# Research articles for the 2020-12-10

A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics
Stefan Kremsner,Alexander Steinicke,Michaela Szölgyenyi
arXiv

In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In this paper we propose a deep neural network algorithm for solving such partial differential equations in high dimensions. The algorithm is based on the correspondence of elliptic partial differential equations to backward stochastic differential equations with random terminal time.

A novel algorithm for clearing financial obligations between companies -- an application within the Romanian Ministry of Economy
Lucian-Ionut Gavrila,Alexandru Popa
arXiv

The concept of clearing or netting, as defined in the glossaries of European Central Bank, has a great impact on the economy of a country influencing the exchanges and the interactions between companies. On short, netting refers to an alternative to the usual way in which the companies make the payments to each other: it is an agreement in which each party sets off amounts it owes against amounts owed to it. Based on the amounts two or more parties owe between them, the payment is substituted by a direct settlement. In this paper we introduce a set of graph algorithms which provide optimal netting solutions for the scale of a country economy. The set of algorithms computes results in an efficient time and is tested on invoice data provided by the Romanian Ministry of Economy. Our results show that classical graph algorithms are still capable of solving very important modern problems.

Affiliated Analysts and Loan Contracting
Chu, Yongqiang,Ma, Tao,Wang, Cong (Roman)
SSRN
We examine whether coverage by analysts affiliated with lenders affects loan contracting. We find that loans to borrowers covered by affiliated analysts have lower spreads but more covenants. Further analyses suggest the results are driven mostly by ex post monitoring, instead of ex ante screening. Exploiting plausibly exogenous variation in affiliated analysts generated by changes in brokerage house affiliation, we find that the result is likely to be causal. The results suggest that analysts could transfer private information about the borrowers to the lending arms of their affiliated financial conglomerates.

An unsupervised deep learning approach in solving partial integro-differential equations
Ali Hirsa,Weilong Fu
arXiv

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep learning, pre-calculated labels are used to train neural networks to fit the solution of the PIDE. In an unsupervised deep learning, neural networks are employed as the solution, and the derivatives and the integrals in the PIDE are calculated based on the neural network. By matching the PIDE and its boundary conditions, the neural network gives an accurate solution of the PIDE. Once trained, it would be fast for calculating options values as well as option Greeks.

Applications of Mean Field Games in Financial Engineering and Economic Theory
Rene Carmona
arXiv

This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront that several of the examples reviewed in this chapter were already discussed in book form. Still, they are here accompanied with discussions of, and references to, works which appeared over the last three years. Moreover, several completely new sections are added to show how recent developments in financial engineering and economics can benefit from being viewed through the lens of the Mean Field Game paradigm. The new financial engineering applications deal with bitcoin mining and the energy markets, while the new economic applications concern models offering a smooth transition between macro-economics and finance, and contract theory.

Born in Hard Times: Startups Selection and Intangible Capital During the Financial Crisis
Manaresi, Francesco,Gonzales-Torres, Guzman,Scoccianti, Filippo
SSRN
We show that the credit crunch of 2007-2013 favoured the adoption by startups of more efficient, intangible-intensive technologies. Using data for the universe of Italian corporations, we document that the cohorts of firms born during the crisis significantly increased their share of intangible capital relative to both incumbents and comparable young firms born before the crisis. Moreover, the entry rates of intangible-intensive startups decreased by less than those of other firms. We estimate that this selection is directly linked to the tightening of credit conditions. We use a firm dynamics model to unveil the mechanism behind these patterns. Intangible goods make firms more efficient and profitable, reducing their demand of total capital and, crucially, their leverage at entry: this increases their resiliency to a financial shock. In the aggregate, a credit tightening changes the composition of new cohorts in favor of intangible-intensive producers, resulting in a persistent increase in intangible capital accumulation.

China and the Rise of Law-Proof Insiders
Fried, Jesse M.,Kamar, Ehud
SSRN
Alibaba, the e-commerce giant that completed a record-breaking IPO in the United States in 2014 and in mid-2020 was valued at over $500 billion, is one of hundreds of China-based U.S.-listed firms whose controlling insiders are largely â€œlaw-proofâ€: the corporate and securities laws governing these firms are effectively unenforceable because the firmsâ€™ insiders, records, and assets are in China. Legal remedies thus cannot reliably prevent diversion of most of these firmsâ€™ value. Our analysis casts doubt on the claim that foreign firms list in the United States to bond insiders to tough securities regulation. In fact, for China-based firms not also listed in China, a U.S. listing has the opposite effect: it effectively insulates insiders from any securities law. Yet U.S. securities regulation not only allows these firms to list, but also requires less disclosure from them than from domestic firms. The system, we show, is biased against American entrepreneurs and likely harms American investors. We suggest ways to reduce this bias and better protect U.S. investors. More generally, our analysis makes clear that one cannot understand corporate governance arrangements without taking into account enforceability. Communication Affects Financial Decisions and Outcomes Henriques-de-Brito, Marcelo SSRN The goal of this essay with practical applications is to address and develop visual models to discuss and ease the understanding of the communication process in finance, taking into account impacts from feedback and the surrounding environment. This work also targets the relationship between a client and a financial practitioner. Besides discussing the visual models, this work describes how these models may be used to improve financial human communication. In the end of this article are key points and suggestions for future work in the field of human behavior, communication, and interaction when implementing financial decisions. Comprehensive Financial Modeling of Solar PV Systems Baschieri, Davide,Magni, Carlo Alberto,Marchioni, Andrea SSRN The adoption of a photovoltaic system has positive environmental effects, but the main driver of the choice in the industrial and commercial sector is economic profitability. Switching from acquisition of energy to production of energy is an investment with costs (e.g. leasing annual payment, O&M costs, capital expenditure) and benefits (e.g. savings in the electric bill, sale of the energy exceeding consumptions). In this work, we use an accounting-and-finance model to calculate the Equity Net Present Value in different scenarios and a sensitivity-analysis method (Finite Change Sensitivity Index) to explain the reasons for differences in results. This technique enables identifying the contribution of any input factor in the output value variation. In this way, the investor can draw attention on the most significant critical variables in the initial estimations to ensure success in forecasting. Cyclicality of Capital Adequacy Ratios in Heterogeneous Environment: a Non-linear Panel Smooth Transition Regression Explanation Rubbaniy, Ghulame,Cheema, Ali Awais,Polyzos, Stathis SSRN This study aims to investigate the cyclicality of capital adequacy ratios (CARs) in US bank holding companies using a new business cycle index and a non-linear panel smooth transition regression model. The suggested index can predict US business activity with a higher accuracy than existing proxies, while the regression methodology deals with the heterogeneity bias of linear models and can capture asymmetric effects, thus improving forecasting efficiency. Our results show that the equity capital to assets ratio is countercyclical, while the risk-based capital adequacy ratios are procyclical. In addition, the response of capital adequacy ratios to changes in economic activity is asymmetric across recessions and expansions. The findings of this study can assist policymakers and bank regulators as the estimation of capital adequacy ratios using the non-linear method and new proxy of BC can improve both the time-lag and accuracy issues in the regulatorsâ€™ decision making and results in improved compliance behavior of the banks. Dealing with Carbon Risk and the Cost of Debt: Evidence from the European Market Pizzutilo, Fabio,Mariani, Massimo,Caragnano, Alessandra,Zito, Marianna SSRN The ever-increasing attention towards climate change has led to investigate the economic and financial impact of environmental risk. In this scenario, we aimed at investigating the relationship between a specific component of environmental risk, namely the so-called carbon risk, and the cost of debt. This research is motivated by the fact that few studies have focused on the aforementioned relationship. We fill this gap by using a sample of companies listed on the Eurostoxx 600 Index. Our results evidence a positive relationship between carbon risk and cost of debt, providing a relevant contribution to the scarce existing literature on this topic. Denting the FRTB IMA computational challenge via Orthogonal Chebyshev Sliding Technique Mariano Zeron-Medina Laris,Ignacio Ruiz arXiv In this paper we introduce a new technique based on high-dimensional Chebyshev Tensors that we call \emph{Orthogonal Chebyshev Sliding Technique}. We implemented this technique inside the systems of a tier-one bank, and used it to approximate Front Office pricing functions in order to reduce the substantial computational burden associated with the capital calculation as specified by FRTB IMA. In all cases, the computational burden reductions obtained were of more than$90\%\$, while keeping high degrees of accuracy, the latter obtained as a result of the mathematical properties enjoyed by Chebyshev Tensors.

DoubleEnsemble: A New Ensemble Method Based on Sample Reweighting and Feature Selection for Financial Data Analysis
Chuheng Zhang,Yuanqi Li,Xi Chen,Yifei Jin,Pingzhong Tang,Jian Li
arXiv

Modern machine learning models (such as deep neural networks and boosting decision tree models) have become increasingly popular in financial market prediction, due to their superior capacity to extract complex non-linear patterns. However, since financial datasets have very low signal-to-noise ratio and are non-stationary, complex models are often very prone to overfitting and suffer from instability issues. Moreover, as various machine learning and data mining tools become more widely used in quantitative trading, many trading firms have been producing an increasing number of features (aka factors). Therefore, how to automatically select effective features becomes an imminent problem. To address these issues, we propose DoubleEnsemble, an ensemble framework leveraging learning trajectory based sample reweighting and shuffling based feature selection. Specifically, we identify the key samples based on the training dynamics on each sample and elicit key features based on the ablation impact of each feature via shuffling. Our model is applicable to a wide range of base models, capable of extracting complex patterns, while mitigating the overfitting and instability issues for financial market prediction. We conduct extensive experiments, including price prediction for cryptocurrencies and stock trading, using both DNN and gradient boosting decision tree as base models. Our experiment results demonstrate that DoubleEnsemble achieves a superior performance compared with several baseline methods.

Effects of Eligibility for Central Bank Purchases on Corporate Bond Spreads
MÃ¤kinen, Taneli,Mercatanti, Andrea,Silvestrini, Andrea,Li, Fan
SSRN
The causal effect of the European Central Bank's corporate bond purchase program on bond spreads in the primary market is evaluated, making use of a novel regression discontinuity design. The results indicate that the program did not, on average, permanently alter the yield spreads of eligible bonds relative to those of noneligible. Combined with evidence from previous studies, this finding suggests the effects of central bank asset purchase programs are in no way limited to the prices of the specific assets acquired.

Investment and Financing Perspectives for a Solar Photovoltaic Project
Marchioni, Andrea,Magni, Carlo Alberto,Baschieri, Davide
SSRN
In this work we illustrate a simple logical framework serving the purpose of measuring value creation in a real-life solar photovoltaic project, funded with a lease contract, a loan contract and internal financing (i.e., withdrawal from liquid assets). We use the projected accounting data to compute the value created. We assess the project from both an investment perspective (operating assets and liquid assets) and a financing perspective (debt and equity). Furthermore, focusing on value creation for equity-holders, we calculate the expected contribution on shareholders wealth increase of operating and financing activity. In particular, we highlight the role of the distribution policy in financial modeling, by underlining the strict logical connections between estimated data and financial decisions.

Large Non-Stationary Noisy Covariance Matrices: A Cross-Validation Approach
Vincent W. C. Tan,Stefan Zohren
arXiv

We introduce a novel covariance estimator that exploits the heteroscedastic nature of financial time series by employing exponential weighted moving averages and shrinking the in-sample eigenvalues through cross-validation. Our estimator is model-agnostic in that we make no assumptions on the distribution of the random entries of the matrix or structure of the covariance matrix. Additionally, we show how Random Matrix Theory can provide guidance for automatic tuning of the hyperparameter which characterizes the time scale for the dynamics of the estimator. By attenuating the noise from both the cross-sectional and time-series dimensions, we empirically demonstrate the superiority of our estimator over competing estimators that are based on exponentially-weighted and uniformly-weighted covariance matrices.

Modeling asset allocation strategies and a new portfolio performance score
Apostolos Chalkis,Ioannis Z. Emiris
arXiv

We discuss a powerful, geometric representation of financial portfolios and stock markets, which identifies the space of portfolios with the points lying in a simplex convex polytope. The ambient space has dimension equal to the number of stocks, or assets. Although our statistical tools are quite general, in this paper we focus on the problem of portfolio scoring. Our contribution is to introduce an original computational framework to model portfolio allocation strategies, which is of independent interest for computational finance. To model asset allocation strategies, we employ log-concave distributions centered on portfolio benchmarks. Our approach addresses the crucial question of evaluating portfolio management, and is relevant to the individual private investors as well as financial organizations. We evaluate the performance of an allocation, in a certain time period, by providing a new portfolio score, based on the aforementioned framework and concepts. In particular, it relies on the expected proportion of actually invested portfolios that it outperforms when a certain set of strategies take place in that time period. We also discuss how this set of strategies -- and the knowledge one may have about them -- could vary in our framework, and we provide additional versions of our score in order to obtain a more complete picture of its performance. In all cases, we show that the score computations can be performed efficiently. Last but not least, we expect this framework to be useful in portfolio optimization and in automatically identifying extreme phenomena in a stock market.

Monetizing Customer Load Data for an Energy Retailer: A Cooperative Game Approach
Liyang Han,Jalal Kazempour,Pierre Pinson
arXiv

When energy customers schedule loads ahead of time, this information, if acquired by their energy retailer, can improve the retailer's load forecasts. Better forecasts lead to wholesale purchase decisions that are likely to result in lower energy imbalance costs, and thus higher profits for the retailer. Therefore, this paper monetizes the value of the customer schedulable load data by quantifying the retailer's profit gain from adjusting the wholesale purchase based on such data. Using a cooperative game theoretic approach, the retailer translates their increased profit in expectation into the value of cooperation, and redistributes a portion of it among the customers as monetary incentives for them to continue providing their load data. Through case studies, this paper demonstrates the significance of the additional profit for the retailer from using the proposed framework, and evaluates the long-term monetary benefits to the customers based on different payoff allocation methods.

On Detecting Spoofing Strategies in High Frequency Trading
Xuan Tao,Andrew Day,Lan Ling,Samuel Drapeau
arXiv

Spoofing is an illegal act of artificially modifying the supply to drive temporarily prices in a given direction for profit. In practice, detection of such an act is challenging due to the complexity of modern electronic platforms and the high frequency at which orders are channeled. We present a micro-structural study of spoofing in a simple static setting. A multilevel imbalance which influences the resulting price movement is introduced upon which we describe the optimization strategy of a potential spoofer. We provide conditions under which a market is more likely to admit spoofing behavior as a function of the characteristics of the market. We describe the optimal spoofing strategy after optimization which allows us to quantify the resulting impact on the imbalance after spoofing. Based on these results we calibrate the model to real Level 2 datasets from TMX, and provide some monitoring procedures based on the Wasserstein distance to detect spoofing strategies in real time.

Quantum Technology for Economists
Isaiah Hull,Or Sattath,Eleni Diamanti,Göran Wendin
arXiv

Research on quantum technology spans multiple disciplines: physics, computer science, engineering, and mathematics. The objective of this manuscript is to provide an accessible introduction to this emerging field for economists that is centered around quantum computing and quantum money. We proceed in three steps. First, we discuss basic concepts in quantum computing and quantum communication, assuming knowledge of linear algebra and statistics, but not of computer science or physics. This covers fundamental topics, such as qubits, superposition, entanglement, quantum circuits, oracles, and the no-cloning theorem. Second, we provide an overview of quantum money, an early invention of the quantum communication literature that has recently been partially implemented in an experimental setting. One form of quantum money offers the privacy and anonymity of physical cash, the option to transact without the involvement of a third party, and the efficiency and convenience of a debit card payment. Such features cannot be achieved in combination with any other form of money. Finally, we review all existing quantum speedups that have been identified for algorithms used to solve and estimate economic models. This includes function approximation, linear systems analysis, Monte Carlo simulation, matrix inversion, principal component analysis, linear regression, interpolation, numerical differentiation, and true random number generation. We also discuss the difficulty of achieving quantum speedups and comment on common misconceptions about what is achievable with quantum computing.

Recovering Election Winner Probabilities from Stock Prices
Hanke, Michael,StÃ¶ckl, Sebastian,Weissensteiner, Alex
SSRN
After the 2020 U.S. presidential election, counting votes and calling states took more time than usual, particularly in battleground states. In the days following the election, winning probabilities changed frequently as new results were tabulated. Based on the sensitivity of stocks to changes in winning probabilities observed before the election, we show how the stock market's assessment of the unobserved post-election winning probabilities can be backed out from stock prices. Our approach is based solely on publicly available data.

SynthETIC: an individual insurance claim simulator with feature control
Benjamin Avanzi,Gregory Clive Taylor,Melantha Wang,Bernard Wong
arXiv

Recent years have seen rapid increase in the application of machine learning to insurance loss reserving. They yield most value when applied to large data sets, such as individual claims, or large claim triangles. In short, they are likely to be useful in the analysis of any data set whose volume is sufficient to obscure a naked-eye view of its features. Unfortunately, such large data sets are in short supply in the actuarial literature. Accordingly, one needs to turn to synthetic data. Although the ultimate objective of these methods is application to real data, the use of synthetic data containing features commonly observed in real data is also to be encouraged.

While there are a number of claims simulators in existence, each valuable within its own context, the inclusion of a number of desirable (but complicated) data features requires further development. Accordingly, in this paper we review those desirable features, and propose a new simulator of individual claim experience called SynthETIC.

Our simulator is publicly available, open source, and fills a gap in the non-life actuarial toolkit. The simulator specifically allows for desirable (but optionally complicated) data features typically occurring in practice, such as variations in rates of settlements and development patterns; as with superimposed inflation, and various discontinuities, and also enables various dependencies between variables. The user has full control of the mechanics of the evolution of an individual claim. As a result, the complexity of the data set generated (meaning the level of difficulty of analysis) may be dialled anywhere from extremely simple to extremely complex.

The In-house Credit Assessment System of Banca d'Italia
Levy, Aviram,Orlandi, Marco,Giovannelli, Filippo,Iannamorelli, Alessandra
SSRN
Banca dâ€™Italiaâ€™s In-house Credit Assessment System (ICAS) is one of the sources for the valuation of collateral agreed upon within the Eurosystemâ€™s monetary policy framework. It helps to provide liquidity to those Italian banks that cannot rely on an internal model (IRB). Its role has become all the more important in the aftermath of the financial crisis relating to the COVID-19 pandemic of 2020. The paper first outlines the Eurosystemâ€™s collateral framework and describes Banca dâ€™Italiaâ€™s ICAS in terms of architecture and governance. It then presents in detail the underlying statistical model, including the definition of default adopted, and the validation process for the statistical model and for the expert system. The paper concludes by providing data on the amount of collateral pledged with an ICAS rating and on the main features, including the probabilities of default, of the Italian non-financial companies rated by the system.

The Regulatory Cycle in Banking: What Lessons from the U.S. Experience? (From the Dodd-Frank Act to Covid-19)
Trapanese, Maurizio
SSRN
Ten years after the 2007-08 global financial crisis, this paper examines the implementation of the G-20 financial reforms in the main regulatory areas and jurisdictions. The analysis includes banks, insurance companies, derivatives markets and non-bank financial intermediation. Notwithstanding the progress made, which has improved the resilience of the global financial system, some sources of concern remain: the implementation of reforms is still uneven across areas and jurisdictions; there are regulatory interventions still to be completed, above all in non-banking sectors, and others to be implemented at the domestic level. The global financial system may be exposed to risks, such as markets fragmentation, regulatory arbitrages and the volatility of cross-border financial flows. At international level there should be consensus on the need to complete the regulatory reforms in all sectors of financial intermediation and to implement them consistently and in a timely way. For these reasons, the implementation should increasingly become a priority for the G-20 and for the Italian Presidency in 2021.

Unutilized Productive Capacity, Binary Economics and the Case for Broadening Capital Ownership
Ashford, Robert
SSRN
Binary economics holds that a broader distribution of capital acquisition with the earnings of capital promises more consumer demand in future years and therefore greater incentive to employ labor and capital in earlier years. Therefore broadening individual participation in capital acquisition with the earnings of capital has a potent (but presently untapped) positive distributive relationship to growth that is not caused by productivity gains and governmental strategies to redistribute or regulate demand. Compared to classical, neoclassical, Keynesian, Austrian, institutional, socialist, and other schools of economics, binary economics specifically offers (1) a distinct explanation for the persistence of long-run unutilized productive capacity (2) a unique paradigm for understanding economic production, prices, efficiency, growth, and justice, and (3) a market-based policy alternative that promises a wholly voluntary means to employ productive capacity more fully, profitably and sustainably to produce much greater and broadly shared abundance by way of a more inclusive, competitive, and democratic private property system that universalizes the competitive market right to acquire capital with the earnings of capital. To achieve these goals, no transactions are mandated and no government taxation, redistribution, or borrowing is required. Rather, with a binary understanding of market economics, and with modest reform of the existing system of corporate finance, these goals could be achieved entirely by way of voluntary transactions that yield widespread, and eventually universal, individual, capital acquisition with the earnings of capital. When judged by the criteria of (1) reasonable assumptions, (2) internal consistency, and (3) plausible descriptive, predictive, and prescriptive utility, compared to the other economic approaches that are routinely taught and employed, the binary approach is more consistent with scientific principles. Based on widely accepted principles underlying the philosophy of science, professional ethics, secular morality, and spiritual values, educational institutions and foundations have a responsibility to teach binary economics in most contexts in which issues of economic growth, efficiency, sustainability, and justice are taught or considered. Professional ethics governing fiduciaries, advisors, and government officials also call for the inclusion of binary economic principles in their positive and normative analysis of those subjects and in the discharge of their professional duties.

What Can We Learn About Mortgage Supply from Online Data?
Carella, Agnese,Ciocchetta, Federica,Signoretti, Federico Maria,Michelangeli, Valentina
SSRN
We exploit a novel dataset on mortgages offered by banks through Italyâ€™s main online mortgage broker, which works with banks representing over 80 per cent of mortgages granted, to gain an up-to-date assessment of loan supply conditions. Characteristics of mortgages are reported for about 85,000 borrower-contract profiles, constant over time, available at the beginning of each month starting from March 2018. We document that riskier applications, characterized by high loan-to-value ratios and long maturity, are, on average, offered by a smaller number of banks that charge higher interest rates. Online banks tend to provide better price conditions than traditional intermediaries. We use the online rates offered to nowcast bank-level official (MIR) interest rate statistics, available only several weeks later. By using both regression analysis and machine learning algorithms, we show that the rates offered have significant predictive content for fixed-rate contracts, also after controlling for time-varying demand conditions, market reference rates, and unobserved time-invariant bank characteristics. Machine learning algorithms provide further improvements over regression models in out of sample predictions.