Research articles for the 2021-02-14

A structural approach to default modelling with pure jump processes
Jean-Philippe Aguilar,Nicolas Pesci,Victor James

We present a general framework for the estimation of corporate default based on a firm's capital structure, when its assets are assumed to follow a pure jump L\'evy processes; this setup provides a natural extension to usual default metrics defined in diffusion (log-normal) models, and allows to capture extreme market events such as sudden drops in asset prices, which are closely linked to default occurrence. Within this framework, we introduce several processes featuring negative jumps only and derive practical closed formulas for equity prices, which enable us to use a moment-based algorithm to calibrate the parameters from real market data and to estimate the associated default metrics. A notable feature of these models is the redistribution of credit risk towards shorter maturity: this constitutes an interesting improvement to diffusion models, which are known to underestimate short term default probabilities. We also provide extensions to a model featuring both positive and negative jumps and discuss qualitative and quantitative features of the results. For readers convenience, practical tools for model implementation and R code are also included.

Approximate Expected Utility Rationalization
Federico Echenique,Kota Saito,Taisuke Imai

We propose a new measure of deviations from expected utility theory. For any positive number~$e$, we give a characterization of the datasets with a rationalization that is within~$e$ (in beliefs, utility, or perceived prices) of expected utility theory. The number~$e$ can then be used as a measure of how far the data is to expected utility theory. We apply our methodology to data from three large-scale experiments. Many subjects in those experiments are consistent with utility maximization, but not with expected utility maximization. Our measure of distance to expected utility is correlated with subjects' demographic characteristics.

At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem
Sean Ledger,Andreas Sojmark

We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to `blow-up' phenomena whereby solutions develop jump-discontinuities. Our main results are twofold and concern the conditional McKean--Vlasov formulation of the model. First and foremost, we show that there are global solutions to this McKean--Vlasov problem, which can be realised as limit points of a motivating particle system with common noise. Furthermore, we derive results on the occurrence of blow-ups, thereby showing how these events can be triggered or prevented by the pathwise realisations of the common noise.

Bank Supervision: A Legal Scholarship Review
Hill, Julie Andersen
Banks always have someone watching over their shoulders, gauging compliance with law, evaluating risk, and correcting behavior. This is bank supervision. We expect a lot from bank supervision. It is supposed to ensure that banks operate in a safe and sound manner, mitigate systemic risk in the larger financial system, promote fair and efficient markets, protect consumers and other bank customers, and maybe more. Legal scholarship scrutinized bank supervision and asks whether legal changes could help supervision more completely reach its goals. Often, however, legal scholarship passes briefly over bank supervision, instead focusing bank regulation (the establishment of the legal rules that banks must operate within). This literature review summarizes existing legal scholarship on banking supervision, examines why supervision is overlooked, and provides possible avenues for future work on supervision.

Challenges of Equitable Vaccine Distribution in the COVID-19 Pandemic
Joseph Bae,Darshan Gandhi,Jil Kothari,Sheshank Shankar,Jonah Bae,Parth Patwa,Rohan Sukumaran,T. V. Sethuraman,Vanessa Yu,Krutika Mishra,Srinidhi Murali,Aishwariya Saxena,Kasia Jakimowicz,Vivek Sharma,Rohan Iyer,Ashley Mehra,Alex Radunsky,Priyanshi Katiyar,Sunaina Anand,Shailesh Advani,Jagjit Dhaliwal,Ramesh Raskar

As several COVID-19 vaccine candidates approach approval for human use, governments around the world are preparing comprehensive standards for vaccine distribution and monitoring to avoid long-term consequences that may result from rush-to-market. In this early draft article, we identify challenges for vaccine distribution in four core areas - logistics, health outcomes, user-centric impact, and communication. Each of these challenges is analyzed against five critical consequences impacting disease-spread, individual behaviour, society, the economy, and data privacy. Disparities in equitable distribution, vaccine efficacy, duration of immunity, multi-dose adherence, and privacy-focused record keeping are among the most critical difficulties that must be addressed. While many of these challenges have been previously identified and planned for, some have not been acknowledged from a comprehensive view to account for unprecedented repercussions in specific subsets of the population.

Deep Reinforcement Learning for Portfolio Optimization using Latent Feature State Space (LFSS) Module
Kumar Yashaswi

Dynamic Portfolio optimization is the process of distribution and rebalancing of a fund into different financial assets such as stocks, cryptocurrencies, etc, in consecutive trading periods to maximize accumulated profits or minimize risks over a time horizon. This field saw huge developments in recent years, because of the increased computational power and increased research in sequential decision making through control theory. Recently Reinforcement Learning(RL) has been an important tool in the development of sequential and dynamic portfolio optimization theory. In this paper, we design a Deep Reinforcement Learning(DRL) framework as an autonomous portfolio optimization agent consisting of a Latent Feature State Space(LFSS) Module for filtering and feature extraction of financial data which is used as a state space for deep RL model. We develop an extensive RL agent with high efficiency and performance advantages over several benchmarks and model-free RL agents used in prior work. The noisy and non-stationary behaviour of daily asset prices in the financial market is addressed through Kalman Filter. Autoencoders, ZoomSVD, and restricted Boltzmann machines were the models used and compared in the module to extract relevant time series features as state space. We simulate weekly data, with practical constraints and transaction costs, on a portfolio of S&P 500 stocks. We introduce a new benchmark based on technical indicator Kd-Index and Mean-Variance Model as compared to equal weighted portfolio used in most of the prior work. The study confirms that the proposed RL portfolio agent with state space function in the form of LFSS module gives robust results with an attractive performance profile over baseline RL agents and given benchmarks.

Forecasting e-scooter substitution with direct and access trips by mode and distance in New York City
Mina Lee,Joseph Y. J. Chow,Gyugeun Yoon,Brian Yueshuai He

An e-scooter trip model is estimated from four U.S. cities: Portland, Austin, Chicago and New York City. A log-log regression model is estimated for e-scooter trips based on user age, population, land area, and the number of scooters. The model predicts 75K daily e-scooter trips in Manhattan for 2000 scooters, which translates to $77 million USD in annual revenue. We propose a novel nonlinear, multifactor model to break down the number of daily trips by the alternative modes of transportation that they would likely substitute. The model parameters reveal a relationship with direct trips of bike, walk, carpool, automobile and taxi as well as access/egress trips with public transit in Manhattan. Our model estimates that e-scooters would replace at most 32% of carpool; 13% of bike; and 7.2% of taxi trips. The distance structure of revenue from access/egress trips is found to differ from that of other substituted trips.

Hedging of Financial Derivative Contracts via Monte Carlo Tree Search
Oleg Szehr

The construction of approximate replication strategies for derivative contracts in incomplete markets is a key problem of financial engineering. Recently Reinforcement Learning algorithms for pricing and hedging under realistic market conditions have attracted significant interest. While financial research mostly focused on variations of $Q$-learning, in Artificial Intelligence Monte Carlo Tree Search is the recognized state-of-the-art method for various planning problems, such as the games of Hex, Chess, Go,... This article introduces Monte Carlo Tree Search for the hedging of financial derivatives in realistic markets and shows that there are good reasons, both on the theoretical and practical side, to favor it over other Reinforcement Learning methods.

Learning Risk Preferences from Investment Portfolios Using Inverse Optimization
Shi Yu,Haoran Wang,Chaosheng Dong

The fundamental principle in Modern Portfolio Theory (MPT) is based on the quantification of the portfolio's risk related to performance. Although MPT has made huge impacts on the investment world and prompted the success and prevalence of passive investing, it still has shortcomings in real-world applications. One of the main challenges is that the level of risk an investor can endure, known as \emph{risk-preference}, is a subjective choice that is tightly related to psychology and behavioral science in decision making. This paper presents a novel approach of measuring risk preference from existing portfolios using inverse optimization on the mean-variance portfolio allocation framework. Our approach allows the learner to continuously estimate real-time risk preferences using concurrent observed portfolios and market price data. We demonstrate our methods on real market data that consists of 20 years of asset pricing and 10 years of mutual fund portfolio holdings. Moreover, the quantified risk preference parameters are validated with two well-known risk measurements currently applied in the field. The proposed methods could lead to practical and fruitful innovations in automated/personalized portfolio management, such as Robo-advising, to augment financial advisors' decision intelligence in a long-term investment horizon.

Learning a functional control for high-frequency finance
Laura Leal,Mathieu Laurière,Charles-Albert Lehalle

We use a deep neural network to generate controllers for optimal trading on high frequency data. For the first time, a neural network learns the mapping between the preferences of the trader, i.e. risk aversion parameters, and the optimal controls. An important challenge in learning this mapping is that in intraday trading, trader's actions influence price dynamics in closed loop via the market impact. The exploration--exploitation tradeoff generated by the efficient execution is addressed by tuning the trader's preferences to ensure long enough trajectories are produced during the learning phase. The issue of scarcity of financial data is solved by transfer learning: the neural network is first trained on trajectories generated thanks to a Monte-Carlo scheme, leading to a good initialization before training on historical trajectories. Moreover, to answer to genuine requests of financial regulators on the explainability of machine learning generated controls, we project the obtained "blackbox controls" on the space usually spanned by the closed-form solution of the stylized optimal trading problem, leading to a transparent structure. For more realistic loss functions that have no closed-form solution, we show that the average distance between the generated controls and their explainable version remains small. This opens the door to the acceptance of ML-generated controls by financial regulators.

Like Attract Like? A Structural Comparison of Homogamy across Same-Sex and Different-Sex Households
Edoardo Ciscato,Alfred Galichon,Marion Goussé

In this paper, we extend Gary Becker's empirical analysis of the marriage market to same-sex couples. Becker's theory rationalizes the well-known phenomenon of homogamy among different-sex couples: individuals mate with their likes because many characteristics, such as education, consumption behaviour, desire to nurture children, religion, etc., exhibit strong complementarities in the household production function. However, because of asymmetries in the distributions of male and female characteristics, men and women may need to marry "up" or "down" according to the relative shortage of their characteristics among the populations of men and women. Yet, among same-sex couples, this limitation does not exist as partners are drawn from the same population, and thus the theory of assortative mating would boldly predict that individuals will choose a partner with nearly identical characteristics. Empirical evidence suggests a very different picture: a robust stylized fact is that the correlation of the characteristics is in fact weaker among same-sex couples. In this paper, we build an equilibrium model of same-sex marriage market which allows for straightforward identification of the gains to marriage. We estimate the model with 2008-2012 ACS data on California and show that positive assortative mating is weaker for homosexuals than for heterosexuals with respect to age and race. Our results suggest that positive assortative mating with respect to education is stronger among lesbians, and not significantly different when comparing gay men and married different-sex couples. As regards labor market outcomes, such as hourly wages and working hours, we find some indications that the process of specialization within the household mainly applies to different-sex couples.

Modeling and Controlling the Spread of Epidemic with Various Social and Economic Scenarios
S.P. Lukyanets,I.S. Gandzha,O.V. Kliushnichenko

We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe various scenarios of epidemic spreading. As compared to the basic SIR model, our model takes into account two possible routes of contagion transmission: direct from the infected compartment to the susceptible compartment and indirect via some intermediate medium or fomites. Transmission rates are estimated in terms of average distances between the individuals in selected social environments and characteristic time spans for which the individuals stay in each of these environments. We also introduce a collective economic resource associated with the average amount of money or income per individual to describe the socioeconomic interplay between the spreading process and the resource available to infected individuals. The epidemic-resource coupling is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law. Our model brings an advantage of building various control strategies to mitigate the effect of epidemic and can be applied, in particular, to modeling the spread of COVID-19.

On Human Capital and Team Stability
Pierre-André Chiappori,Alfred Galichon,Bernard Salanié

In many economic contexts, agents from a same population team up to better exploit their human capital. In such contexts (often called "roommate matching problems"), stable matchings may fail to exist even when utility is transferable. We show that when each individual has a close substitute, a stable matching can be implemented with minimal policy intervention. Our results shed light on the stability of partnerships on the labor market. Moreover, they imply that the tools crafted in empirical studies of the marriage problem can easily be adapted to many roommate problems.

On the Fragility of Third-party Punishment: The Context Effect of a Dominated Risky Investment Option
Changkuk Im,Jinkwon Lee

Some studies have shown that third-party punishment (TPP) substantially exists in a controlled laboratory setting. However, only a few studies investigate the robustness of TPP. This study experimentally investigates to what extent TPP can be robust by offering an additional but unattractive risky investment option to a third party. We find that when both the punishment and investment options are available, the demand for punishment decreases whereas the demand for investment increases. These findings support our hypothesis that the seemingly unrelated and dominated investment option may work as a compromise and suggest the fragility of TPP.

Ordinal and cardinal solution concepts for two-sided matching
Federico Echenique,Alfred Galichon

We characterize solutions for two-sided matching, both in the transferable and in the nontransferable-utility frameworks, using a cardinal formulation. Our approach makes the comparison of the matching models with and without transfers particularly transparent. We introduce the concept of a no-trade matching to study the role of transfers in matching. A no-trade matching is one in which the availability of transfers do not affect the outcome.

The Golden Age of the Mathematical Finance
José Manuel Corcuera

This paper is devoted, mainly, to show that the last quarter of the past century can be considered as the golden age of the Mathematical Finance. In this period the collaboration of great economist and the best generation of probabilists, most of them from the Strasbourg's School led by Paul Andr\'e Meyer, gave rise to the foundations of this discipline. They established the two fundamentals theorems of arbitrage theory, close formulas for options, the main modelling approaches and created the appropriate framework for the posterior development.12

Uncertainty spill-overs: when policy and financial realms overlap
Emanuele Bacchiocchi,Catalin Dragomirescu-Gaina

No matter its source, financial- or policy-related, uncertainty can feed onto itself, inflicting the real economic sector, altering expectations and behaviours, and leading to identification challenges in empirical applications. The strong intertwining between policy and financial realms prevailing in Europe, and in Euro Area in particular, might complicate the problem and create amplification mechanisms difficult to pin down. To reveal the complex transmission of country-specific uncertainty shocks in a multi-country setting, and to properly account for cross-country interdependencies, we employ a global VAR specification for which we adapt an identification approach based on magnitude restrictions. Once we separate policy uncertainty from financial uncertainty shocks, we find evidence of important cross-border uncertainty spill-overs. We also uncover a new amplification mechanism for domestic uncertainty shocks, whose true nature becomes more blurred once they cross the national boundaries and spill over to other countries. With respect to ECB policy reactions, we reveal stronger but less persistent responses to financial uncertainty shocks compared to policy uncertainty shocks. This points to ECB adopting a more (passive or) accommodative stance towards the former, but a more pro-active stance towards the latter shocks, possibly as an attempt to tame policy uncertainty spill-overs and prevent the fragmentation of the Euro Area financial markets.