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Despite the impressive success of deep neural networks in many application areas, neural network models have so far not been widely adopted in the context of volatility forecasting. In this work, we aim to bridge the conceptual gap between established time series approaches, such as the Heterogeneous Autoregressive (HAR) model (Corsi, 2009), and state-of-the-art deep neural network models. The newly introduced HARNet is based on a hierarchy of dilated convolutional layers, which facilitates an exponential growth of the receptive field of the model in the number of model parameters. HARNets allow for an explicit initialization scheme such that before optimization, a HARNet yields identical predictions as the respective baseline HAR model. Particularly when considering the QLIKE error as a loss function, we find that this approach significantly stabilizes the optimization of HARNets. We evaluate the performance of HARNets with respect to three different stock market indexes. Based on this evaluation, we formulate clear guidelines for the optimization of HARNets and show that HARNets can substantially improve upon the forecasting accuracy of their respective HAR baseline models. In a qualitative analysis of the filter weights learnt by a HARNet, we report clear patterns regarding the predictive power of past information. Among information from the previous week, yesterday and the day before, yesterday's volatility makes by far the most contribution to today's realized volatility forecast. Moroever, within the previous month, the importance of single weeks diminishes almost linearly when moving further into the past.
Non-standard errors
(2021)
In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in sample estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: non-standard errors. To study them, we let 164 teams test six hypotheses on the same sample. We find that non-standard errors are sizeable, on par with standard errors. Their size (i) co-varies only weakly with team merits, reproducibility, or peer rating, (ii) declines significantly after peer-feedback, and (iii) is underestimated by participants.
Revisiting the stealth trading hypothesis: does time-varying liquidity explain the size-effect?
(2019)
Large trades have a smaller price impact per share than medium-sized trades. So far, the literature has attributed this effect to the informational content of trades. In this paper, we show that this effect can arise from strategic order placement. We introduce the concept of a liquidity elasticity, measuring the responsiveness of liquidity demand with respect to changes in liquidity supply, as a major driver for a declining price impact per share. Empirical evidence based on Nasdaq stocks strongly supports theoretical predictions and shows that the aspect of liquidity coordination is an important complement to rationales based on asymmetric information.
Distributed ledger technologies rely on consensus protocols confronting traders with random waiting times until the transfer of ownership is accomplished. This time consuming settlement process exposes arbitrageurs to price risk and imposes limits to arbitrage. We derive theoretical arbitrage boundaries under general assumptions and show that they increase with expected latency, latency uncertainty, spot volatility, and risk aversion. Using high-frequency data from the Bitcoin network, we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, covering 88% of the observed cross-exchange price differences. Settlement through decentralized systems thus induces non-trivial frictions affecting market efficiency and price formation.
We theoretically and empirically study large-scale portfolio allocation problems when transaction costs are taken into account in the optimization problem. We show that transaction costs act on the one hand as a turnover penalization and on the other hand as a regularization, which shrinks the covariance matrix. As an empirical framework, we propose a flexible econometric setting for portfolio optimization under transaction costs, which incorporates parameter uncertainty and combines predictive distributions of individual models using optimal prediction pooling. We consider predictive distributions resulting from highfrequency based covariance matrix estimates, daily stochastic volatility factor models and regularized rolling window covariance estimates, among others. Using data capturing several hundred Nasdaq stocks over more than 10 years, we illustrate that transaction cost regularization (even to small extent) is crucial in order to produce allocations with positive Sharpe ratios. We moreover show that performance differences between individual models decline when transaction costs are considered. Nevertheless, it turns out that adaptive mixtures based on high-frequency and low-frequency information yield the highest performance. Portfolio bootstrap reveals that naive 1=N-allocations and global minimum variance allocations (with and without short sales constraints) are significantly outperformed in terms of Sharpe ratios and utility gains.
A counterparty credit limit (CCL) is a limit imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. Although CCLs are designed to help institutions mitigate counterparty risk by selective diversification of their exposures, their implementation restricts the liquidity that institutions can access in an otherwise centralized pool. We address the question of how this mechanism impacts trade prices and volatility, both empirically and via a new model of trading with CCLs. We find empirically that CCLs cause little impact on trade. However, our model highlights that in extreme situations, CCLs could serve to destabilize prices and thereby influence systemic risk.
We show an ambivalent role of high-frequency traders (HFTs) in the Eurex Bund Futures market around high-impact macroeconomic announcements and extreme events. Around macroeconomic announcements, HFTs serve as market makers, post competitive spreads, and earn most of their profits through liquidity supply. Right before the announcement, however, HFTs significantly widen spreads and cause a rapid but short-lived drying-out of liquidity. In turbulent periods, such as after the U.K. Brexit announcement, HFTs shift their focus from market making activities to aggressive (but not necessarily profitable) directional strategies. Then, HFT activity becomes dominant and market quality can degrade.
Exploiting NASDAQ order book data and difference-in-differences methodology, we identify the distinct effects of trading pause mechanisms introduced on U.S. stock exchanges after May 2010. We show that the mere existence of such a regulation constitutes a safeguard which makes market participants behave differently in anticipation of a pause. Pauses tend to break local price trends, make liquidity suppliers revise positions, and enhance price discovery. In contrast, pauses do not have a “cool off” effect on markets, but rather accelerate volatility and bid-ask spreads. This implies a regulatory trade-off between the protective role of trading pauses and their adverse effects on market quality.
We extend the classical ”martingale-plus-noise” model for high-frequency prices by an error correction mechanism originating from prevailing mispricing. The speed of price reversal is a natural measure for informational efficiency. The strength of the price reversal relative to the signal-to-noise ratio determines the signs of the return serial correlation and the bias in standard realized variance estimates. We derive the model’s properties and locally estimate it based on mid-quote returns of the NASDAQ 100 constituents. There is evidence of mildly persistent local regimes of positive and negative serial correlation, arising from lagged feedback effects and sluggish price adjustments. The model performance is decidedly superior to existing stylized microstructure models. Finally, we document intraday periodicities in the speed of price reversion and noise-to-signal ratios.
We propose a multivariate dynamic intensity peaks-over-threshold model to capture extreme events in a multivariate time series of returns. The random occurrence of extreme events exceeding a threshold is modeled by means of a multivariate dynamic intensity model allowing for feedback effects between the individual processes. We propose alternative specifications of the multivariate intensity process using autoregressive conditional intensity and Hawkes-type specifications. Likewise, temporal clustering of the size of exceedances is captured by an autoregressive multiplicative error model based on a generalized Pareto distribution. We allow for spillovers between both the intensity processes and the process of marks. The model is applied to jointly model extreme returns in the daily returns of three major stock indexes. We find strong empirical support for a temporal clustering of both the occurrence of extremes and the size of exceedances. Moreover, significant feedback effects between both types of processes are observed. Backtesting Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts show that the proposed model does not only produce a good in-sample fit but also reliable out-of-sample predictions. We show that the inclusion of temporal clustering of the size of exceedances and feedback with the intensity thereof results in better forecasts of VaR and ES.
We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al. (2014). We extend the LMM estimator to allow for autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. We prove the consistency and asymptotic normality of the proposed spot covariance estimator. Based on extensive simulations we provide empirical guidance on the optimal implementation of the estimator and apply it to high-frequency data of a cross-section of NASDAQ blue chip stocks. Employing the estimator to estimate spot covariances, correlations and betas in normal but also extreme-event periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, (iii) are strongly serially correlated, and (iv) can increase strongly and nearly instantaneously if new information arrives.
We develop a model of an order-driven exchange competing for order flow with off-exchange trading mechanisms. Liquidity suppliers face a trade-off between benefits and costs of order exposure. If they display trading intentions, they attract additional trade demand. We show, in equilibrium, hiding trade intentions can induce mis-coordination between liquidity supply and demand, generate excess price fluctuations and harm price efficiency. Econometric high-frequency analysis based on unique data on hidden orders from NASDAQ reveals strong empirical support for these predictions: We find abnormal reactions in prices and order flow after periods of high excess-supply of hidden liquidity.
We propose a framework for estimating network-driven time-varying systemic risk contributions that is applicable to a high-dimensional financial system. Tail risk dependencies and contributions are estimated based on a penalized two-stage fixed-effects quantile approach, which explicitly links bank interconnectedness to systemic risk contributions. The framework is applied to a system of 51 large European banks and 17 sovereigns through the period 2006 to 2013, utilizing both equity and CDS prices. We provide new evidence on how banking sector fragmentation and sovereign-bank linkages evolved over the European sovereign debt crisis and how it is reflected in network statistics and systemic risk measures. Illustrating the usefulness of the framework as a monitoring tool, we provide indication for the fragmentation of the European financial system having peaked and that recovery has started.
We propose an iterative procedure to efficiently estimate models with complex log-likelihood functions and the number of parameters relative to the observations being potentially high. Given consistent but inefficient estimates of sub-vectors of the parameter vector, the procedure yields computationally tractable, consistent and asymptotic efficient estimates of all parameters. We show the asymptotic normality and derive the estimator's asymptotic covariance in dependence of the number of iteration steps. To mitigate the curse of dimensionality in high-parameterized models, we combine the procedure with a penalization approach yielding sparsity and reducing model complexity. Small sample properties of the estimator are illustrated for two time series models in a simulation study. In an empirical application, we use the proposed method to estimate the connectedness between companies by extending the approach by Diebold and Yilmaz (2014) to a high-dimensional non-Gaussian setting.
We propose the realized systemic risk beta as a measure for financial companies’ contribution to systemic risk given network interdependence between firms’ tail risk exposures. Conditional on statistically pre-identified network spillover effects and market as well as balance sheet information, we define the realized systemic risk beta as the total time-varying marginal effect of a firm’s Value-at-risk (VaR) on the system’s VaR. Statistical inference reveals a multitude of relevant risk spillover channels and determines companies’ systemic importance in the U.S. financial system. Our approach can be used to monitor companies’ systemic importance allowing for a transparent macroprudential supervision.
We introduce a copula-based dynamic model for multivariate processes of (non-negative) high-frequency trading variables revealing time-varying conditional variances and correlations. Modeling the variables’ conditional mean processes using a multiplicative error model we map the resulting residuals into a Gaussian domain using a Gaussian copula. Based on high-frequency volatility, cumulative trading volumes, trade counts and market depth of various stocks traded at the NYSE, we show that the proposed copula-based transformation is supported by the data and allows capturing (multivariate) dynamics in higher order moments. The latter are modeled using a DCC-GARCH specification. We suggest estimating the model by composite maximum likelihood which is sufficiently flexible to be applicable in high dimensions. Strong empirical evidence for time-varying conditional (co-)variances in trading processes supports the usefulness of the approach. Taking these higher-order dynamics explicitly into account significantly improves the goodness-of-fit of the multiplicative error model and allows capturing time-varying liquidity risks.
Trading under limited pre-trade transparency becomes increasingly popular on financial markets. We provide first evidence on traders’ use of (completely) hidden orders which might be placed even inside of the (displayed) bid-ask spread. Employing TotalView-ITCH data on order messages at NASDAQ, we propose a simple method to conduct statistical inference on the location of hidden depth and to test economic hypotheses. Analyzing a wide cross-section of stocks, we show that market conditions reflected by the (visible) bid-ask spread, (visible) depth, recent price movements and trading signals significantly affect the aggressiveness of ’dark’ liquidity supply and thus the ’hidden spread’. Our evidence suggests that traders balance hidden order placements to (i) compete for the provision of (hidden) liquidity and (ii) protect themselves against adverse selection, front-running as well as ’hidden order detection strategies’ used by high-frequency traders. Accordingly, our results show that hidden liquidity locations are predictable given the observable state of the market.
Capturing the zero: a new class of zero-augmented distributions and multiplicative error processes
(2011)
We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed at high frequencies, such as cumulated trading volumes. We introduce a flexible point-mass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model (MEM) based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of both liquid and illiquid NYSE stocks, we show that the model captures the dynamic and distributional properties of the data well and is able to correctly predict future distributions.
This paper addresses the open debate about the usefulness of high-frequency (HF) data in large-scale portfolio allocation. Daily covariances are estimated based on HF data of the S&P 500 universe employing a blocked realized kernel estimator. We propose forecasting covariance matrices using a multi-scale spectral decomposition where volatilities, correlation eigenvalues and eigenvectors evolve on different frequencies. In an extensive out-of-sample forecasting study, we show that the proposed approach yields less risky and more diversified portfolio allocations as prevailing methods employing daily data. These performance gains hold over longer horizons than previous studies have shown.
Capturing the zero: a new class of zero-augmented distributions and multiplicative error processes
(2010)
We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed on high frequencies, such as cumulated trading volumes or the time between potentially simultaneously occurring market events. We introduce a flexible pointmass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model (MEM) based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of liquid NYSE stocks, we show that the model captures both the dynamic and distribution properties of the data very well and is able to correctly predict future distributions. Keywords: High-frequency Data , Point-mass Mixture , Multiplicative Error Model , Excess Zeros , Semiparametric Specification Test , Market Microstructure JEL Classification: C22, C25, C14, C16, C51