Correlation and Lead–Lag Relationships in a Hawkes Microstructure Model

Fonseca, José Da; Zaatour, Riadh

doi:10.1002/fut.21800

Cited by 10 publications

(5 citation statements)

References 46 publications

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“…for any λ 1 , λ 2 ∈ R. (22) implies that F is absolutely continuous, so F is differentiable almost everywhere on R and f := F ′ ∈ L 1 loc (R) by Theorem 7.20 from [40]. Thus f satisfies (10) due to (21). Moreover, (12) follows from (22) and Theorem 1.40 from [40].…”

Section: Proofsmentioning

confidence: 97%

“…Empirical applications of Hoffmann et al [27]'s methodology are found in [2,6,8,28]. Apart from Brownian motion driven models, the Hawkes processes may be a credible candidate to describe lead-lag effects in the continuous-time framework; see Bacry et al [3] and Da Fonseca & Zaatour [10] for example. However, none of them takes account of potential multi-scale structure of lead-lag effects.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet-Based Methods for High-Frequency Lead-Lag Analysis

Hayashi¹,

Koike

2018

SIAM J. Finan. Math.

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We propose a novel framework to investigate lead-lag relationships between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice. J for some universal constant c 4 > 0, hence we obtainWe rewrite the target quantity as, we obtain (35) by the dominated convergence theorem once we prove Ξ J (i 1 , i 2 ) → 0 for any fixed i 1 , i 2 . By Lemma 7 we haveWe can take sufficiently large r such that 2/r < 1 − κ. Then we haveJ )|X]| r ] = O τ 1−2/r J L 2 log 2 τ J r/2 = o(1) by Lemma 12. This yields the desired result. N τ J by the triangle and Schwarz inequalities. Therefore, the Markov inequality yields P max l∈L + J |I J (l)| > ε ≤ ε −1 l∈L + J I J (l) 2 2 N 2 τ J for any ε > 0, hence max l∈L + J |I J (l)| → p 0.Noting that L 2 τ J → 0, we can prove max l∈L + J |II J (l)| → p 0 in an analogous manner to the above.Next we prove max l∈L + J |III J (l)| → p 0. For any k ∈ I m,N (i) we haveWe can prove max l∈L + J |IV J (l)| → p 0 in an analogous manner.Now we prove max l∈L + J |V J (l)| → p 0. By Lemma 14 and the boundedness of σ 1 and σ 2 , we haveψ 1 → 0 by assumptions. This especially implies that max l∈L + J |V J (l)| → p 0. Finally, by Lemmas 4(b) and 8 we have max l∈L + J |VI J (l)| = o p (M J · τ −1 J τ m · τ J ). Since M J = O(τ −1 m ), we obtain max l∈L + J |VI J (l)| → p 0. This completes the proof. Completion of the proof of Theorem 2We need the following auxiliary result:Lemma 15. Λ −j D(λ)Π(λ)e

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Section: Proofsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Wavelet-Based Methods for High-Frequency Lead-Lag Analysis

Hayashi¹,

Koike

2018

SIAM J. Finan. Math.

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“…The idea of capturing the joint dynamic of multiple assets via Hawkes processes has only been considered in few recent papers. Let us mention the work proposed by Bormetti et al (2015) which models the simultaneous cojumps of different assets using a one-dimensional Hawkes process, and a more recent work (Da Fonseca and Zaatour (2017)) which focuses on the correlation and lead-lag relationships between the price changes of two assets, in the spirit of Bacry et al (2013).…”

Section: Multi-asset Modelmentioning

confidence: 99%

Analysis of order book flows using a non-parametric estimation of the branching ratio matrix

Achab

Bacry

Muzy

et al. 2017

Quantitative Finance

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We introduce a new non parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We show that it is able to uncover (or recover) various relationships between all the first level order book events associated with some asset when mapped to a 12-dimensional process. We then scale up the model so as to account for events on two assets simultaneously and we discuss the joint high-frequency dynamics.

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“…Most earlier studies on lead-lag relationships used methods such as regression, cointegration tests, multivariate vector error correction models, Granger causality, and generalized autoregressive conditional heteroskedasticity (GARCH). However, a number of studies have made methodological contributions by measuring such relationships using novel techniques such as thermal optimal path analysis (Jiang et al, 2019;Ren et al, 2019;Shao et al, 2019;Yang and Shao, 2020), the Hayashi-Yoshida cross-correlation estimator (Huth and Abergel, 2014), synchronous correlation networks (Curme et al, 2015), the Hawkes model (Da Fonseca and Zaatour, 2017), the multi-asset lagged adjustment model (Buccheri et al, 2020), and wavelet multiple correlations and cross-correlations (Tweneboah and Alagidede, 2018). Basdas (2009) used an error correction model (ECM) with cost of carry (COC), autoregressive integrated moving average (ARIMA), and vector autoregression (VAR) on the same dataset to observe differences in the results obtained.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Numerous studies have been conducted to explore the lead-lag relationship between various market indicators. Most of these originated in developed economies and indicate that futures markets tend to lead spot markets (see Abhyankar, 1995;Asche and Guttormsen, 2002;Brooks et al, 2001;Chan, 1992;Chen et al, 2017;Da Fonseca and Zaatour, 2017;Finnerty and Park, 1987;Ghosh, 1993;Grünbichler et al, 1994;Harris, 1989;Huth and Abergel, 2014;Kawaller et al, 1987;Martikainen and Puttonen, 1992;Shyy et al, 1996;Stoll and Whaley, 1990;Tang et al, 1992;Tse, 1995;Tse and Chan, 2010;Zhang and Liu, 2018). However, there has been an increase in studies in emerging economies, most of which have also found that futures markets tend to lead spot markets (see Choudhary and Bajaj, 2012;Debasish and Mishra, 2008;Demir et al, 2019;Floros and Vougas, 2007;Gong et al, 2016;Jiang et al, 2019;Kavussanos et al, 2008).…”

Section: Introductionmentioning

confidence: 99%