Roel C. A. Oomen

Properties of Realized Variance Under Alternative Sampling Schemes

This article investigates the statistical properties of the realized variance estimator in the presence of market microstructure noise. Different from the existing literature, the analysis relies on a pure jump process for high-frequency security prices and explicitly distinguishes among alternative sampling schemes, including calendar time sampling, business time sampling, and transaction time sampling. The main finding in this article is that transaction time sampling is generally superior to the common practice of calendar time sampling in that it leads to a lower mean squared error (MSE) of the realized variance. The benefits of sampling in transaction time are particularly pronounced when the trade intensity pattern is volatile. Based on IBM transaction data over the period 2000–2004, the empirical analysis finds an average optimal sampling frequency of about 3 minutes with a steady downward trend and significant day-to-day variation related to market liquidity and a consistent reduction in MSE of the realized variance due to sampling in transaction time that is about 5% on average but can be as high as 40% on days with irregular trading.

Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?

This article introduces a new model for transaction prices in the presence of market microstructure noise in order to study the properties of the price process on two different time scales, namely, transaction time where prices are sampled with every transaction and tick time where prices are sampled with every price change. Both sampling schemes have been used in the literature on realized variance, but a formal investigation into their properties has been lacking. Our empirical and theoretical results indicate that the return dynamics in transaction time are very different from those in tick time and the choice of sampling scheme can therefore have an important impact on the properties of realized variance. For RV we find that tick time sampling is superior to transaction time sampling in terms of mean-squared-error, especially when the level of noise, number of ticks, or the arrival frequency of efficient price moves is low. Importantly, we show that while the microstructure noise may appear close to IID in transaction time, in tick time it is highly dependent. As a result, bias correction procedures that rely on the noise being independent, can fail in tick time and are better implemented in transaction time.

Fact or Friction: Jumps at Ultra High Frequency

In this paper, we demonstrate that jumps in financial asset prices are not nearly as common as generally thought, and that they account for only a very small proportion of total return variation. We base our investigation on an extensive set of ultra high-frequency equity and foreign exchange rate data recorded at milli-second precision, allowing us to view the price evolution at a microscopic level. We show that both in theory and practice, traditional measures of jump variation based on low-frequency tick data tend to spuriously attribute a burst of volatility to the jump component thereby severely overstating the true variation coming from jumps. Indeed, our estimates based on tick data suggest that the jump variation is an order of magnitude smaller. This finding has a number of important implications for asset pricing and risk management and we illustrate this with a delta hedging example of an option trader that is short gamma. Our econometric analysis is build around a pre-averaging theory that allows us to work at the highest available frequency, where the data are polluted bymicrostructure noise. We extend the theory in a number of directions important for jump estimation and testing. This also reveals that pre-averaging has a built-in robustness property to outliers in high-frequency data, and allows us to show that some of the few remaining jumps at tick frequency are in fact induced by data-cleaning routines aimed at removing the outliers.

Zero-Intelligence Realized Variance Estimation

Given a time series of intra-day tick-by-tick price data, how can realized variance be estimated? The obvious estimator—the sum of squared returns between trades—is biased by microstructure effects such as bid–ask bounce and so in the past, practitioners were advised to drop most of the data and sample at most every five minutes or so. Recently, however, numerous alternative estimators have been developed that make more efficient use of the available data and improve substantially over those based on sparsely sampled returns. Yet, from a practical viewpoint, the choice of which particular estimator to use is not a trivial one because the study of their relative merits has primarily focused on the speed of convergence to their asymptotic distributions, which in itself is not necessarily a reliable guide to finite sample performance (especially when the assumptions on the price or noise process are violated). In this paper we compare a comprehensive set of nineteen realized variance estimators using simulated data from an artificial “zero-intelligence” market that has been shown to mimic some key properties of actual markets. In evaluating the competing estimators, we concentrate on efficiency but also pay attention to implementation, practicality, and robustness. One of our key findings is that for scenarios frequently encountered in practice, the best variance estimator is not always the one suggested by theory. In fact, an ad hoc implementation of a subsampling estimator, realized kernel, or maximum likelihood realized variance, delivers the best overall result. We make firm practical recommendations on choosing and implementing a realized variance estimator, as well as data sampling.

Using high frequency stock market index data to calculate, model and forecast realized return variance

The objective of this paper is to calculate, model and forecast realized volatility, using high frequency stock market index data. The approach taken differs from the existing literature in several aspects. First, it is shown that the decay of the serial dependence of high frequency returns with the sampling frequency, is consistent with an ARMA process under temporal aggregation. This finding has important implications for the modelling of high frequency returns and the optimal choice of sampling frequency when calculating realized volatility. Second, motivated by the outcome of several test statistics for long memory in realized volatility, it is found that the realized volatility series can be modelled as an ARFIMA process. Significant exogenous regressors include lagged returns and contemporaneous trading volume. Finally, the ARFIMAs forecasting performance is assessed in a simulation study. Although it outperforms representative GARCH models, the simplicity and flexibility of the GARCH may outweigh the modest gain in forecasting performance of the more complex and data intensive ARFIMA model.

International Dynamic Asset Allocation and Return Predictability

The presence of time varying investment opportunity sets has been documented in the context of international asset allocation, and the economic value associated with these is a topic of lively debate in the academic literature. This paper constructs simple, real-time dynamic international asset allocation strategies based on daily data that exploit the return predictability arising from time varying market integration. Our timing strategies outperform the major (US, UK, Japanese and German) country indices and related portfolios, particularly in down markets. The strategies appear to capture much of the economic value of the return predictability implied by market integration and have many of the characteristics of successful timing strategies.

High-dimensional covariance forecasting for short intra-day horizons

Asset return covariances at intra-day horizons are known to tend towards zero due to market microstructure effects. Thus, traders who simply scale their daily covariance forecast to match their trading horizon are likely to over-estimate the actual experienced asset dependence. In this paper, some of the key challenges are discussed that are encountered when forecasting high-dimensional covariance matrices for short intra-day horizons. Based on a novel evaluation methodology, and extensive empirical analysis, specific recommendations are made regarding model design and data sampling.

Execution in an aggregator

An aggregator is a technology that consolidates liquidity—in the form of bid and ask prices and amounts—from multiple sources into a single unified order book to facilitate ‘best-price’ execution. It is widely used by traders in financial markets, particularly those in the globally fragmented spot currency market. In this paper, I study the properties of execution in an aggregator where multiple liquidity providers (LPs) compete for a trader’s uninformed flow. There are two main contributions. Firstly, I formulate a model for the liquidity dynamics and contract formation process, and use this to characterize key trading metrics such as the observed inside spread in the aggregator, the reject rate due to the so-called ‘last-look’ trade acceptance process, the effective spread that the trader pays, as well as the market share and gross revenues of the LPs. An important observation here is that aggregation induces adverse selection where the LP that receives the trader’s deal request will suffer from the ‘Winner’s curse’, and this effect grows stronger when the trader increases the number of participants in the aggregator. To defend against this, the model allows LPs to adjust the nominal spread they charge or alter the trade acceptance criteria. This interplay is a key determinant of transaction costs. Secondly, I analyse the properties of different execution styles. I show that when the trader splits her order across multiple LPs, a single provider that has quick market access and for whom it is relatively expensive to internalize risk can effectively force all other providers to join her in externalizing the trader’s flow thereby maximizing the market impact and aggregate hedging costs. It is therefore not only the number, but also the type of LP and execution style adopted by the trader that determines transaction costs.

Appendix to Covariance Measurement in the Presence of Non-Synchronous Trading and Market Microstructure Noise

This web-appendix provides further details on simulation design, additional empirical results, and an illustration of the proportional bias correction of RCLL.

The Drift Burst Hypothesis

The Drift Burst Hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent US equity and Treasury flash crashes can be viewed as two high profile manifestations of such dynamics, but we argue that drift bursts of varying magnitude are an expected and regular occurrence in financial markets that can arise through established mechanisms such as feedback trading. At a theoretical level, we show how to build drift bursts into the continuous-time Ito semi-martingale model in such a way that the fundamental arbitrage-free property is preserved. We then develop a non-parametric test statistic that allows for the identification of drift bursts from noisy high-frequency data. We apply this methodology to a comprehensive set of tick data and show that drift bursts form an integral part of the price dynamics across equities, fixed income, currencies and commodities. We find that the majority of identified drift bursts are accompanied by strong price reversals and these can therefore be regarded as “flash crashes” that span brief periods of severe market disruption without any material longer term price impacts.