Following an approach originally suggested by Balland in the context of the SABR model, we derive an ODE that is satisfied by normalized volatility smiles for short maturities under a rough volatility extension of the SABR model that extends also the rough Bergomi model. We solve this ODE numerically and further present a very accurate approximation to the numerical solution that we dub the rough SABR formula.

Global warming is one of the main threats to the future of humanity and extensive emissions of greenhouse gases are found to be the main cause of global temperature rise as well as climate change. During the last decades international attention has focused on this issue, as well as on searching for viable solutions to mitigate global warming. In this context, the pricing of greenhouse gas emissions turned out to be the most prominent mechanism: First, to lower the emissions, and second, to capture their external costs. By now, various carbon dioxide taxes have been adopted by several countries in Europe and around the world; moreover, the list of these countries is growing. However, there is no standardized approach and the price for carbon varies significantly from one country to another. Regionally diversified carbon prices in turn lead to carbon leakage, which will offset the climate protection goals. In this paper, a simplified European power system with flexible carbon prices regarding the Gross Domestic Product (GDP) is investigated. A distribution parameter that quantifies carbon leakage is defined and varied together with the base carbon price, where the combination of both parameters describes the spatially resolved price distribution, i.e. the effective carbon pricing among the European regions. It is shown that inhomogeneous carbon prices will indeed lead to significant carbon leakage across the continent, and that coal-fired electricity generation will remain a cheap and therefore major source of power in Eastern and South-Eastern Europe - representing a potential risk for the long term decarbonization targets within the European Union.

The study examines the essential features of the so-called platform-based work, which is rapidly evolving into a major, potentially game-changing force in the labor market. From low-skilled, low-paid services (such as passenger transport) to highly skilled and high-paying project-based work (such as the development of artificial intelligence algorithms), a broad range of tasks can be carried out through a variety of digital platforms. Our paper discusses the platform-based content, working conditions, employment status, and advocacy problems. Terminological and methodological problems are dealt with in-depth in the course of the literature review, together with the 'gray areas' of work and employment regulation. To examine some of the complex dynamics of this fast-evolving arena, we focus on the unsuccessful market entry of the digital platform company Uber in Hungary 2016 and the relationship to institutional-regulatory platform-based work standards. Dilemmas relevant to the enforcement of labor law regarding platform-based work are also paid special attention to the study. Employing a digital workforce is a significant challenge not only for labor law regulation but also for stakeholder advocacy.

How are economies in a modern age impacted by epidemics? In what ways is economic life disrupted? How can pandemics be modeled? What can be done to mitigate and manage the danger? Does the threat of pandemics increase or decrease in the modern world? The Covid-19 pandemic has demonstrated the importance of these questions and the potential of complex systems science to provide answers. This article offers a broad overview of the history of pandemics, of established facts, and of models of infection diffusion, mitigation strategies, and economic impact. The example of the Covid-19 pandemic is used to illustrate the theoretical aspects, but the article also includes considerations concerning other historic epidemics and the danger of more infectious and less controllable outbreaks in the future.

Based on a model of optimal information acquisition, I propose an approach to measure attention to inflation in the data. Applying this approach to US consumers and professional forecasters provides substantial evidence that attention to inflation in the US decreased significantly over the last five decades. Consistent with the theoretical model, attention is higher in times of volatile inflation. To examine the consequences of limited attention for monetary policy, I augment the standard New Keynesian model with a lower-bound constraint on the nominal interest rate and inflation expectations that are characterized by limited attention. Accounting for the lower bound fundamentally alters the normative implications of low attention. While lower attention raises welfare absent the lower-bound constraint, it decreases welfare when accounting for the lower bound. In the presence of the lower bound, limited attention can lead to inflation-attention traps: prolonged periods of a binding lower bound and low inflation due to slowly-adjusting inflation expectations. To prevent these traps, it is optimal to increase the inflation target as attention declines.

We study the ex-ante minimization of market inefficiency, defined in terms of minimum deviation of market prices from fundamental values, from a centralized planner's perspective. Prices are pressured from exogenous trading actions of leverage targeting banks, which rebalance their portfolios in response to asset shocks. We characterize market inefficiency in terms of two key drivers, the banks' systemic significance and the statistical moments of asset shocks, and develop an explicit expression for the matrix of asset holdings which minimizes such inefficiency. Our analysis shows that to reduce inefficiencies, portfolio holdings should deviate more from a full diversification strategy if there is little heterogeneity in banks' systemic significance.

We consider the pricing of VIX options in the rough Bergomi model [Bayer, Friz, and Gatheral, Pricing under rough volatility, Quantitative Finance 16(6), 887-904, 2016]. In this setting, the VIX random variable is defined by the one-dimensional integral of the exponential of a Gaussian process with correlated increments, hence approximate samples of the VIX can be constructed via discretization of the integral and simulation of a correlated Gaussian vector. A Monte-Carlo estimator of VIX options based on a rectangle discretization scheme and exact Gaussian sampling via the Cholesky method has a computational complexity of order $\mathcal O(\varepsilon^{-4})$ when the mean-squared error is set to $\varepsilon^2$. We demonstrate that this cost can be reduced to $\mathcal O(\varepsilon^{-2} \log^2(\varepsilon))$ combining the scheme above with the multilevel method [Giles, Multilevel Monte Carlo path simulation, Oper. Res. 56(3), 607-617, 2008], and further reduced to the asymptotically optimal cost $\mathcal O(\varepsilon^{-2})$ when using a trapezoidal discretization. We provide numerical experiments highlighting the efficiency of the multilevel approach in the pricing of VIX options in such a rough forward variance setting.

We propose a new optimal consumption model in which the degree of addictiveness of habit formation is directly controlled through a consumption constraint. In particular, we assume that the individual is unwilling to consume at a rate below a certain proportion $0<\alpha\le1$ of her consumption habit, which is the exponentially-weighted average of past consumption rates. $\alpha=1$ prohibits the habit process to decrease and corresponds to the completely addictive model. $\alpha=0$ makes the habit-formation constraint moot and corresponds to the non-addictive model. $0<\alpha<1$ leads to partially addictive models, with the level of addictiveness increasing with $\alpha$. In contrast to the existing habit-formation literature, our constraint cannot be incorporated in the objective function through infinite marginal utility. Assuming that the individual invests in a risk-free market, we formulate and solve an infinite-horizon, deterministic control problem to maximize the discounted CRRA utility of the consumption-to-habit process subject to the habit-formation constraint. Optimal consumption policies are derived explicitly in terms of the solution of a nonlinear free-boundary problem, which we analyze in detail. Impatient always consume above the minimum rate; thus, they eventually attain the minimum wealth-to-habit ratio. Patient individuals consume at the minimum rate if their wealth-to-habit ratio is below a threshold, and above it otherwise. By consuming patiently, these individuals maintain a wealth-to-habit ratio that is greater than the minimum acceptable level. Additionally, we prove that the optimal consumption path is hump-shaped if the initial wealth-to-habit ratio is either: (1) larger than a high threshold; or (2) below a low threshold and the agent is less risk averse. Thus, we provide a simple explanation for the consumption hump observed by various empirical studies.

This research explores the opportunities for the application of network analytic techniques to prevent money laundering. We worked on real world data by analyzing the central database of a factoring company, mainly operating in Italy, over a period of 19 months. This database contained the financial operations linked to the factoring business, together with other useful information about the company clients. We propose a new approach to sort and map relational data and present predictive models, based on network metrics, to assess risk profiles of clients involved in the factoring business. We find that risk profiles can be predicted by using social network metrics. In our dataset, the most dangerous social actors deal with bigger or more frequent financial operations; they are more peripheral in the transactions network; they mediate transactions across different economic sectors and operate in riskier countries or Italian regions. Finally, to spot potential clusters of criminals, we propose a visual analysis of the tacit links existing among different companies who share the same owner or representative. Our findings show the importance of using a network-based approach when looking for suspicious financial operations and potential criminals.

In quantitative finance, modeling the volatility structure of underlying assets is a key component in the pricing of options. Rough stochastic volatility models, such as the rough Bergomi model [Bayer, Friz, Gatheral, Quantitative Finance 16(6), 887-904, 2016], seek to fit observed market data based on the observation that the log-realized variance behaves like a fractional Brownian motion with small Hurst parameter, $H < 1/2$, over reasonable timescales. Both time series data of asset prices and option derived price data indicate that $H$ often takes values close to $0.1$ or smaller, i.e. rougher than Brownian Motion. This change greatly improves the fit to time series data of underlying asset prices as well as to option prices while maintaining parsimoniousness. However, the non-Markovian nature of the driving fractional Brownian motion in the rough Bergomi model poses severe challenges for theoretical and numerical analyses as well as for computational practice. While the explicit Euler method is known to converge to the solution of the rough Bergomi model, its strong rate of convergence is only $H$. For a simplified rough Bergomi model, we prove rate $H + 1/2$ for the weak convergence of the Euler method and, surprisingly, in the case of quadratic payoff functions we obtain rate one. Indeed, the problem of weak convergence for rough Bergomi is very subtle; we provide examples demonstrating that the rate of convergence for payoff functions well approximated by second-order polynomials, as weighted by the law of the fractional Brownian motion, may be hard to distinguish from rate one empirically. Our proof relies on Taylor expansions and an affine Markovian representation of the underlying and is further supported by numerical experiments.