Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the subsequent local volatility surface is never considered. In this article, we develop a deep learning approach for interpolation of European vanilla option prices which jointly yields the full surface of local volatilities. We demonstrate the modification of the loss function or the feed forward network architecture to enforce (hard constraints approach) or favor (soft constraints approach) the no-arbitrage conditions and we specify the experimental design parameters that are needed for adequate performance. A novel component is the use of the Dupire formula to enforce bounds on the local volatility associated with option prices, during the network fitting. Our methodology is benchmarked numerically on real datasets of DAX vanilla options.

This paper investigates the impact of COVID-19 on financial markets. It focuses on the evolution of the market efficiency, using two efficiency indicators: the Hurst exponent and the memory parameter of a fractional L\'evy-stable motion. The second approach combines, in the same model of dynamic, an alpha-stable distribution and a dependence structure between price returns. We provide a dynamic estimation method for the two efficiency indicators. This method introduces a free parameter, the discount factor, which we select so as to get the best alpha-stable density forecasts for observed price returns. The application to stock indices during the COVID-19 crisis shows a strong loss of efficiency for US indices. On the opposite, Asian and Australian indices seem less affected and the inefficiency of these markets during the COVID-19 crisis is even questionable.

We introduce a formal framework for analyzing trades in financial markets. These days, all big exchanges use computer algorithms to match buy and sell requests and these algorithms must abide by certain regulatory guidelines. For example, market regulators enforce that a matching produced by exchanges should be fair, uniform and individual rational. To verify these properties of trades, we first formally define these notions in a theorem prover and then develop many important results about matching demand and supply. Finally, we use this framework to verify properties of two important classes of double sided auction mechanisms. All the definitions and results presented in this paper are completely formalized in the Coq proof assistant without adding any additional axioms to it.

Green hydrogen can help to decarbonize transportation, but its power sector interactions are not well understood. It may contribute to integrating variable renewable energy sources if production is sufficiently flexible in time. Using an open-source co-optimization model of the power sector and four options for supplying hydrogen at German filling stations, we find a trade-off between energy efficiency and temporal flexibility: for lower shares of renewables and hydrogen, more energy-efficient and less flexible small-scale on-site electrolysis is optimal. For higher shares of renewables and/or hydrogen, more flexible but less energy-efficient large-scale hydrogen supply chains gain importance as they allow disentangling hydrogen production from demand via storage. Liquid hydrogen emerges as particularly beneficial, followed by liquid organic hydrogen carriers and gaseous hydrogen. Large-scale hydrogen supply chains can deliver substantial power sector benefits, mainly through reduced renewable surplus generation. Energy modelers and system planners should consider the distinct flexibility characteristics of hydrogen supply chains in more detail when assessing the role of green hydrogen in future energy transition scenarios.

We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general cadlag measurable processes. The main novelties are that we do not assume a Markovian nature of the game nor a particular structure of the information available to the players. This allows us to go beyond the variational methods (based on PDEs) developed in the related literature on Dynkin games in continuous time with partial/asymmetric information. Instead, we focus on a probabilistic and functional analytic approach based on the general theory of stochastic processes and Sion's min-max theorem (M. Sion, Pacific J. Math., 8, 1958, pp. 171-176). Our framework encompasses examples found in the literature on continuous time Dynkin games with asymmetric information and we provide counterexamples to show that our assumptions cannot be further relaxed.

The threat of the new coronavirus (COVID-19) is increasing. Regarding the difference in the infection rate observed in each region, in addition to studies seeking the cause due to differences in the social distance (population density), there is an increasing trend toward studies seeking the cause due to differences in social capital. However, studies have not yet been conducted on whether social capital could influence the infection rate even if it controls the effect of population density. Therefore, in this paper, we analyzed the relationship between infection rate, population density, and social capital using statistical data for each prefecture. Statistical analysis showed that social capital not only correlates with infection rates and population densities but still has a negative correlation with infection rates controlling for the effects of population density. Besides, controlling the relationship between variables by mean age showed that social capital had a greater correlation with infection rate than population density. In other words, social capital mediates the correlation between population density and infection rates. This means that social distance alone is not enough to deter coronavirus infection, and social capital needs to be recharged.

Agricultural research has fostered productivity growth, but the historical influence of anthropogenic climate change on that growth has not been quantified. We develop a robust econometric model of weather effects on global agricultural total factor productivity (TFP) and combine this model with counterfactual climate scenarios to evaluate impacts of past climate trends on TFP. Our baseline model indicates that anthropogenic climate change has reduced global agricultural TFP by about 21% since 1961, a slowdown that is equivalent to losing the last 9 years of productivity growth. The effect is substantially more severe (a reduction of ~30-33%) in warmer regions such as Africa and Latin America and the Caribbean. We also find that global agriculture has grown more vulnerable to ongoing climate change.

The European Union Emission Trading Scheme is a carbon emission allowance trading system designed by Europe to achieve emission reduction targets. The amount of carbon emission caused by production activities is closely related to the socio-economic environment. Therefore, from the perspective of economic policy uncertainty, this article constructs the GARCH-MIDAS-EUEPU and GARCH-MIDAS-GEPU models for the impact of European and global economic policy uncertainty on carbon price fluctuations. The results show that both European and global economic policy uncertainty will exacerbate the volatility of carbon price returns, with the latter having a stronger impact. Moreover, the volatility of carbon price returns can be forecasted better with the predictor of global economic policy uncertainty. This research can provide some implications for market managers in grasping market trends and helping participants control the risk of fluctuations in carbon allowances.