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What deep learning can bring to...

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What deep learning can bring to...

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... two decades of correlation, hierarchies, networks and clustering in financial markets

Summary of some of my past research work at Complex Networks 2022.

The study of correlations, hierarchies, networks and communities (or clustering) has more than 20 years of history in econophysics.

However, for the practitioner, it seems that these tools are not fully ready yet:
Many questions around their proper use for trading or risk monitoring are left unanswered.

Deep Learning might help solve some hard problems such as finding more reliably communities (or clusters) and their number.
Running large simulations (based on GANs, VAEs or realistic market simulators) could also help understand when complex networks methods can give wrong insights (e.g. not enough data, or not stationary enough; too low correlations).

Conference: Complex Networks 2022 in Palermo, Sicily, Italy.

... two decades of correlation, hierarchies, networks and clustering in financial markets

Summary of some of my past research work at Complex Networks 2022.

The study of correlations, hierarchies, networks and communities (or clustering) has more than 20 years of history in econophysics.

However, for the practitioner, it seems that these tools are not fully ready yet:
Many questions around their proper use for trading or risk monitoring are left unanswered.

Deep Learning might help solve some hard problems such as finding more reliably communities (or clusters) and their number.
Running large simulations (based on GANs, VAEs or realistic market simulators) could also help understand when complex networks methods can give wrong insights (e.g. not enough data, or not stationary enough; too low correlations).

Conference: Complex Networks 2022 in Palermo, Sicily, Italy.

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What deep learning can bring to...

  1. 1. G a utier M a rti, COMPLEX NETWORKS 2022 Whatdeeplearningcanbringto two dec a des of correl a tion, hier a rchies, networks a nd clustering in f in a nci a l m a rkets
  2. 2. Fromseminalpaper(1999) to recent st a te of the a rt (2020) Conclusion from sota review: Deep Learning is not a widely used tool (yet?)
  3. 3. Quanttraderconcerns Problems poorly a ddressed by the liter a ture • Which datasets are relevant to build fi nancial networks between companies, to predict what? • We cannot use future data, i.e. using rolling or expanding window: How long is enough? • (Too) many clustering and network-methods available: Which one should we use, and why? • Very expensive, IP-protected, not very suitable for academic research; Explains focus on stocks returns... • Many studies are full sample without out-of-sample validation: Prediction is not the focus. • No well de fi ned benchmarks: It makes hard to compare methods.
  4. 4. Howlongisenough? for my rolling window...
  5. 5. • Deep Learning for simulations, and fi nding 'laws' in large amount of data. Howmuchdataisnecessary? One possible criterion to choose a mongst methods The Hierarchical Correlation Block Model (HCBM) is a convenient assumption to do some math (matrix concentration inequalities) but it is challenging to obtain practical results. Within this model, simulations help to chooseg best method: Ward + Spearman correlation with at least 200 days of past returns.
  6. 6. Manychallengestoovercome... before implementing the 'simul a tor' • The simulator module: • Financial time series simulators: Generative Adversarial Networks for Financial Trading Strategies Fine-Tuning and Combination (2019) • Financial correlations simulator: CorrGAN: Sampling Realistic Financial Correlation Matrices Using Generative Adversarial Networks (2019) • Both at the same time? => It does not exist yet (TTBOMK) X
  7. 7. Fromsimulations... to supervised le a rning of clustering a ccur a cy • For a given fuzzy HCBM model, one can collect X := noisy estimates (empirical correlation matrices from the simulated time series of length T), y := clustering accuracy wrt model. • How can we go from (empirical correlation matrix, T) to an expected clustering accuracy? => supervised learning. ? What is a relevant feature space to describe empirical correlation matrices? For example: - correlation coe ffi cients summary statistics - percentage of variance explained by the k- fi rst eigenvalues - fi rst eigenvector summary statistics - minimum spanning tree statistics (centrality, average shortest path length) - cophenetic correlation coe ffi cient - condition number - ... A poor choice of a somewhat arbitrary feature space may bias learning and results... Deep learning provides an end-to-end approach from raw empirical matrices to target variables (clustering accuracy). - CNN (seeing the correlation matrix as an image) - GNN/GCN (the correlation matrix as a network) We plan to investigate using convolutional and graph neural networks, and compare predictive results with standard machine learning approaches. https://marti.ai/q fi n/2020/08/17/empirical-matrices-portfolio-comparisons.html
  8. 8. Applicationtoclustering... for qu a nts • One can use the predictive model to determine the smallest possible window in order to get a valid clustering, given what the empirical correlation matrices look like. • It should be useful for: • statistical arbitrage • risk factors and risk models • portfolio allocation methods (HRP, HCAA, HERC) Clustering of global CDS based on Hellebore Capital's proprietary data
  9. 9. Otherpotentialemergingapplications
  10. 10. Numberofclusters,hierarchies a nd their a utom a tic detection • Automated detection of: • fl at clustering • hierarchical clustering • altogether with the relevant number of clusters or hierarchical levels. • Not all clusters found by standard methods are true clusters! Filtering criteria are ad hoc and not stable for trading/risk systems. • A task similar to Object Detection and Recognition with Deep Learning in Computer Vision
  11. 11. NewopenPiTdatasets for empiric a l f in a nci a l networks rese a rch • Networks from text instead of correlation of stock returns • Use of novel large language models easily available from Hugging Face to build networks of similar products & services companies (cf. Hoberg and Phillips Text Based Industry Classi fi cations for early work using crude NLP techniques) Illustrations from Text-Based Representations of Market Structures, Gerard Hoberg
  12. 12. Whyclusteringatall? end-to-end deep le a rning • End-to-end approach with a particular downstream task in mind can, maybe, recover the 'optimal' clustering, which is then used implicitly... • Is it better than relying on expert knowledge to fi nd a good combination of relevant distance, clustering algo., hyper-params, su ffi cient rolling window, and post-processing of the signals based on clusters obtained? ?

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