arXiv subjects

Tomaso Aste

Publications and source records attributed to Tomaso Aste.

At least 37 records · Page 2Linked to original sources

arXiv2023

Homological Neural Networks: A Sparse Architecture for Multivariate Complexity

The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In this study, we apply advanced network-based information filtering techniques to design a novel deep neural network unit characterized by a sparse higher-order graphical architecture built over the homological structure of underlying data. We demonstrate its effectiveness in two application domains which are traditionally challenging for deep learning: tabular data and time series regression problems. Results demonstrate the advantages of this novel design which can tie or overcome the results of state-of-the-art machine learning and deep learning models using only a fraction of parameters.

cs.LG↗

arXiv2022

Dependency structures in cryptocurrency market from high to low frequency

We investigate logarithmic price returns cross-correlations at different time horizons for a set of 25 liquid cryptocurrencies traded on the FTX digital currency exchange. We study how the structure of the Minimum Spanning Tree (MST) and the Triangulated Maximally Filtered Graph (TMFG) evolve from high (15 s) to low (1 day) frequency time resolutions. For each horizon, we test the stability, statistical significance and economic meaningfulness of the networks. Results give a deep insight into the evolutionary process of the time dependent hierarchical organization of the system under analysis. A decrease in correlation between pairs of cryptocurrencies is observed for finer time sampling resolutions. A growing structure emerges for coarser ones, highlighting multiple changes in the hierarchical reference role played by mainstream cryptocurrencies. This effect is studied both in its pairwise realizations and intra-sector ones.

q-fin.ST↗

arXiv2022

Regime-based Implied Stochastic Volatility Model for Crypto Option Pricing

The increasing adoption of Digital Assets (DAs), such as Bitcoin (BTC), rises the need for accurate option pricing models. Yet, existing methodologies fail to cope with the volatile nature of the emerging DAs. Many models have been proposed to address the unorthodox market dynamics and frequent disruptions in the microstructure caused by the non-stationarity, and peculiar statistics, in DA markets. However, they are either prone to the curse of dimensionality, as additional complexity is required to employ traditional theories, or they overfit historical patterns that may never repeat. Instead, we leverage recent advances in market regime (MR) clustering with the Implied Stochastic Volatility Model (ISVM). Time-regime clustering is a temporal clustering method, that clusters the historic evolution of a market into different volatility periods accounting for non-stationarity. ISVM can incorporate investor expectations in each of the sentiment-driven periods by using implied volatility (IV) data. In this paper, we applied this integrated time-regime clustering and ISVM method (termed MR-ISVM) to high-frequency data on BTC options at the popular trading platform Deribit. We demonstrate that MR-ISVM contributes to overcome the burden of complex adaption to jumps in higher order characteristics of option pricing models. This allows us to price the market based on the expectations of its participants in an adaptive fashion.

q-fin.CP↗

arXiv2022

Anatomy of a Stablecoin's failure: the Terra-Luna case

We quantitatively describe the main events that led to the Terra project's failure in May 2022. We first review, in a systematic way, news from heterogeneous social media sources; we discuss the fragility of the Terra project and its vicious dependence on the Anchor protocol. We hence identify the crash's trigger events, analysing hourly and transaction data for Bitcoin, Luna, and TerraUSD. Finally, using state-of-the-art techniques from network science, we study the evolution of dependency structures for 61 highly capitalised cryptocurrencies during the down-market and we also highlight the absence of herding behaviour analysing cross-sectional absolute deviation of returns.

q-fin.GN↗

arXiv2022

Sparsification and Filtering for Spatial-temporal GNN in Multivariate Time-series

We propose an end-to-end architecture for multivariate time-series prediction that integrates a spatial-temporal graph neural network with a matrix filtering module. This module generates filtered (inverse) correlation graphs from multivariate time series before inputting them into a GNN. In contrast with existing sparsification methods adopted in graph neural network, our model explicitly leverage time-series filtering to overcome the low signal-to-noise ratio typical of complex systems data. We present a set of experiments, where we predict future sales from a synthetic time-series sales dataset. The proposed spatial-temporal graph neural network displays superior performances with respect to baseline approaches, with no graphical information, and with fully connected, disconnected graphs and unfiltered graphs.

cs.LG↗

arXiv2022

Dynamic Portfolio Optimization with Inverse Covariance Clustering

Market conditions change continuously. However, in portfolio's investment strategies, it is hard to account for this intrinsic non-stationarity. In this paper, we propose to address this issue by using the Inverse Covariance Clustering (ICC) method to identify inherent market states and then integrate such states into a dynamic portfolio optimization process. Extensive experiments across three different markets, NASDAQ, FTSE and HS300, over a period of ten years, demonstrate the advantages of our proposed algorithm, termed Inverse Covariance Clustering-Portfolio Optimization (ICC-PO). The core of the ICC-PO methodology concerns the identification and clustering of market states from the analytics of past data and the forecasting of the future market state. It is therefore agnostic to the specific portfolio optimization method of choice. By applying the same portfolio optimization technique on a ICC temporal cluster, instead of the whole train period, we show that one can generate portfolios with substantially higher Sharpe Ratios, which are statistically more robust and resilient with great reductions in maximum loss in extreme situations. This is shown to be consistent across markets, periods, optimization methods and selection of portfolio assets.

q-fin.ST↗

arXiv2022

Heterogenous criticality in high frequency finance: a phase transition in flash crashes

Flash crashes in financial markets have become increasingly important attracting attention from financial regulators, market makers as well as from the media and the broader audience. Systemic risk and propagation of shocks in financial markets is also a topic of great relevance that attracted increasing attention in recent years. In the present work we bridge the gap between these two topics with an in-depth investigation of the systemic risk structure of co-crashes in high frequency trading. We find that large co-crashes are systemic in their nature and differ from small crashes. We demonstrate that there is a phase transition between co-crashes of small and large sizes, where the former involves mostly illiquid stocks while large and liquid stocks are the most represented and central in the latter. This suggests that systemic effects and shock propagation might be triggered by simultaneous withdrawals or movement of liquidity by HFTs, arbitrageurs and market makers with cross-asset exposures.

q-fin.TR↗

arXiv2021

Topological regularization with information filtering networks

A methodology to perform topological regularization via information filtering network is introduced. This methodology can be directly applied to covariance selection problem providing an instrument for sparse probabilistic modeling with both linear and non-linear multivariate probability distributions such as the elliptical and generalized hyperbolic families. It can also be directly implemented for $L_0$-norm regularized multicollinear regression. In this paper, I describe in detail an application to sparse modeling with multivariate Student-t. A specific $L_0$-norm regularized expectation-maximization likelihood maximization procedure is proposed for this sparse Student-t case. Examples with real data from stock prices log-returns and from artificially generated data demonstrate the applicability, performances, and potentials of this methodology.

cs.LG↗

arXiv2021

Self-organised criticality in high frequency finance: the case of flash crashes

With the rise of computing and artificial intelligence, advanced modeling and forecasting has been applied to High Frequency markets. A crucial element of solid production modeling though relies on the investigation of data distributions and how they relate to modeling assumptions. In this work we investigate volume distributions during anomalous price events and show how their tail exponents < 2 indicate a diverging second moment of the distribution, i.e. variance. We then tie the dynamics of flash crashes to self-organised criticality. The findings are of great relevance for regulators and market makers as they advocate for rigorous heavy-tailed modeling of risk and changes in regulation to avoid simultaneous liquidity withdrawals and hard risk constraints which lead to synchronisation and critical events.

q-fin.TR↗

arXiv2021

An Information Filtering approach to stress testing: an application to FTSE markets

We present a novel methodology to quantify the "impact" of and "response" to market shocks. We apply shocks to a group of stocks in a part of the market, and we quantify the effects in terms of average losses on another part of the market using a sparse probabilistic elliptical model for the multivariate return distribution of the whole market. Sparsity is introduced with an $L_0$-norm regularization, which forces to zero some elements of the inverse covariance according to a dependency structure inferred from an information filtering network. Our study concerns the FTSE 100 and 250 markets and analyzes impact and response to shocks both applied to and received from individual stocks and group of stocks. We observe that the shock pattern is related to the structure of the network associated with the sparse structure of the inverse covariance of stock returns. Central sectors appear more likely to be affected by shocks, and stocks with a large level of underlying diversification have a larger impact on the rest of the market when experiencing shocks. By analyzing the system during times of crisis and comparative market calmness, we observe changes in the shock patterns with a convergent behavior in times of crisis.

q-fin.RM↗

arXiv2021

Learning Clique Forests

We propose a topological learning algorithm for the estimation of the conditional dependency structure of large sets of random variables from sparse and noisy data. The algorithm, named Maximally Filtered Clique Forest (MFCF), produces a clique forest and an associated Markov Random Field (MRF) by generalising Prim's minimum spanning tree algorithm. To the best of our knowledge, the MFCF presents three elements of novelty with respect to existing structure learning approaches. The first is the repeated application of a local topological move, the clique expansion, that preserves the decomposability of the underlying graph. Through this move the decomposability and calculation of scores is performed incrementally at the variable (rather than edge) level, and this provides better computational performance and an intuitive application of multivariate statistical tests. The second is the capability to accommodate a variety of score functions and, while this paper is focused on multivariate normal distributions, it can be directly generalised to different types of statistics. Finally, the third is the variable range of allowed clique sizes which is an adjustable topological constraint that acts as a topological penalizer providing a way to tackle sparsity at $l_0$ semi-norm level; this allows a clean decoupling of structure learning and parameter estimation. The MFCF produces a representation of the clique forest, together with a perfect ordering of the cliques and a perfect elimination ordering for the vertices. As an example we propose an application to covariance selection models and we show that the MCFC outperforms the Graphical Lasso for a number of classes of matrices.

stat.ML↗

arXiv2021

Stress testing and systemic risk measures using multivariate conditional probability

The multivariate conditional probability distribution models the effects of a set of variables onto the statistical properties of another set of variables. In the study of systemic risk in a financial system, the multivariate conditional probability distribution can be used for stress-testing by quantifying the propagation of losses from a set of `stressing' variables to another set of `stressed' variables. In this paper I describe how to compute such conditional probability distributions for the vast family of multivariate elliptical distributions, and in particular for the multivariate Student-t and the multivariate Normal distributions. Measures of stress impact and systemic risk are proposed. An application to the US equity market illustrates the potentials of this approach.

q-fin.RM↗

arXiv2021

Portfolio Optimization with Sparse Multivariate Modelling

Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2. uncertainties resulting from parameters' sampling error; 3. intrinsic non-stationarity of these systems. For what concerns point 1. we propose a L0-norm sparse elliptical modeling and show that sparsification is effective. The effects of points 2. and 3. are quantifified by studying the models' likelihood in- and out-of-sample for parameters estimated over train sets of different lengths. We show that models with larger off-sample likelihoods lead to better performing portfolios up to when two to three years of daily observations are included in the train set. For larger train sets, we found that portfolio performances deteriorate and detach from the models' likelihood, highlighting the role of non-stationarity. We further investigate this phenomenon by studying the out-of-sample likelihood of individual observations showing that the system changes significantly through time. Larger estimation windows lead to stable likelihood in the long run, but at the cost of lower likelihood in the short-term: the `optimal' fit in finance needs to be defined in terms of the holding period. Lastly, we show that sparse models outperform full-models in that they deliver higher out of sample likelihood, lower realized portfolio volatility and improved portfolios' stability, avoiding typical pitfalls of the Mean-Variance optimization.

q-fin.ST↗

arXiv2021

Sector Neutral Portfolios: Long memory motifs persistence in market structure dynamics

We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We observe long-memory processes in these structures in the form of power law decays in the number of persistent motifs. The decays then transition to a plateau regime with a power-law decay with smaller exponent. We demonstrate that identifying persistent motifs allows for forecasting and applications to portfolio diversification. Balanced portfolios are often constructed from the analysis of historic correlations, however not all past correlations are persistently reflected into the future. Sector neutrality has also been a central theme in portfolio diversification and systemic risk. We present an unsupervised technique to identify persistently correlated sets of stocks. These are empirically found to identify sectors driven by strong fundamentals. Applications of these findings are tested in two distinct ways on four different markets, resulting in significant reduction in portfolio volatility. A persistence-based measure for portfolio allocation is proposed and shown to outperform volatility weighting when tested out of sample.

q-fin.ST↗

arXiv2020

Deep Learning modeling of Limit Order Book: a comparative perspective

The present work addresses theoretical and practical questions in the domain of Deep Learning for High Frequency Trading. State-of-the-art models such as Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are reviewed and compared on the same tasks, feature space and dataset, and then clustered according to pairwise similarity and performance metrics. The underlying dimensions of the modeling techniques are hence investigated to understand whether these are intrinsic to the Limit Order Book's dynamics. We observe that the Multilayer Perceptron performs comparably to or better than state-of-the-art CNN-LSTM architectures indicating that dynamic spatial and temporal dimensions are a good approximation of the LOB's dynamics, but not necessarily the true underlying dimensions.

q-fin.TR↗

arXiv2020

Simplicial persistence of financial markets: filtering, generative processes and portfolio risk

We introduce simplicial persistence, a measure of time evolution of network motifs in subsequent temporal layers. We observe long memory in the evolution of structures from correlation filtering, with a two regime power law decay in the number of persistent simplicial complexes. Null models of the underlying time series are tested to investigate properties of the generative process and its evolutional constraints. Networks are generated with both TMFG filtering technique and thresholding showing that embedding-based filtering methods (TMFG) are able to identify higher order structures throughout the market sample, where thresholding methods fail. The decay exponents of these long memory processes are used to characterise financial markets based on their stage of development and liquidity. We find that more liquid markets tend to have a slower persistence decay. This is in contrast with the common understanding that developed markets are more random. We find that they are indeed less predictable for what concerns the dynamics of each single variable but they are more predictable for what concerns the collective evolution of the variables. This could imply higher fragility to systemic shocks.

q-fin.ST↗

arXiv2020

Wisdom of Crowds Detects COVID-19 Severity Ahead of Officially Available Data

During the unfolding of a crisis, it is crucial to determine its severity, yet access to reliable data is challenging. We investigate the relation between geolocated Tweet Intensity of initial COVID-19 related tweet at the beginning of the pandemic across Italian, Spanish and USA regions and mortality in the region a month later. We find significant proportionality between early social media reaction and the cumulative number of COVID-19 deaths almost a month later. Our findings suggest that "the crowds" perceived the risk correctly. This is one of the few examples where the "wisdom of crowds" can be quantified and applied in practice. This can be used to create real-time alert systems that could be of help for crisis-management and intervention, especially in developing countries. Such systems could contribute to inform fast-response policy making at early stages of a crisis.

physics.soc-ph↗

arXiv2020

The cost of Bitcoin mining has never really increased

The Bitcoin network is burning a large amount of energy for mining. In this paper we estimate the lower bound for the global energy cost for a period of ten years from 2010, taking into account changing oil costs, improvements in hashing technologies and hashing activity. Despite a ten-billion-fold increase in hashing activity and a ten-million-fold increase in total energy consumption, we find the cost relative to the volume of transactions has not increased nor decreased since 2010. This is consistent with the perspective that, in order to keep a the Blockchain system secure from double spending attacks, the proof or work must cost a sizable fraction of the value that can be transferred through the network. We estimate that in the Bitcoin network this fraction is of the order of 1%.

cs.CR↗