ACD Modeling High-Frequency FX and Market Microstructure

This thesis is a compilation of three main studies with the common theme: point process based high-frequency volatility estimation. The first chapter introduces a new class of high-frequency volatility estimators and examines its asymptotic properties. The second chapter studies the relative importance of market microstructure (MMS) variables on high-frequency volatility estimation. The third chapter proposes a Markov-switching model for high-frequency volatility estimation and provides intraday measures of information contents in the trading process using the proposed model. In the first chapter, we propose a novel class of volatility estimators named the Renewal Based Volatility (RBV) estimator, and derive its asymptotic properties. This class of estimators is motivated by the work of Engle and Russell (1998), Gerhard and Hautsch (2002), Andersen, Dobrev, and Schaumburg (2008), Tse and Yang (2012), Nolte, Taylor, and Zhao (2018), which use price durations to construct highfrequency volatility estimators. We show that our RBV estimator nests the volatility estimator using price duration, thus providing a theoretical framework to analyse its asymptotic properties. Our theoretical results support the simulation and empirical findings in Tse and Yang (2012) and Nolte, Taylor, and Zhao (2018) that: (1) both the non-parametric duration (NPD) based and the parametric duration (PD) based volatility estimators are more efficient than the Realized Volatility (RV) estimator; (2) a parametric design can greatly improve the efficiency of volatility estimation; (3) the PD estimator can provide accurate intraday volatility estimates. We provide simulation evidence for the performance of the NPD estimator and propose an exponentially smoothed version that can outperform noise-robust RV-type estimators under general market microstructure noise and jumps. In the second chapter, we augment the PD estimator by including MMS variables in the parametric model. Specifically, we use a lognormal version of the Autoregressive Conditional Duration (ACD) model by Engle and Russell (1998), and include trading volume, bid-ask spread, total quote depth, quote depth difference, number of trades, order imbalance and order flow in the ACD model. Moreover, we use a best subset regression (BSR) approach to rank and select the included MMS variables. Our empirical study based on high-frequency trade and quote data from 29 highly liquid securities and a market index ETF shows that, by benchmarking on a Realized Kernel measure, the inclusion of MMS covariates significantly improves the performance of volatility estimates on both daily and intraday levels. The BSR approach is very effective in selecting the most relevant MMS covariates for volatility estimation, and it suggests that contemporaneous number of trades and order flow are the most important variables for intraday volatility estimation. More importantly, intraday volatility estimates can be constructed from the ACD model even in the case when the RV-type estimators cannot be reliably constructed due to a lack of data. In the third chapter, we extend the Autoregressive Conditional Intensity (ACI) model (Russell, 1999) with a Markov-switching (MS) structure. We propose to use the Stochastic Approximation Expectation Maximization (SAEM) (Celeux and Diebolt, 1992) to estimate the MS-ACI model, and provide simulation evidence supporting the validity of the estimation procedure. We apply our MS-ACI model to high-frequency trade and quote data from 9 highly liquid securities and a market index ETF. Our empirical findings suggest that the MS-ACI model captures two distinct volume-volatility regimes in the high-frequency data: a dominant regime that spreads evenly throughout the trading day with strong correlation between cumulative trading volume and price duration, and a minor regime that concentrates at the beginning and end of a trading day with much weaker correlation between cumulative trading volume and price duration. We link this phenomenon to the firm-specific information arrival process into the market, and provide a measure of intraday information content of the transaction process.

Engle and Russell (1998) introduce the autoregressive conditional duration (ACD) model to model the dynamics of financial duration. It is recognized that the ACD model can be specified in ARMA form. We show that as long as the innovations of the ACD model follows a lognormal distribution, the equivalent ARMA model will be Gaussian distributed. Motivated by this fact, we develop a lognormal autoregressive conditional duration (LNACD) model. The LNACD model permits a humped-shaped hazard function with one free shape parameter, which has a computational advantage compared to the existing ACD specification in the literature. We compare the performance of the LNACD model with alternative specification of ACD model. The empirical results show that the LNACD model is always superior to Exponential and Weibull ACD models and its performance is similar to the Burr and Generalized Gamma ACD models.

We formulate a market microstructure model of exchange determination we employ to investigate the impact of foreign exchange (FX) intervention on exchange rates and on FX market conditions. With our formulation we show: (i) how FX intervention influences exchange rates via both a portfolio-balance and a signalling channel; and (ii) derive a series of testable implications which are coherent with a large body of empirical research. Our investigation also proposes some normative recommendations, as we show: (i) that in extreme circumstances large-scale FX intervention can have destabilizing effects for the functioning of FX markets; and (ii) that the route chosen for the implementation of official intervention has important implications for its impact on exchange rates and on market conditions. Copyright © 2010 John Wiley & Sons, Ltd.

The Interest Rate Parity Theorem: A Reinterpretation

This article analyzes current trends in foreign exchange (FX) market liquidity and trading costs. In addition, the authors study the dynamics of various liquidity and volatility measures around the 2014 FIFA World Cup. Their major focus is on the size-adjusted spread cost—that is, the instantaneous cost of sweeping the limit-order book up to a specified deal size. However, the conclusions apply to other liquidity and volatility measures as well. The evidence obtained from analyzing consolidated FX data suggests that a great deal of emphasis should be put on detecting favorable times of the day and making trading decisions accordingly. FX trading costs, if not measured and managed correctly, constitute a significant drag on investment performance. Solutions now exist that could be leveraged to achieve better performance. Focus and measurement are the first necessary steps toward this goal.

This chapter deals with dynamic models for financial duration processes. As already discussed in Chapter 2, duration approaches are the most common way to model point processes since they are easy to estimate and allow for straightforward computations of forecasts. In Section 5.1, we discuss autoregressive models for log durations as a natural starting point. In Section 5.2, we present the basic form of the autoregressive conditional duration (ACD) model proposed by Engle and Russell (1997, 1998). Because it is the most common type of autoregressive duration model and is extensively considered in recent econometrics literature, we discuss the theoretical properties and estimation issues in more detail. Section 5.3 deals with extensions of the basic ACD model. In this section, we discuss generalizations with respect to the functional form of the basic specification. Section 5.4 is devoted to specification tests for the ACD model. Here, we focus on (integrated) conditional moment tests as a valuable framework to test the conditional mean restriction implied by the ACD model. Finally, in Section 5.5 we illustrate several applications of the ACD model. The first application deals with the evaluation of different ACD specifications based on trade and price durations by using the testing framework considered in Section 5.4. A further objective is to empirically test the market microstructure hypotheses derived in Chapter 3. Moreover, we apply the ACD model to quantify illiquidity risks on the basis of excess volume durations.

The foreign exchange (FX) market has many features including (1) Each trader’s payoff depends not only on his own behavior, but also on other traders’ decisions; (2) The number of traders is too large to make them all know the other dealers’ methods of decision making; and (3) The FX market has many levels. The FX market is complex because of these features. A diversity of techniques are required to deal with such complex problems. That is hybrid solutions are crucial for the FX market. On the other hand, research into the FX market has revealed that it demonstrates some characteristics of multi-agent systems such as autonomy, interaction, and emergence. To this end, an agent-based hybrid intelligent system was developed for FX trading, which is based on our proposed agent-based hybrid framework. This paper is to discuss the analysis, design, and implementation such a system. Some experimental results and comparisons with related works are also provided. The interest of this paper does not reside in improving the predictive capabilities of different FX models, but rather in how to integrate different models into one system under the unifying agent framework. The success of this system indicates that agent perspectives are very appropriate to model complex problems such as the FX trading.

This article has two aims. First, I revisit Khemiri (2009 Khemiri, R. 2009. Parameter stability in foreign exchange market microstructure: a Markov switching approach. la Revue Tunisienne d'Economie et de Gestion (Tunisian Journal of Economics and Business), 29: 171–200. [Google Scholar]) and I find support to Lyons (1995 Lyons, RK. 1995. Tests of microstructural hypotheses in the foreign exchange market. Journal of Financial Economics, 39: 321–51. [Crossref], [Web of Science ®] , [Google Scholar]) seminal dealer level specification with a still richer picture of the conditional volatility dynamics. For this reason, I develop an estimation procedure for a variety of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Markov Switching Exponential GARCH (MSGARCH) models which provide a richer modelling of volatility dynamics and I find that the Markov Switching Exponential GARCH (MSEGARCH) model fits the intraday data better. In addition, the second aim of this article is to study the relationship between trading volume and volatility in the Foreign Exchange (FX) market microstructure by using a Markov switching approach that captures asymmetry and regime shifts in the Lyons (1995 Lyons, RK. 1995. Tests of microstructural hypotheses in the foreign exchange market. Journal of Financial Economics, 39: 321–51. [Crossref], [Web of Science ®] , [Google Scholar]) dataset. In this context, the empirical results support the Mixture of Distribution Hypothesis (MDH) where I find a new result showing that that there is a positive correlation between volume and volatility of the Deutsche Mark (DM)/$ prices as well as a positive effect of order flow on returns. This confirms the role of order flow as a mean of transmission of information in the new microexchange rate economics.

The foreign exchange (FOREX) market is an over‐the‐counter market characterized by intermediation and significant bid–ask spreads. However, most of the existing international macroeconomics literature models the FOREX as a standard Walrasian market. This article constructs a dynamic general equilibrium model of intermediation in the FOREX market. We use our framework to compute standard measures of FOREX liquidity, such as bid–ask spreads and trade volume, and study how they are affected by macroeconomic fundamentals and market microstructure. We also study how FOREX market microstructure affects the volume of international trade and, consequently, welfare. Our empirical exercise offers support to the models' main predictions.

This paper develops mew robust inference procedures for analyzing the intraday return volatility patterns that constitute a focal point of much market microstructure theory. Our empirical analysis is motivated by the recent lifting of trading restrictions in the interbank foreign exchange (FX) market for Japanese banks during the Tokyo lunch period. Ito, Lyons, and Melvin (1998) (ILM) argue that this deregulation resulted in a highly significant shift in the volatility pattern across the entire Japanese trading day, indicating that private information is an important component of the price formation process in the FX market. In contrast, our robust analysis finds no evidence for any discernible change in the pattern outside of the Tokyo lunch period. Moreover, we document that the standard variance-ratio methodology inference in this high-frequency data context.

Many existing extensions of the Engle and Russell's (1998) Autoregressive Conditional Duration (ACD) model in the literature are aimed at providing additional flexibility either on the dynamics of the conditional duration model or the allowed shape of the hazard function, i.e., its two most essential components. This article introduces an alternative semiparametric regression approach to a nonlinear ACD model; the use of a semiparametric functional form on the dynamics of the duration process suggests the model being called the Semiparametric ACD (SEMI–ACD) model. Unlike existing alternatives, the SEMI–ACD model allows simultaneous generalizations on both of the above-mentioned components of the ACD framework. To estimate the model, we establish an alternative use of the existing Bühlmann and McNeil's (2002) iterative estimation algorithm in the semiparametric setting and provide the mathematical proof of its statistical consistency in our context. Furthermore, we investigate the asymptotic properties of the semiparametric estimators employed in order to ensure the statistical rigor of the SEMI–ACD estimation procedure. These asymptotic results are presented in conjunction with simulated examples, which provide an empirical evidence of the SEMI–ACD model's robust finite-sample performance. Finally, we apply the proposed model to study price duration process in the foreign exchange market to illustrate its usefulness in practice.

In this article, we search for the evidence of intraweek and intraday anomalies on the spot foreign exchange (FOREX) market. Having in mind the international scope of this market, empirical evidence against market efficiency (i.e. market anomalies) will have important consequences for the substantial number of FOREX investors all around the globe. We explore intraweek, intraday and interaction between days and hour trade anomalies on the FOREX market over the period of 10 years using hourly time-series data of Euro and US Dollar (EUR/USD) exchange rate on Swiss FOREX market from 1 January 2004 to 11 January 2014. We compare by analysis of variance test all pairs of mean returns on a daily, hourly and daily/hourly basis. t-Test is used to test whether intraday returns are significantly different from zero. We employ Tukey’s honestly significant difference test to explore which intraday pairs of hourly mean returns are significantly greater than zero. We find that intraday and interaction between day and hour anomalies are present in trading EUR/USD on the spot FOREX market over the period of 10 years. The best arbitrage opportunity is evidenced on Fridays, when selling USD and buying EUR at 00:00 and selling EUR and buying USD at 03:00 the same day.

Self-weighted quantile estimation of autoregressive conditional duration model

The Foreign Exchange (FOREX) market is the largest and most complex financial market in the world. With the advent of behavioural and micro-structural studies, many properties of the market have been revealed. However, previous studies contain only aggregate transaction data that do not distinguish between the activities of the different participants, formulating the market collective behavior. Understanding the FOREX market dynamics and the forces driving its behaviour is a very fertile research area that still needs extensive research. In this paper, we propose a new approach for analyzing and understanding the high-frequency FOREX market beyond what is offered in previous work. The proposed approach is a bottom-up study of the FOEX market. It starts with conducting a microscopic analysis of actual traders' behaviour using a unique transaction dataset at an account level provided by OANDA Ltd. Using the identified market properties from the microscopic analysis we build then an artificial FOREX market attempting to replicate the real market behavior and provide an empirical understanding of the market dynamics.

Forecasting is the process of estimating future events using past data. Financial time series forecasting often prioritizes stock price variables. Apart from the stock price variable, inter-transaction time or duration is also an important variable to predict, because the timing of changes in financial prices cannot be predicted. Duration modeling and forecasting can be done using the autoregressive conditional duration (ACD) model. In this research, modeling and forecasting using the ACD model was carried out on Ethereum. This research aims to predict the duration of Ethereum in order to help traders know the time needed to reach the next price change. Several ACD models with four distributions, i.e., exponential, Weibull, Burr, and generalized gamma were fit to the Ethereum duration. The research results suggest that the Burr-ACD model produces the smallest AIC value compared to other distributed ACD models. However, the forecast results using the Burr-ACD models show increasing duration and hence are less accurate. The generalized gamma-ACD (2,2) model was then chosen as an alternative for forecasting Ethereum duration, showing that Ethereum duration forecast results are less than one second, which indicates the high frequency of transactions that occur on Ethereum.