The paper builds an econometric model for estimating the volatility of unobserved efficient price change using tick by tick data. We model the joint density of the marked point process of duration and tick by tick returns within an ACD-GARCH framework. We first model the duration variable as an ACD process that could potentially depend on past returns. We then model the return variable conditioning on its current duration as well as past information. The observed return process admits a state space model, where the unobserved efficient price innovation and microstructure noises serve as state variables. After adjusting for bid-ask spread and a non-linear function of durations, tick by tick returns are distributed independently of durations, with volatility that admits a GARCH process. We apply the above model to frequently traded NYSE stock transactions data. It appears that contemporaneous duration has little affect on the conditional volatility per trade, which means per second volatility is inversely related to the duration between trades. This is consistent with the result of Engle (2000) and Easley and O'Hara (1987). The model is used to obtain a new, model-based estimate of daily, realized volatility as well as the volatility of efficient price changes.Volatility is forecasted over calendar time intervals by simulation. The distribution of the number of trades is central in forming these forecasts.
本文建立了一个计量经济模型，用于估计未观察到的有效价格变化的波动率。我们在ACD-GARCH框架内对持续时间和逐点返回的标记点过程的联合密度进行建模。我们首先将持续时间变量建模为可能依赖于过去收益的ACD过程。然后，我们根据当前持续时间和过去的信息对返回变量条件进行建模。观察到的收益过程允许一个状态空间模型，其中未观察到的有效价格创新和微观结构噪声作为状态变量。在对买卖价差和持续时间的非线性函数进行调整后，每一笔交易的收益独立于持续时间分布，其波动性允许GARCH过程。我们将上述模型应用于频繁交易的纽约证券交易所股票交易数据。同时持续时间似乎对每笔交易的条件波动率几乎没有影响，这意味着每秒波动率与交易之间的持续时间成反比。这与Engle(2000)和Easley and O’hara(1987)的研究结果一致。该模型用于对每日、已实现波动率以及有效价格变化的波动率进行新的、基于模型的估计。波动性通过模拟在日历时间间隔内进行预测。交易数量的分布是形成这些预测的核心。
{"title":"Forecasting Volatility Using Tick by Tick Data","authors":"R. Engle, Zheng Sun","doi":"10.2139/ssrn.676462","DOIUrl":"https://doi.org/10.2139/ssrn.676462","url":null,"abstract":"The paper builds an econometric model for estimating the volatility of unobserved efficient price change using tick by tick data. We model the joint density of the marked point process of duration and tick by tick returns within an ACD-GARCH framework. We first model the duration variable as an ACD process that could potentially depend on past returns. We then model the return variable conditioning on its current duration as well as past information. The observed return process admits a state space model, where the unobserved efficient price innovation and microstructure noises serve as state variables. After adjusting for bid-ask spread and a non-linear function of durations, tick by tick returns are distributed independently of durations, with volatility that admits a GARCH process. We apply the above model to frequently traded NYSE stock transactions data. It appears that contemporaneous duration has little affect on the conditional volatility per trade, which means per second volatility is inversely related to the duration between trades. This is consistent with the result of Engle (2000) and Easley and O'Hara (1987). The model is used to obtain a new, model-based estimate of daily, realized volatility as well as the volatility of efficient price changes.Volatility is forecasted over calendar time intervals by simulation. The distribution of the number of trades is central in forming these forecasts.","PeriodicalId":161664,"journal":{"name":"Empirical Microstructure","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124201594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we perform an empirical analysis of the trading process in a pure limit order book market, the Xetra system which operates at various European exchanges. We study how present and past liquidity supply and demand as well as price volatility affect future trading activity and market resiliency, and discuss the results in the light of predictions implied by theoretical models of financial market microstructure. Using time series of reconstructed limit order books we identify latent factors which explain future order submission and cancelation decisions, according to hypotheses put forth by microstructure theory. We test these hypotheses with a new econometric methodology for the analysis of multivariate count processes.
{"title":"Trading Activity and Liquidity Supply in a Pure Limit Order Book Market. An Empirical Analysis Using a Multivariate Count Data Model","authors":"J. Grammig, Andréas Heinen, E. Rengifo","doi":"10.2139/ssrn.676567","DOIUrl":"https://doi.org/10.2139/ssrn.676567","url":null,"abstract":"In this paper we perform an empirical analysis of the trading process in a pure limit order book market, the Xetra system which operates at various European exchanges. We study how present and past liquidity supply and demand as well as price volatility affect future trading activity and market resiliency, and discuss the results in the light of predictions implied by theoretical models of financial market microstructure. Using time series of reconstructed limit order books we identify latent factors which explain future order submission and cancelation decisions, according to hypotheses put forth by microstructure theory. We test these hypotheses with a new econometric methodology for the analysis of multivariate count processes.","PeriodicalId":161664,"journal":{"name":"Empirical Microstructure","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117251097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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