COMPARING PRICE MOVEMENTS OF OPTIONS AND THE UNDERLYING INDEX

In theory, a call option and its underlying index should move in the same direction, while a put option and its underlying index should move in opposite directions. This property is referred to as the Empirical Monotonicity Property (EMP) when applied to time series of prices. In this paper, we use daily call and put options? data to conduct empirical tests of the EMP, including three violation types. Further, we investigate the effect of grouping the option prices by their Black-Scholes implied volatility and by moneyness, and also the effect of using different quotes (bid, offer, and bid-offer midpoint). In addition to EMP, which depends on the signs of the price changes, we also test another theoretical constraint concerning the magnitude of these changes. This is followed by a discussion of the possible causes for violations of the EMP. We use regression analysis to test whether volatility changes may be one of these causes. Lastly, we summarize the implications of our study to hedging strategies

TiO2: A Critical Interfacial Material for Incorporating Photosynthetic Protein Complexes and Plasmonic Nanoparticles into Biophotovoltaics

TiO2, a photosensitive semiconducting material, has been widely reported as a good photoanode material in dye-sensitized solar cells and new emerging perovskite cells. Its proper electronic band structure, surface chemistry and hydrophilic nature provide a reactive surface for interfacing with different organic and inorganic photon capturing materials in photovoltaics. Here, we review its enabling role in incorporating two special materials toward biophotovoltaics, including photosynthetic protein complexes extracted from plants and plasmonic nanoparticles (e.g., gold or silver nanoparticles), which interplay to enhance the absorption and utilization of sun light. We will first give a brief introduction to the TiO2 photoanode, including preparation, optical and electrochemical properties, and then summarize our recent research and other related literature on incorporating photosynthetic light harvest complexes and plasmonic nanoparticles onto anatase TiO2 photoanodes as a means to tap into the charge separation, electron and energy transfer, and photovoltaic enhancements in the bio-photovoltaics

A time-fractional optimal transport and mean-field planning: Formulation and algorithm

The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial density distribution to the terminal one with the minimal cost. We derive a strongly coupled nonlinear system of a time-fractional transport equation and a backward time-fractional Hamilton-Jacobi equation based on the first-order optimality condition. The general-proximal primal-dual hybrid gradient (G-prox PDHG) algorithm is applied to discretize the OT and MFP formulations, in which a preconditioner induced by the numerical approximation to the time-fractional PDE is derived to accelerate the convergence of the algorithm for both problems. Numerical experiments for OT and MFP problems between Gaussian distributions and between image densities are carried out to investigate the performance of the OT and MFP formulations. Those numerical experiments also demonstrate the effectiveness and flexibility of our proposed algorithm

Exploiting Label Skews in Federated Learning with Model Concatenation

Federated Learning (FL) has emerged as a promising solution to perform deep learning on different data owners without exchanging raw data. However, non-IID data has been a key challenge in FL, which could significantly degrade the accuracy of the final model. Among different non-IID types, label skews have been challenging and common in image classification and other tasks. Instead of averaging the local models in most previous studies, we propose FedConcat, a simple and effective approach that concatenates these local models as the base of the global model to effectively aggregate the local knowledge. To reduce the size of the global model, we adopt the clustering technique to group the clients by their label distributions and collaboratively train a model inside each cluster. We theoretically analyze the advantage of concatenation over averaging by analyzing the information bottleneck of deep neural networks. Experimental results demonstrate that FedConcat achieves significantly higher accuracy than previous state-of-the-art FL methods in various heterogeneous label skew distribution settings and meanwhile has lower communication costs. Our code is publicly available at https://github.com/sjtudyq/FedConcat