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We introduce a multivariate multiplicative error model which is driven by componentspecific observation driven dynamics as well as a common latent autoregressive factor. The model is designed to explicitly account for (information driven) common factor dynamics as well as idiosyncratic effects in the processes of high-frequency return volatilities, trade sizes and trading intensities. The model is estimated by simulated maximum likelihood using efficient importance sampling. Analyzing five minutes data from four liquid stocks traded at the New York Stock Exchange, we find that volatilities, volumes and intensities are driven by idiosyncratic dynamics as well as a highly persistent common factor capturing most causal relations and cross-dependencies between the individual variables. This confirms economic theory and suggests more parsimonious specifications of high-dimensional trading processes. It turns out that common shocks affect the return volatility and the trading volume rather than the trading intensity. JEL Classification: C15, C32, C52
Analyzing interest rate risk: stochastic volatility in the term structure of government bond yields
(2009)
We propose a Nelson-Siegel type interest rate term structure model where the underlying yield factors follow autoregressive processes with stochastic volatility. The factor volatilities parsimoniously capture risk inherent to the term structure and are associated with the time-varying uncertainty of the yield curve’s level, slope and curvature. Estimating the model based on U.S. government bond yields applying Markov chain Monte Carlo techniques we find that the factor volatilities follow highly persistent processes. We show that slope and curvature risk have explanatory power for bond excess returns and illustrate that the yield and volatility factors are closely related to industrial capacity utilization, inflation, monetary policy and employment growth. JEL Classification: C5, E4, G1
Bayesian learning provides the core concept of processing noisy information. In standard Bayesian frameworks, assessing the price impact of information requires perfect knowledge of news’ precision. In practice, however, precision is rarely dis- closed. Therefore, we extend standard Bayesian learning, suggesting traders infer news’ precision from magnitudes of surprises and from external sources. We show that interactions of the different precision signals may result in highly nonlinear price responses. Empirical tests based on intra-day T-bond futures price reactions to employment releases confirm the model’s predictions and show that the effects are statistically and economically significant.
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.
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.
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 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.
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
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 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.