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Register a new userLinear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact
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Damian Eduardo Taranto
Publication date
2016
fields
Financial
and research's language is
English
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Market impact is a key concept in the study of financial markets and several models have been proposed in the literature so far. The Transient Impact Model (TIM) posits that the price at high frequency time scales is a linear combination of the signs of the past executed market orders, weighted by a so-called propagator function. An alternative description -- the History Dependent Impact Model (HDIM) -- assumes that the deviation between the realised order sign and its expected level impacts the price linearly and permanently. The two models, however, should be extended since prices are a priori influenced not only by the past order flow, but also by the past realisation of returns themselves. In this paper, we propose a two-event framework, where price-changing and non price-changing events are considered separately. Two-event propagator models provide a remarkable improvement of the description of the market impact, especially for large tick stocks, where the events of price changes are very rare and very informative. Specifically the extended approach captures the excess anti-correlation between past returns and subsequent order flow which is missing in one-event models. Our results document the superior performances of the HDIMs even though only in minor relative terms compared to TIMs. This is somewhat surprising, because HDIMs are well grounded theoretically, while TIMs are, strictly speaking, inconsistent.
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Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be obtained when one incorporates the impact of past returns on the future order flow. However, impact models presented in Part I consider the order flow as an exogenous process, only characterized by its two-point correlations. This assumption seriously limits the forecasting ability of the model. Here we attempt to model directly the stream of discrete events with a so-called Mixture Transition Distribution (MTD) framework, introduced originally by Raftery (1985). We distinguish between price-changing and non price-changing events and combine them with the order sign in order to reduce the order flow dynamics to the dynamics of a four-state discrete random variable. The MTD represents a parsimonious approximation of a full high-order Markov chain. The new approach captures with adequate realism the conditional correlation functions between signed events for both small and large tick stocks and signature plots. From a methodological viewpoint, we discuss a novel and flexible way to calibrate a large class of MTD models with a very large number of parameters. In spite of this large number of parameters, an out-of-sample analysis confirms that the model does not overfit the data.
In this work we introduce two variants of multivariate Hawkes models with an explicit dependency on various queue sizes aimed at modeling the stochastic time evolution of a limit order book. The models we propose thus integrate the influence of both the current book state and the past order flow. The first variant considers the flow of order arrivals at a specific price level as independent from the other one and describes this flow by adding a Hawkes component to the arrival rates provided by the continuous time Markov Queue Reactive model of Huang et al. Empirical calibration using Level-I order book data from Eurex future assets (Bund and DAX) show that the Hawkes term dramatically improves the pure Queue-Reactive model not only for the description of the order flow properties (as e.g. the statistics of inter-event times) but also with respect to the shape of the queue distributions. The second variant we introduce describes the joint dynamics of all events occurring at best bid and ask sides of some order book during a trading day. This model can be considered as a queue dependent extension of the multivariate Hawkes order-book model of Bacry et al. We provide an explicit way to calibrate this model either with a Maximum-Likelihood method or with a Least-Square approach. Empirical estimation from Bund and DAX level-I order book data allow us to recover the main features of Hawkes interactions uncovered in Bacry et al. but also to unveil their joint dependence on bid and ask queue sizes. We notably find that while the market order or mid-price changes rates can mainly be functions on the volume imbalance this is not the case for the arrival rate of limit or cancel orders. Our findings also allows us to clearly bring to light various features that distinguish small and large tick assets.
We revisit the epsilon-intelligence model of Toth et al.(2011), that was proposed as a minimal framework to understand the square-root dependence of the impact of meta-orders on volume in financial markets. The basic idea is that most of the daily liquidity is latent and furthermore vanishes linearly around the current price, as a consequence of the diffusion of the price itself. However, the numerical implementation of Toth et al. was criticised as being unrealistic, in particular because all the intelligence was conferred to market orders, while limit orders were passive and random. In this work, we study various alternative specifications of the model, for example allowing limit orders to react to the order flow, or changing the execution protocols. By and large, our study lends strong support to the idea that the square-root impact law is a very generic and robust property that requires very few ingredients to be valid. We also show that the transition from super-diffusion to sub-diffusion reported in Toth et al. is in fact a cross-over, but that the original model can be slightly altered in order to give rise to a genuine phase transition, which is of interest on its own. We finally propose a general theoretical framework to understand how a non-linear impact may appear even in the limit where the bias in the order flow is vanishingly small.
It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence order book simulator with arrival times of limit and market orders following mutually (asymmetrically) exciting Hawkes processes. Modelling is based on empirical observations on time intervals between orders that we verify on several markets (equity, bond futures, index futures). We show that this simple feature enables a much more realistic treatment of the bid-ask spread of the simulated order book.
Many independent studies on stocks and futures contracts have established that market impact is proportional to the square-root of the executed volume. Is market impact quantitatively similar for option markets as well? In order to answer this question, we have analyzed the impact of a large proprietary data set of option trades. We find that the square-root law indeed holds in that case. This finding supports the argument for a universal underlying mechanism.
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