Causality in financial markets : time reversal asymmetry and multi-scale lead-lag networks

Abstract : This thesis aims to uncover the underlyingcausality structure of financial markets by focusing onthe inference of investor causal networks at multipletimescales in two trader-resolved datasets.The first part of this thesis is devoted to the causal strengthof Hawkes processes. These processes describe in a clearlycausal way how the activity rate of e.g. an investor dependson his past activity rate; its multivariate version alsomakes it possible to include the interactions between theagents, at all time scales. The main result of this part isthat the classical MLE estimation of the process parametersdoes not vary significantly if the arrow of time is reversedin the univariate and symmetric multivariate case.This means that blindly trusting univariate and symmetricmultivariate Hawkes processes to infer causality from datais problematic. In addition, we find a dependency betweenthe level of causality in the process and its endogeneity.For long time series of synthetic data, one can discriminatebetween the forward and backward arrows of time byperforming rigorous statistical tests on the processes, butfor empirical data the situation is much more ambiguous,as it is entirely possible to find a better Hawkes process fitwhen time runs backwards compared to forwards.Asymmetric Hawkes processes do not suffer from veryweak causality. Fitting them to the individual traders’ actionsfound in our datasets is unfortunately not very successfulfor two reasons. We carefully checked that tradersactions in both datasets are highly non-stationary, andthat local stationarity cannot be assumed to hold as thereis simply not enough data, even if each dataset containsabout one million trades. This is also compounded by thefact that Hawkes processes encode the pairwise influenceof traders for all timescales simultaneously.In order to alleviate this problem, the second part ofthis thesis focuses on causality between specific pairs oftimescales. Further filtering is achieved by reducing theeffective number of investors; Statistically Validated Networksare applied to cluster investors into groups basedon the statistically high synchronisation of their actions(buy, sell or neutral) in time intervals of a given timescale.This part then generalizes single-timescale lead-lag SVNsto lead-lag networks between two timescales and introducesthree slightly different methodsThese methods make it possible to characterize causalityin a novel way. We are able to compare the time reversalasymmetry of trader activity and that of price volatility,and conclude that the causal structure of trader activity isconsiderably more complex than that of the volatility for agiven category of traders. Expectedly, institutional traders,whose impact on prices is much larger than that of retailclients, have a causality structure that is closer to that ofvolatility. This is because volatility, being a macroscopicquantity, aggregates the behaviour of all types of traders,thereby hiding the causality structure of minor players.
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Marcus Cordi. Causality in financial markets : time reversal asymmetry and multi-scale lead-lag networks. Other. Université Paris-Saclay, 2019. English. ⟨NNT : 2019SACLC013⟩. ⟨tel-02063380⟩

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