Research articles for the 2020-04-12

Anomalous diffusions in option prices: connecting trade duration and the volatility term structure
Antoine Jacquier,Lorenzo Torricelli

Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to different distribution spread rates compared to standard models. In financial modelling this has been used to accommodate for random trade duration in the tick-by-tick price process. We show here that anomalous diffusions are able to reproduce the market behaviour of the implied volatility more consistently than usual L\'evy or stochastic volatility models. We focus on two distinct classes of underlying asset models, one with independent price innovations and waiting times, and one allowing dependence between these two components. These two models capture the well-known paradigm according to which shorter trade duration is associated with higher return impact of individual trades. We fully describe these processes in a semimartingale setting leading no-arbitrage pricing formulae, and study their statistical properties. We observe that skewness and kurtosis of the asset returns do not tend to zero as time goes by. We also characterize the large-maturity asymptotics of Call option prices, and find that the convergence rate is slower than in standard L\'evy regimes, which in turn yields a declining implied volatility term structure and a slower decay of the skew.

Asset Prices with Investor Protection and Past Information
Jia Yue,Ben-Zhang Yang,Ming-Hui Wang,Nan-Jing Huang

In this paper, we consider a dynamic asset pricing model in an approximate fractional economy to address empirical regularities related to both investor protection and past information. Our newly developed model features not only in terms with a controlling shareholder who diverts a fraction of the output, but also good (or bad) memory in his budget dynamics which can be well-calibrated by a pathwise way from the historical data. We find that poorer investor protection leads to higher stock holdings of controlling holders, lower gross stock returns, lower interest rates, and lower modified stock volatilities if the ownership concentration is sufficiently high. More importantly, by establishing an approximation scheme for good (bad) memory of investors on the historical market information, we conclude that good (bad) memory would increase (decrease) aforementioned dynamics and reveal that good (bad) memory strengthens (weakens) investor protection for minority shareholder when the ownership concentration is sufficiently high, while good (bad) memory inversely weakens (strengthens) investor protection for minority shareholder when the ownership concentration is sufficiently low. Our model's implications are consistent with a number of interesting facts documented in the recent literature.

Exploring the Effect of 2019-nCoV Containment Policies on Crime: The Case of Los Angeles
Gian Maria Campedelli,Alberto Aziani,Serena Favarin

The global spread of 2019-nCoV, a new virus belonging to the coronavirus family, forced national and local governments to apply different sets of measures aimed at containing its outbreak. Los Angeles has been one of the first cities in the United States to declare the state of emergency on March 4th, progressively issuing stronger policies involving--among the others--social distancing, the prohibition of crowded private and public gatherings and closure of leisure premises. These interventions highly disrupt and modify daily activities and habits, urban mobility and micro-level interactions between citizens. One of the many social phenomena that could be influenced by such measures is crime. Exploiting public data on crime in Los Angeles, and relying on routine activity and pattern theories of crime, this work investigates whether and how new coronavirus containment policies have an impact on crime trends in a metropolis using Bayesian structural time-series (BSTS) models. The article specifically focuses on nine urban crime categories, daily monitored from January 1st 2017 to March 28th 2020. The analyses have been updated bi-weekly (up to March 16\ts{th} and up to March 28\ts{th} 2020) to dynamically assess the short-term effects of mild and hard interventions to shed light on how crime adapts to such structural modification of the environment. The results show that overall crime in Las Angeles is significantly decreasing, as well as robbery, shoplifting, theft and battery. No significant effect has been found for stolen vehicle, burglary, assault with deadly weapon, intimate partner violence and homicide. In the last section of this article, policy implications are also discussed.

On approximations of Value at Risk and Expected Shortfall involving kurtosis
Matyas Barczy,Adam Dudas,Jozsef Gall

We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal and compound (Poisson) distributions. Our approximations are motivated by that kind of extensions of the so-called Normal Power Approximation, used for approximating the cumulative distribution function of a random variable, which incorporate not only the skewness but the kurtosis of the random variable in question as well. We show the performance of our approximations in numerical examples and we also give comparisons with some known ones in the literature.

The Benefits and Costs of Social Distancing in Rich and Poor Countries
Zachary Barnett-Howell,Ahmed Mushfiq Mobarak

Social distancing is the primary policy prescription for combating the COVID-19 pandemic, and has been widely adopted in Europe and North America. We estimate the value of disease avoidance using an epidemiological model that projects the spread of COVID-19 across rich and poor countries. Social distancing measures that "flatten the curve" of the disease to bring demand within the capacity of healthcare systems are predicted to save many lives in high-income countries, such that practically any economic cost is worth bearing. These social distancing policies are estimated to be less effective in poor countries with younger populations less susceptible to COVID-19, and more limited healthcare systems, which were overwhelmed before the pandemic. Moreover, social distancing lowers disease risk by limiting people's economic opportunities. Poorer people are less willing to make those economic sacrifices. They place relatively greater value on their livelihood concerns compared to contracting COVID-19. Not only are the epidemiological and economic benefits of social distancing much smaller in poorer countries, such policies may exact a heavy toll on the poorest and most vulnerable. Workers in the informal sector lack the resources and social protections to isolate themselves and sacrifice economic opportunities until the virus passes. By limiting their ability to earn a living, social distancing can lead to an increase in hunger, deprivation, and related mortality and morbidity. Rather than a blanket adoption of social distancing measures, we advocate for the exploration of alternative harm-reduction strategies, including universal mask adoption and increased hygiene measures.