacts positively to the lagged average trade size. However, the realized volatility forms a negative relationship with the first few lagged number of trades. As a result, the intraday causal relationship among realized volatility, volume and the number of trades is quite different from that obtained on a daily basis. The findings of this paper can enhance the understanding of how the number of trades and the average trade size per transaction affect the risk evolution of financial securities and thus improve the risk management of day trading strategies.     

Option pricing under fast-varying and rough stochastic volatility

Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the origin. Another classic stylistic feature often assumed for the volatility is that it is mean reverting. In this paper it is shown that the price impact of a rapidly mean reverting rough volatility model coincides with that associated with fast mean reverting Markov stochastic volatility models. This reconciles the empirical observation of rough volatility paths with the good fit of the implied volatility surface to models of fast mean reverting Markov volatilities. Moreover, the result conforms with recent numerical results regarding rough stochastic volatility models. It extends the scope of models for which the asymptotic results of fast mean reverting Markov volatilities are valid. The paper concludes with a general discussion of fractional volatility asymptotics and their interrelation. The regimes discussed there include fast and slow volatility factors with strong or small volatility fluctuations and with the limits not commuting in general. The notion of a characteristic term structure exponent is introduced, this exponent governs the implied volatility term structure in the various asymptotic regimes.     

Forecasting Financial Market Volatility Using a Dynamic Topic Model

This study employs big data and text data mining techniques to forecast financial market volatility. We incorporate financial information from online news sources into time series volatility models. We categorize a topic for each news article using time stamps and analyze the chronological evolution of the topic in the set of articles using a dynamic topic model. After calculating a topic score, we develop time series models that incorporate the score to estimate and forecast realized volatility. The results of our empirical analysis suggest that the proposed models can contribute to improving forecasting accuracy.     

Treasury Bond Volatility and Uncertainty about Monetary Policy

We show that dispersion‐based uncertainty about the future course of monetary policy is the single most important determinant of Treasury bond volatility across all maturities. The link between Treasury bond volatility and uncertainty about macroeconomic variables is much stronger than for the more traditional time series measures of macroeconomic volatility and adds beyond the information contained in lagged bond market volatility. Uncertainty about monetary policy subsumes the uncertainty about future inflation (consumer price index and the deflator) and economic activity (unemployment, real and nominal gross domestic product and industrial production). In addition, causality clearly runs one way: from monetary policy uncertainty to Treasury bond volatility.     

Non-parametric estimation of historical volatility

Evolving volatility is a dominant feature observed in most financial time series and a key parameter used in option pricing and many other financial risk analyses. A number of methods for non-parametric scale estimation are reviewed and assessed with regard to the stylized features of financial time series. A new non-parametric procedure for estimating historical volatility is proposed based on local maximum likelihood estimation for the t-distribution. The performance of this procedure is assessed using simulated and real price data and is found to be the best among estimators we consider. We propose that it replaces the moving variance historical volatility estimator.     

A multivariate distance nonlinear causality test based on partial distance correlation: a machine learning application to energy futures

This paper proposes a multivariate distance nonlinear causality test (MDNC) using the partial distance correlation in a time series framework. Partial distance correlation as an extension of the Brownian distance correlation calculates the distance correlation between random vectors X and Y controlling for a random vector Z. Our test can detect nonlinear lagged relationships between time series, and when integrated with machine learning methods it can improve the forecasting power. We apply our method as a feature selection procedure and combine it with the support vector machine and random forests algorithms to study the forecast of the main energy financial time series (oil, coal, and natural gas futures). It shows substantial improvement in forecasting the fuel energy time series in comparison to the classical Granger causality method in time series.     

Quant GANs: deep generation of financial time series

Modeling financial time series by stochastic processes is a challenging task and a central area of research in financial mathematics. As an alternative, we introduce Quant GANs, a data-driven model which is inspired by the recent success of generative adversarial networks (GANs). Quant GANs consist of a generator and discriminator function, which utilize temporal convolutional networks (TCNs) and thereby achieve to capture long-range dependencies such as the presence of volatility clusters. The generator function is explicitly constructed such that the induced stochastic process allows a transition to its risk-neutral distribution. Our numerical results highlight that distributional properties for small and large lags are in an excellent agreement and dependence properties such as volatility clusters, leverage effects, and serial autocorrelations can be generated by the generator function of Quant GANs, demonstrably in high fidelity.     

Pricing options under stochastic volatility: a power series approach

In this paper we present a new approach for solving the pricing equations (PDEs) of European call options for very general stochastic volatility models, including the Stein and Stein, the Hull and White, and the Heston models as particular cases. The main idea is to express the price in terms of a power series of the correlation parameter between the processes driving the dynamics of the price and of the volatility. The expansion is done around correlation zero and each term is identified via a probabilistic expression. It is shown that the power series converges with positive radius under some regularity conditions. Besides, we propose (as in Alós in Finance Stoch. 10:353–365, 2006) a further approximation to make the terms of the series easily computable and we estimate the error we commit. Finally we apply our methodology to some well-known financial models.      

Multiresolution approximation for volatility processes

Abstract

We present an application of wavelet techniques to non-stationary time series with the aim of detecting the dependence structure which is typically found to characterize intraday stock index financial returns. It is particularly important to identify what components truly belong to the underlying volatility process, compared with those features appearing instead as a result of the presence of disturbance processes. The latter may yield misleading inference results when standard financial time series models are adopted. There is no universal agreement on whether long memory really affects financial series, or instead whether it could be that non-stationarity, once detected and accounted for, may allow for more power in detecting the dependence structure and thus suggest more reliable models. Wavelets are still a novel tool in the domain of applications in finance; thus, one goal is to try to show their potential use for signal decomposition and approximation of time-frequency signals. This might suggest a better interpretation of multi-scaling and aggregation effects in high-frequency returns. We show, by using special dictionaries of functions and ad hoc algorithms, that a pre-processing procedure for stock index returns leads to a more accurate identification of dependent and non-stationary features, whose detection results are improved compared with those obtained by other traditional Fourier-based methods. This allows generalized autoregressive conditional heteroscedastic models to be more effective for statistical estimation purposes.     

Volatility spillover in the foreign exchange market: the Indian experience

We find evidence of significant volatility co-movements and/or spillover from different financial markets to the forex market in India. Among a large number of variables examined, volatility spillovers from domestic stock, government securities, overnight index swap, Ted spread and international crude oil markets to the foreign exchange market are found to be significant. There is evidence of asymmetric reactions in the forex market volatility. Comparisons between pre-crisis and post-crisis volatility indicate that the reform measures and changes in financial markets microstructure during the crisis period had significant impact on volatility spillover. During the post-crisis period, the lagged volatility component that represents persistent or fundamental changes had significant spillover effect on forex volatility, rather than the temporary shocks component. There is evidence of a decline in the asymmetric response in the forex volatility during the post-crisis period in India.     

Long-memory and heterogeneous components in high frequency Pacific-Basin exchange rate volatility

Recent research examining high-frequency financial data has suggested that volatility dynamics may be confounded by the existence of an intra-day periodic pattern and multiple sources of volatility. This paper examines whether these dynamics are present in the US Dollar exchange rates of five Pacific Basin economies. Using 30-min sampled returns, evidence of a ‘U’-shape intra-day pattern in volatility for regional markets is reported and controlled for using a Flexible Fourier transform. Supportive evidence for the existence of multiple volatility components is offered by semi-parametric fractional difference estimates of the long-memory properties of absolute exchange rate returns at various intra-day data sampling frequencies. Further parametric evidence of an explicit component structure in such high frequency exchange rate volatility is offered by the estimates of a component-GARCH model which comprises both a long-run volatility component exhibiting slow shock decay and a short-run volatility component exhibiting far more rapid decay, and provides a generally superior fit to the data. Further application of these C-GARCH models in the analysis of high frequency volatility spillovers between the currencies considered also reveals that such spillovers are predominantly transitory rather than highly persistent in nature, but that where volatility spillovers do impact on the long-run component of exchange rate volatility the Australian Dollar plays a pivotal role in the localised causality transmission mechanism.      

Re-examining the asymmetric predictability of conditional variances: The role of sudden changes in variance

The existence of “spillover effects” in financial markets is well documented and multivariate time series techniques have been used to study the transmission of conditional variances among large and small market value firms. Earlier research has suggested that volatility surprises to large capitalization firms are a reliable predictor of the volatility of small capitalization firms. A related line of research has examined how regime shifts in volatility may account for a considerable amount of the persistence in volatility. However, these studies have focused on univariate modeling and many have imposed regime changes on a priori grounds. This paper re-examines the asymmetry in the predictability of the volatilities of large versus small market value firms allowing for sudden changes in variance. Our method of analysis extends the existing literature in two important ways. First, recent advances in time series econometrics allow us to detect the time periods of sudden changes in volatility of large cap and small cap stocks endogenously using the iterated cumulated sums of squares (ICSS) algorithm. Second, we directly incorporate the information obtained on sudden changes in volatility in a Bivariate GARCH model of small and large cap stock returns. Our findings indicate that accounting for volatility shifts considerably reduces the transmission in volatility and, in essence, removes the spillover effects. We conclude that ignoring regime changes may lead one to significantly overestimate the degree of volatility transmission that actually exists between the conditional variances of small and large firms.     

Euclidean (dis)similarity in financial network analysis

Interdependence among financial return series primarily originate from correlation between underlying assets. However, correlation fully describes interdependence only if the financial system behaves linearly and if an assumption of multivariate normal distribution additionally holds true. At the same time, with intrinsic z score normalization, correlation ignores means (expected return) and variances (risk) when calibrating the interdependence. Such oversight raises the significant question of whether security return networks can be realistically modelled and interpreted by market correlations. This paper proposes the Euclidean (dis)similarity metric which enables incorporation of risk and return along with the primary correlation component. We apply this metric to explain the collective behavior of the MSCI world market and compare the results with other correlation networks. Findings show that realized volatility accounts for 71% of the observed topology whereas correlation explains only 29% of market structure. No evidence was found supporting the importance of expected return. Power law exponents and degree distributions reveal that the centrality of hub nodes are considerably higher in the Euclidean as opposed to correlation networks. Accordingly, the importance and influence of central countries (like US and Japan hubs) in the spreading of high volatility is considerably higher than what correlation networks report.     

How Do Investors' Expectations Drive Asset Prices?

Based on an extension of the process of investors' expectations to stochastic volatility we derive asset price processes in a general continuous time pricing kernel framework. Our analysis suggests that stochastic volatility of asset price processes results from the fact that investors do not know the risk of an asset and therefore the volatility of the process of their expectations is stochastic, too. Furthermore, our model is consistent with empirical studies reporting negative correlation between asset prices and their volatility as well as significant variations in the Sharpe ratio.     

On the stability of stablecoins

This paper investigates the volatility processes of stablecoins and their potential stochastic interdependencies with Bitcoin volatility. We employ a novel approach to choose the optimal combination for the power law exponent and the minimum value for the volatilities bending the power law. Our results indicate that Bitcoin volatility is well-behaved in a statistical sense with a finite theoretical variance. Surprisingly, the volatilities of stablecoins are statistically unstable and contemporaneously respond to Bitcoin volatility. Also, whereas the volatilities of stablecoins are not Granger-causal for Bitcoin volatility, lagged Bitcoin volatility exhibits Granger-causal effects on the volatilities of stablecoins. We conclude that Bitcoin volatility is a fundamental factor that drives the volatilities of stablecoins.