Research articles for the 2021-04-25

Correlators of Polynomial Processes
Fred Espen Benth,Silvia Lavagnini

In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of exponentials of the generator matrix, extending the well-known moment formula for polynomial processes. The developed framework can, for example, be applied in financial pricing, such as for path-dependent options and in a stochastic volatility models context. In applications to options, having closed and compact formulations is attractive for sensitivity analysis and risk management, since Greeks can be derived explicitly.

Does home advantage without crowd exist in American football?
Dávid Zoltán Szabó,Diego Andrés Pérez

It is well-known that home team has an inherent advantage against visiting teams when playing team sports. One of the most obvious underlying reasons, the presence of supporting fans has mostly disappeared in major leagues with the emergence of COVID-19 pandemic. This paper investigates with the help of historical National Football League (NFL) data, how much effect spectators have on the game outcome. Our findings reveal that under no allowance of spectators the home teams' performance is substantially lower than under normal circumstances, even performing slightly worse than the visiting teams. On the other hand, when a limited amount of spectators are allowed to the game, the home teams' performance is no longer significantly different than what we observe with full stadiums. This suggests that from a psychological point of view the effect of crowd support is already induced by a fraction of regular fans.

Dynamic investment portfolio optimization using a Multivariate Merton Model with Correlated Jump Risk
Bahareh Afhami,Mohsen Rezapour,Mohsen Madadi,Vahed Maroufy

In this paper, we are concerned with the optimization of a dynamic investment portfolio when the securities which follow a multivariate Merton model with dependent jumps are periodically invested and proceed by approximating the Condition-Value-at-Risk (CVaR) by comonotonic bounds and maximize the expected terminal wealth. Numerical studies as well as applications of our results to real datasets are also provided.

Extending the Heston Model to Forecast Motor Vehicle Collision Rates
Darren Shannon,Grigorios Fountas

We present an alternative approach to the forecasting of motor vehicle collision rates. We adopt an oft-used tool in mathematical finance, the Heston Stochastic Volatility model, to forecast the short-term and long-term evolution of motor vehicle collision rates. We incorporate a number of extensions to the Heston model to make it fit for modelling motor vehicle collision rates. We incorporate the temporally-unstable and non-deterministic nature of collision rate fluctuations, and introduce a parameter to account for periods of accelerated safety. We also adjust estimates to account for the seasonality of collision patterns. Using these parameters, we perform a short-term forecast of collision rates and explore a number of plausible scenarios using long-term forecasts. The short-term forecast shows a close affinity with realised rates (95% accuracy). The long-term scenarios suggest that modest targets to reduce collision rates (1.83% annually) and targets to reduce the fluctuations of month-to-month collision rates (by half) could have significant benefits for road safety. The median forecast in this scenario suggests a 50% fall in collision rates, with 75% of simulations suggesting that an effective change in collision rates is observed before 2044. The main benefit the model provides is eschewing the necessity for setting unreasonable safety targets that are often missed. Instead, the model presents the effects that modest and achievable targets can have on road safety over the long run, while incorporating random variability. Examining the parameters that underlie expected collision rates will aid policymakers in determining the effectiveness of implemented policies.

Identification of Peer Effects with Miss-specified Peer Groups: Missing Data and Group Uncertainty
Christiern Rose

We consider identification of peer effects under peer group miss-specification. Our model of group miss-specification allows for missing data and peer group uncertainty. Missing data can take the form of some individuals being completely absent from the data, and the researcher need not have any information on these individuals and may not even know that they are missing. We show that peer effects are nevertheless identifiable if these individuals are missing completely at random, and propose a GMM estimator which jointly estimates the sampling probability and peer effects. In practice this means that the researcher need only have access to an individual/household level sample with group identifiers. The researcher may also be uncertain as to what is the relevant peer group for the outcome under study. We show that peer effects are nevertheless identifiable provided that the candidate peer groups are nested within one another (e.g. classroom, grade, school) and propose a non-linear least squares estimator. We conduct a Monte-Carlo experiment to demonstrate our identification results and the performance of the proposed estimators in a setting tailored to real data (the Dartmouth room-mate data).

If it Looks like a Human and Speaks like a Human ... Dialogue and cooperation in human-robot interactions
Mario A. Maggioni,Domenico Rossignoli

The paper presents the results of a behavioral experiment conducted between February 2020 and March 2021 at Universit\`a Cattolica del Sacro Cuore, Milan Campus in which students were matched to either a human or a humanoid robotic partner to play an iterated Prisoner's Dilemma. The results of a Logit estimation procedure show that subjects are more likely to cooperate with human rather robotic partners; that are more likely to cooperate after receiving a dialogic verbal reaction following the realization of a sub-obtimal social outcome; that the effect of the verbal reaction is independent on the nature of the partner. Our findings provide new evidence on the effect of verbal communication in strategic frameworks. Results are robust to the exclusion of students of Economics related subjects, to the inclusion of a set of psychological and behavioral controls, to the way subjects perceive robots' behavior and to potential gender biases in human-human interactions.

Managing mental & psychological wellbeing amidst COVID-19 pandemic: Positive psychology interventions
Maria Tresita V. Paul,Uma N. Devi

COVID-19 pandemic has shaken the roots of healthcare facilities worldwide, with the US being one of the most affected countries irrespective of being a superpower. Along with the current pandemic, COVID-19 can cause a secondary crisis of mental health pandemic if left unignored. Various studies from past epidemics, financial turmoil and pandemic, especially SARS and MERS, have shown a steep increase in mental and psychological issues like depression, low quality of life, self-harm and suicidal tendencies among general populations. The most venerable being the individuals infected and cured due to social discrimination. The government is taking steps to contain and prevent further infections of COVID-19. However, the mental and psychological wellbeing of people is still left ignored in developing countries like India. There is a significant gap in India concerning mental and psychological health still being stigmatized and considered 'non-existent'. This study's effort is to highlight the importance of mental and psychological health and to suggest interventions based on positive psychology literature. These interventions can support the wellbeing of people acting as a psychological first aid.

Keywords: COVID-19, Coronavirus, Pandemic, Mental wellbeing, Psychological Wellbeing, Positive Psychology Interventions.

Pricing Asian Options with Correlators
Silvia Lavagnini

We derive a series expansion by Hermite polynomials for the price of an arithmetic Asian option. This series requires the computation of moments and correlators of the underlying price process, but for a polynomial jump-diffusion, these are given in closed form, hence no numerical simulation is required to evaluate the series. This allows, for example, for the explicit computation of Greeks. The weight function defining the Hermite polynomials is a Gaussian density with scale $b$. We find that the rate of convergence for the series depends on $b$, for which we prove a lower bound to guarantee convergence. Numerical examples show that the series expansion is accurate but unstable for initial values of the underlying process far from zero, mainly due to rounding errors.

Temporal Clustering of Disorder Events During the COVID-19 Pandemic
Gian Maria Campedelli,Maria Rita D'Orsogna

The COVID-19 pandemic has unleashed multiple public health, socio-economic, and institutional crises. Measures taken to slow the spread of the virus have fostered significant strain between authorities and citizens, leading to waves of social unrest and anti-government demonstrations. We study the temporal nature of pandemic-related disorder events as tallied by the "COVID-19 Disorder Tracker" initiative by focusing on the three countries with the largest number of incidents, India, Israel, and Mexico. By fitting Poisson and Hawkes processes to the stream of data, we find that disorder events are inter-dependent and self-excite in all three countries. Geographic clustering confirms these features at the subnational level, indicating that nationwide disorders emerge as the convergence of meso-scale patterns of self-excitation. Considerable diversity is observed among countries when computing correlations of events between subnational clusters; these are discussed in the context of specific political, societal and geographic characteristics. Israel, the most territorially compact and where large scale protests were coordinated in response to government lockdowns, displays the largest reactivity and the shortest period of influence following an event, as well as the strongest nationwide synchrony. In Mexico, where complete lockdown orders were never mandated, reactivity and nationwide synchrony are lowest. Our work highlights the need for authorities to promote local information campaigns to ensure that livelihoods and virus containment policies are not perceived as mutually exclusive.

The Crowd Classification Problem: Social Dynamics of Binary Choice Accuracy
Joshua Becker,Douglas Guilbeault,Ned Smith

Decades of research suggest that information exchange in groups and organizations can reliably improve judgment accuracy in tasks such as financial forecasting, market research, and medical decision-making. However, we show that improving the accuracy of numeric estimates does not necessarily improve the accuracy of decisions. For binary choice judgments, also known as classification tasks--e.g. yes/no or build/buy decisions--social influence is most likely to grow the majority vote share, regardless of the accuracy of that opinion. As a result, initially inaccurate groups become increasingly inaccurate after information exchange even as they signal stronger support. We term this dynamic the "crowd classification problem." Using both a novel dataset as well as a reanalysis of three previous datasets, we study this process in two types of information exchange: (1) when people share votes only, and (2) when people form and exchange numeric estimates prior to voting. Surprisingly, when people exchange numeric estimates prior to voting, the binary choice vote can become less accurate even as the average numeric estimate becomes more accurate. Our findings recommend against voting as a form of decision-making when groups are optimizing for accuracy. For those cases where voting is required, we discuss strategies for managing communication to avoid the crowd classification problem. We close with a discussion of how our results contribute to a broader contingency theory of collective intelligence.