Modelling microstructure noise with mutually exciting point processes

By Emmanuel Bacry, Sylvain Delattre, Marc Hoffmann, Jean-François Muzy. 2011

310 citations recorded by the source corpus.

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By suitably coupling the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable us to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro–Bund and Euro–Bobl in several situations.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/083844cef10c8cd6d9f12e761720914c50d92173

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Citations in the corpus

Limit theorems for nearly unstable Hawkes processes (2013, methodology): “Furthermore, for the price model defined in [6], in the limit, the Brownian motion obtained in [5] is replaced by a Heston model, see [25] for definition.”
Fractional Skellam processes with applications to finance (2014, background): “Difference of Poisson processes is considered in [3, 10], and Hawkes processes are discussed in [1, 2].”
Renewal in Hawkes processes with self-excitation and inhibition (2018, unknown): “1 Introduction and main results Hawkes processes have been introduced by Hawkes [16], and are now widely used in many applications, for example: modelling of earthquake occurrences [17, 22], finance [1, 2, 3], genetics [25], neurosciences [8, 13, 23].”
Hawkes model for price and trades high-frequency dynamics (2013, methodology): “In the large time limit, one can show that these processes converge to correlated Brownian motions (see Bacry et al. (2013a) or section 3.3†).”
The role of volume in order book dynamics: a multivariate Hawkes process analysis (2016, methodology): “All along this paper, we shall estimate the kernels of the multivariate Hawkes process by using the nonparametric method proposed in Bacry and Muzy (2016) and its variant presented in Bacry et al.”
Scaling limits for Hawkes processes and application to financial statistics (2012, unknown): “…7641 and École Polytechnique, 91128 Palaiseau, France †Université Paris Diderot and LPMA CNRS-UMR 7599, Bôıte courrier 7012 75251 Paris, France ‡ENSAE-CREST and LAMA CNRS-UMR 8050, 3, avenue Pierre Larousse, 92245 Malakoff, France §SPE CNRS-UMR 6134 and Université de Corte, 20250 Corte, France”
Hawkes processes and their applications to finance: a review (2018, background): “Some people claim that Bowsher (2007) was the first (his original working paper appeared on the Internet in 2002).”
HAWKES PROCESSES ON LARGE NETWORKS (2016, unknown): “[2] and market impact see Bacry-Muzy [4, 5]), financial price modelling across scales (Bacry et al.”
Statistical inference for ergodic point processes and application to Limit Order Book (2015, unknown): “Lately more complex dynamics have been proposed, including Markovian models [16], Hawkes process driven bid–ask prices [5,40], or even Hawkes processes-based LOB models [2,35,6], the latter being reputed to efficiently capture the time clustering property of orders, and the cross-dependences in the ”
Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes (2015, methodology): “In the last years, the probabilistic and statistical analysis of Hawkes processes has known several interesting developments, driven by the recent use of Hawkes processes in various applied fields such as neurosciences [13, 33, 34, 36], sociology [9, 28, 41], criminology [30, 31], genome analysis [3”
Hawkes Processes in Finance (2015, methodology): “In the second part of their paper, Jaisson and Rosenbaum used their framework to build a version of the 2-dimensional Hawkes model initially introduced by [3] that converges at large scales towards the Heston price model [39] which displays volatility clustering.”
Some limit theorems for Hawkes processes and application to financial statistics (2013, methodology): “The macroscopic trace of microstructure noise Following [7], we introduce a univariate price process S = (St )t≥0 by setting S = N1 − N2, where (N1, N2) is a Hawkes process in the case d = 2, with λ1,t = ν + (0,t) ϕ(t − s)d N2,s, λ2,t = ν + (0,t) ϕ(t − s)d N1,s for some ν ∈ R+ and ϕ : R+ → R+.”
Mixture of Mutually Exciting Processes for Viral Diffusion (2013, methodology): “, 2011) and financial contagions (Bacrya et al., 2012).”