Market structure dynamics during COVID-19 outbreak

In this note, we discuss the impact of the COVID-19 outbreak from the perspective of the market-structure. We observe that the US market-structure has dramatically changed during the past four weeks and that the level of change has followed the number of infected cases reported in the USA. Presently, market-structure resembles most closely the structure during the middle of the 2008 crisis but there are signs that it may be starting to evolve into a new structure altogether. This is the first article of a series where we will be analyzing and discussing market-structure as it evolves to a state of further instability or, more optimistically, stabilization and recovery.Comment: 1 page, figure

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.Comment: 17 pages, 5 figure

Network Filtering of Spatial-temporal GNN for Multivariate Time-series Prediction

We propose an architecture for multivariate time-series prediction that integrates a spatial-temporal graph neural network with a filtering module which filters the inverse correlation matrix into a sparse network structure. In contrast with existing sparsification methods adopted in graph neural networks, our model explicitly leverages 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 volume from a synthetic time-series sales volume dataset. The proposed spatial-temporal graph neural network displays superior performances to baseline approaches with no graphical information, fully connected, disconnected graphs, and unfiltered graphs, as well as the state-of-the-art spatial-temporal GNN. Comparison of the results with Diffusion Convolutional Recurrent Neural Network (DCRNN) suggests that, by combining a (inferior) GNN with graph sparsification and filtering, one can achieve comparable or better efficacy than the state-of-the-art in multivariate time-series regression

Revisiting the duration dependence in the US stock market cycles

There is a big controversy among both investment professionals and academics regarding how the termination probability of a market state depends on its age. Using more than two centuries of data on the broad US stock market index, we revisit the duration dependence in bull and bear markets. Our results suggest that the duration dependence for both bull and bear markets is a nonlinear function of the state age. It appears that the duration dependence in bear markets is strictly positive. For 93% of the bull markets, the duration dependence is also positive. Only about 7% of the bull markets, those with the longest durations, do not exhibit positive duration dependence. We also compare a few selected theoretical distributions on their ability to describe the duration dependence in bull and bear markets. Our results advocate that the gamma distribution most often provides the best fit for both the survivor and hazard functions of bull and bear markets. However, our results reveal that none of the selected distributions accurately describes the right tail of the hazard functions.publishedVersionPaid open acces

Regime-based Implied Stochastic Volatility Model for Crypto Option Pricing

The increasing adoption of Digital Assets (DAs), such as Bitcoin (BTC), raises 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) on a very recent dataset covering BTC options on the popular trading platform Deribit. 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 apply this integrated time-regime clustering and ISVM method (termed MR-ISVM) to high-frequency data on BTC options. 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 and put the procedure to action on a new dataset covering previously unexplored DA dynamics

Stress Testing and Systemic Risk Measures Using Elliptical Conditional Multivariate Probabilities

Systemic risk, in a complex system with several interrelated variables, such as a financial market, is quantifiable from the multivariate probability distribution describing the reciprocal influence between the system’s variables. The effect of stress on the system is reflected by the change in such a multivariate probability distribution, conditioned to some of the variables being at a given stress’ amplitude. Therefore, the knowledge of the conditional probability distribution function can provide a full quantification of risk and stress propagation in the system. However, multivariate probabilities are hard to estimate from observations. In this paper, I investigate the vast family of multivariate elliptical distributions, discussing their estimation from data and proposing novel measures for stress impact and systemic risk in systems with many interrelated variables. Specific examples are described for the multivariate Student-t and the multivariate normal distributions applied to financial stress testing. An example of the US equity market illustrates the practical potentials of this approach

Non Stationarity and Market Structure Dynamics in Financial Time Series

This thesis is an investigation of the time changing nature of financial markets. Financial markets are complex systems having an intrinsic structure defined by the interplay of several variables. The technological advancements of the ’digital age’ have exponentially increased the amount of data available to financial researchers and industry professionals over the last decade and, as a consequence, it has highlighted the key role of iterations amongst variables. A critical characteristic of the financial system, however, is its time changing nature: the multivariate structure of the systems changes and evolves through time. This feature is critically relevant for classical statistical assumptions and has proven challenging to be investigated and researched. This thesis is devoted to the investigation of this property, providing evidences on the time changing nature of the system, analysing the implications for traditional asset allocation practices and proposing a novel methodology to identify and predict ‘market states’. First, I analyse how classical model estimations are affected by time and what are the consequential effects on classical portfolio construction techniques. Focusing on elliptical models of daily returns, I present experiments on both in-sample and out-of-sample likelihood of individual observations and show 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. A key implication of these findings is that the optimality of fit in finance needs to be defined in terms of the holding period. In this context, I also show that sparse models and information filtering significantly cope with the effects of non stationarity avoiding the typical pitfalls of conventional portfolio optimization approaches. Having assessed and documented the time changing nature of the financial system, I propose a novel methodology to segment financial time series into market states that we call ICC - Inverse Covariance Clustering. The ICC methodology allows to study the evolution of the multivariate structure of the system by segmenting the time series based on their correlation structure. In the ICC framework, market states are identified by a reference sparse precision matrix and a vector of expectation values. In the estimation procedure, each multivariate observation is associated to a market state accordingly to a minimisation of a penalized distance measure (e.g. likelihood, mahalanobis distance). The procedure is made computationally very efficient and can be used with a large number of assets. Furthermore, the ICC methodology allows to control for temporal consistency,S making it of high practical relevance for trading systems. I present a set of experiments investigating the features of the discovered clusters and comparing it to standard clustering techniques. I show that the ICC methodology is successful at clustering different states of the markets in an unsupervised manner, outperforming baseline standard models. Further, I show that the procedure can be efficiently used to forecast off-sample future market states with significant prediction accuracy. Lastly, I test the significance of increasing number of states used to model equity returns and how this parameter relates to the number of observations and the time consistency of the states. I present experiments to investigate a) the likelihood of the overall model as more states are spanned, b) the relevance of additional regimes measured by the number of observations clustered. I found that the number of “market states” that optimally define the system is increasing with the time spanned and the number of observations considered

Dynamic portfolio optimization with inverse covariance clustering

Market conditions change continuously. However, in portfolio 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 the maximum loss in extreme situations. This is shown to be consistent across markets, periods, optimization methods and selection of portfolio assets