# Research articles for the 2020-04-13

A new multilayer network construction via Tensor learning
Giuseppe Brandi,T. Di Matteo
arXiv

Multilayer networks proved to be suitable in extracting and providing dependency information of different complex systems. The construction of these networks is difficult and is mostly done with a static approach, neglecting time delayed interdependences. Tensors are objects that naturally represent multilayer networks and in this paper, we propose a new methodology based on Tucker tensor autoregression in order to build a multilayer network directly from data. This methodology captures within and between connections across layers and makes use of a filtering procedure to extract relevant information and improve visualization. We show the application of this methodology to different stationary fractionally differenced financial data. We argue that our result is useful to understand the dependencies across three different aspects of financial risk, namely market risk, liquidity risk, and volatility risk. Indeed, we show how the resulting visualization is a useful tool for risk managers depicting dependency asymmetries between different risk factors and accounting for delayed cross dependencies. The constructed multilayer network shows a strong interconnection between the volumes and prices layers across all the stocks considered while a lower number of interconnections between the uncertainty measures is identified.

An extensive study of stylized facts displayed by Bitcoin returns
F.N.M. de Sousa Filho,J.N. Silva,M.A. Bertella,E. Brigatti
arXiv

In this paper, we explore some stylized facts in the Bitcoin market using the BTC-USD exchange rate time series of historical intraday data from 2013 to 2018. Despite Bitcoin presents some very peculiar idiosyncrasies, like the absence of macroeconomic fundamentals or connections with underlying asset or benchmark, a clear asymmetry between demand and supply and the presence of inefficiency in the form of very strong arbitrage opportunity, all these elements seem to be marginal in the definition of the structural statistical properties of this virtual financial asset, which result to be analogous to general individual stocks or indices. In contrast, we find some clear differences, compared to fiat money exchange rates time series, in the values of the linear autocorrelation and, more surprisingly, in the presence of the leverage effect. We also explore the dynamics of correlations, monitoring the shifts in the evolution of the Bitcoin market. This analysis is able to distinguish between two different regimes: a stochastic process with weaker memory signatures and closer to Gaussianity between the Mt. Gox incident and the late 2015, and a dynamics with relevant correlations and strong deviations from Gaussianity before and after this interval.

Containment efficiency and control strategies for the Corona pandemic costs
Claudius Gros,Roser Valenti,Lukas Schneider,Kilian Valenti,Daniel Gros
arXiv

The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies and the need to balance public health considerations with the economic costs of a persistent lockdown. We introduce a modified epidemic model, the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment policies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated over the entire course of the epidemic. Costs comprise medical care cost, the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, strict measures fare better than a hands-off policy. Strategies based on actual case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic.

Continuous Time Random Walk with correlated waiting times. The crucial role of inter-trade times in volatility clustering
Jarosław Klamut,Tomasz Gubiec
arXiv

In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the Continuous Time Random Walk (CTRW). Despite the popularity of this type of stochastic processes and strong empirical motivation, models with a long-term memory within the sequence of time intervals between observations are missing. Here, we fill this gap by introducing a new family of CTRWs. The memory is introduced to the model by the assumption that many consecutive time intervals can be the same. Surprisingly, in this process we can observe a slowly decaying nonlinear autocorrelation function without a fat-tailed distribution of time intervals. Our model applied to high-frequency stock market data can successfully describe the slope of decay of nonlinear autocorrelation function of stock market returns. The model achieves this result with no dependence between consecutive price changes. It proves the crucial role of inter-event times in the volatility clustering phenomenon observed in all stock markets.

Effective alleviation of rural poverty depends on the interplay between productivity, nutrients, water and soil quality
arXiv

Most of the world poorest people come from rural areas and depend on their local ecosystems for food production. Recent research has highlighted the importance of self-reinforcing dynamics between low soil quality and persistent poverty but little is known on how they affect poverty alleviation. We investigate how the intertwined dynamics of household assets, nutrients (especially phosphorus), water and soil quality influence food production and determine the conditions for escape from poverty for the rural poor. We have developed a suite of dynamic, multidimensional poverty trap models of households that combine economic aspects of growth with ecological dynamics of soil quality, water and nutrient flows to analyze the effectiveness of common poverty alleviation strategies such as intensification through agrochemical inputs, diversification of energy sources and conservation tillage. Our results show that (i) agrochemical inputs can reinforce poverty by degrading soil quality, (ii) diversification of household energy sources can create possibilities for effective application of other strategies, and (iii) sequencing of interventions can improve effectiveness of conservation tillage. Our model-based approach demonstrates the interdependence of economic and ecological dynamics which preclude blanket solution for poverty alleviation. Stylized models as developed here can be used for testing effectiveness of different strategies given biophysical and economic settings in the target region.

Evolving efficiency and robustness of global oil trade networks
Wen-Jie Xie,Na Wei,Wei-Xing Zhou
arXiv

Holding-Based Evaluation upon Actively Managed Stock Mutual Funds in China
Huimin Peng
arXiv

We analyze actively managed mutual funds in China from 2005 to 2017. We develop performance measures for asset allocation and selection. We find that stock selection ability from holding-based model is positively correlated with selection ability estimated from Fama-French three-factor model, which is price-based regression model. We also find that industry allocation from holding-based model is positively correlated with timing ability estimated from price-based Treynor-Mazuy model most of the time. We conclude that most actively managed funds have positive stock selection ability but not asset allocation ability, which is due to the difficulty in predicting policy changes.

Optimal multi-asset trading with linear costs: a mean-field approach
Matt Emschwiller,Benjamin Petit,Jean-Philippe Bouchaud
arXiv

Optimal multi-asset trading with Markovian predictors is well understood in the case of quadratic transaction costs, but remains intractable when these costs are $L_1$. We present a mean-field approach that reduces the multi-asset problem to a single-asset problem, with an effective predictor that includes a risk averse component. We obtain a simple approximate solution in the case of Ornstein-Uhlenbeck predictors and maximum position constraints. The optimal strategy is of the "bang-bang" type similar to that obtained in [de Lataillade et al., 2012]. When the risk aversion parameter is small, we find that the trading threshold is an affine function of the instantaneous global position, with a slope coefficient that we compute exactly. We relate the risk aversion parameter to the desired target risk and provide numerical simulations that support our analytical results.

Pricing of counterparty risk and funding with CSA discounting, portfolio effects and initial margin
Francesca Biagini,Alessandro Gnoatto,Immacolata Oliva
arXiv

In this paper we extend the existing literature on xVA along three directions. First, we enhance current BSDE-based xVA frameworks to include initial margin by following the approach o Cr\'epey (2015a) and Cr\'epey (2015b). Next, we solve the consistency problem that arises when the front-office desk of the bank uses trade-specific discount curves that differ from the discount curve adopted by the xVA desk. Finally, we address the existence of multiple aggregation levels for contingent claims in the portfolio between the bank and the counterparty by providing suitable extensions of our proposed single-claim xVA framework.

Pricing variance swaps with stochastic volatility and stochastic interest rate under full correlation structure
Teh Raihana Nazirah Roslan,Wenjun Zhang,Jiling Cao
arXiv

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables. This full correlation structure possess the limitation to have fully analytical pricing formula for hybrid models of variance swaps, due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions. Subsequently, we implement numerical experiments to evaluate the accuracy of our pricing formula. Our findings confirmed that the impact of the correlation between the underlying and the interest rate is significant for pricing discretely-sampled variance swaps.

Quantifying horizon dependence of asset prices: a cluster entropy approach
L. Ponta,A. Carbone
arXiv

Market dynamic is quantified in terms of the entropy $S(\tau,n)$ of the clusters formed by the intersections between the series of the prices $p_t$ and the moving average $\widetilde{p}_{t,n}$. The entropy $S(\tau,n)$ is defined according to Shannon as $\sum P(\tau,n)\log P(\tau,n),$ with $P(\tau,n)$ the probability for the cluster to occur with duration $\tau$. \par The investigation is performed on high-frequency data of the Nasdaq Composite, Dow Jones Industrial Avg and Standard \& Poor 500 indexes downloaded from the Bloomberg terminal. The cluster entropy $S(\tau,n)$ is analysed in raw and sampled data over a broad range of temporal horizons $M$ varying from one to twelve months over the year 2018. The cluster entropy $S(\tau,n)$ is integrated over the cluster duration $\tau$ to yield the Market Dynamic Index $I(M,n)$, a synthetic figure of price dynamics. A systematic dependence of the cluster entropy $S(\tau,n)$ and the Market Dynamic Index $I(M,n)$ on the temporal horizon $M$ is evidenced. \par Finally, the Market Horizon Dependence}, defined as $H(M,n)=I(M,n)-I(1,n)$, is compared with the horizon dependence of the pricing kernel with different representative agents obtained via a Kullback-Leibler entropy approach. The Market Horizon Dependence $H(M,n)$ of the three assets is compared against the values obtained by implementing the cluster entropy $S(\tau,n)$ approach on artificially generated series (Fractional Brownian Motion).

The effect of stay-at-home orders on COVID-19 infections in the United States
James H. Fowler,Seth J. Hill,Remy Levin,Nick Obradovich
arXiv

In March and April 2020, public health authorities in the United States acted to mitigate transmission of COVID-19. These actions were not coordinated at the national level, which creates an opportunity to use spatial and temporal variation to measure their effect with greater accuracy. We combine publicly available data sources on the timing of stay-at-home orders and daily confirmed COVID-19 cases at the county level in the United States (N = 132,048). We then derive from the classic SIR model a two-way fixed-effects model and apply it to the data with controls for unmeasured differences between counties and over time. Mean county-level daily growth in COVID-19 infections peaked at 17.2% just before stay-at-home orders were issued. Two way fixed-effects regression estimates suggest that orders were associated with a 3.8 percentage point (95% CI 0.7 to 8.6) reduction in the growth rate after one week and an 8.6 percentage point (3.0 to 14.1) reduction after two weeks. By day 22 the reduction (18.2 percentage points, 12.3 to 24.0) had surpassed the growth at the peak, indicating that growth had turned negative and the number of new daily infections was beginning to decline. A hypothetical national stay-at-home order issued on March 13, 2020 when a national emergency was declared might have reduced cumulative county infections by 62.3%, and might have helped to reverse exponential growth in the disease by April 5. The results here suggest that a coordinated nationwide stay-at-home order may have reduced by hundreds of thousands the current number of infections and by thousands the total number of deaths from COVID-19. Future efforts in the United States and elsewhere to control pandemics should coordinate stay-at-home orders at the national level, especially for diseases for which local spread has already occurred and testing availability is delayed.

Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness
Archil Gulisashvili
arXiv

We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have extremely rough sample paths. The drift function and the volatility function are assumed to be time-dependent and locally $\omega$-continuous for some modulus of continuity $\omega$. The main results obtained in the paper are sample path and small-noise large deviation principles for the log-price process in a Gaussian model under very mild restrictions. We use these results to study the asymptotic behavior of binary up-and-in barrier options and binary call options.

What You See and What You Don't See: The Hidden Moments of a Probability Distribution
Nassim Nicholas Taleb
arXiv

Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the properties of the hidden tail and calculate its moments of order $p$. The method is useful in showing how large a bias one can expect, for a given $n$, between the visible in-sample mean and the true statistical mean (or higher moments), which is considerable for $\alpha$ close to 1. Among other properties, we note that the "hidden" moment of order $0$, that is, the exceedance probability for power law distributions, follows an exponential distribution and has for expectation $\frac{1}{n}$ regardless of the parametrization of the scale and tail index.