Distribution of Trading Activity across Strike Prices in the DAX Index Options Market

In this paper we propose and estimate an econometric model for the distribution of trading activity across options written on the DAX index. The model is based on the observation that in this market options with strike prices ending on 000, 200, 400, 600 and 800 (the class of 200-strike options) are more traded than options with strike prices ending on 100, 300, 500, 700 and 900 (the class of 100-strike contracts). We assume that market participants who would like to trade a continuum of contracts have to choose between the options listed by the exchange. When they have to choose between two neighboring 200- and 100-strike contracts, they prefer the 200-strike contract if the degree of substitution between these two options is high. We derive an equation which links the trading volumes of the 200- and 100-strike options and the degree of substitution between them. This equation has convenient analytical properties and can be readily estimated from the data. The estimation results confirm the hypothesised effect of the degree of substitution on the distribution of trading between 200- and 100-strike contracts. Additionally, we are able to derive some quantitative estimates of the percentage of trades attracted to the 200-strike contracts.Market Microstructure, Options Volume

Assesing the Economic Significance of the Intra-daily Volatility Seasonalities

It is a well established empirical fact that volatility follows approxi- mately an inverted U-shaped pattern during the day. It is high in the morning, gradually decreasing, reaching a minimum at lunch time and then starting to increase again until the end of the trading day. In this paper we investigate the dynamic properties of these intra-daily volatility seasonalities. More specifically, we divide daily volatility into several parts and model them separately. Our analysis shows that morning/afternoon volatility has a different time-series behaviour in comparison to lunch time volatility. Also, a substantial improvement in forecasting performance can be obtained by partitioning daily volatility into parts which correspond to the observed intra-daily seasonalities.

Macroeconomic analysis of trade in some CEE countries

The research in this paper is focus on macroeconomic analysis of trade and other relevant indicator for real economy such as government net debt, exchange rate, interest rate, and especially the correlation between trade and growth. Today is widely accepted that openness of counties have important role for economic performance, therefore the investigation of trade is challenge for economists of small developing countries. The mail goal in this paper is theoretical analysis of some macroeconomic indicator as a factor of growth and empirical investigation of trade in some CEE countries.Macroeconomics, CEE countries, trade, exchange rate, PPP, inflation

A Petrov-Galerkin Finite Element Method for Fractional Convection-Diffusion Equations

In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and both convection and potential terms. They arise in the mathematical modeling of asymmetric super-diffusion processes in heterogeneous media. The well-posedness of the formulations and sharp regularity pickup of the variational solutions are established. A novel finite element method is developed, which employs continuous piecewise linear finite elements and "shifted" fractional powers for the trial and test space, respectively. The new approach has a number of distinct features: It allows deriving optimal error estimates in both $L^2(D)$ and $H^1(D)$ norms; and on a uniform mesh, the stiffness matrix of the leading term is diagonal and the resulting linear system is well conditioned. Further, in the Riemann-Liouville case, an enriched FEM is proposed to improve the convergence. Extensive numerical results are presented to verify the theoretical analysis and robustness of the numerical scheme.Comment: 23 p

Honey Sheets: What Happens to Leaked Google Spreadsheets?

Cloud-based documents are inherently valuable, due to the volume and nature of sensitive personal and business content stored in them. Despite the importance of such documents to Internet users, there are still large gaps in the understanding of what cybercriminals do when they illicitly get access to them by for example compromising the account credentials they are associated with. In this paper, we present a system able to monitor user activity on Google spreadsheets. We populated 5 Google spreadsheets with fake bank account details and fake funds transfer links. Each spreadsheet was configured to report details of accesses and clicks on links back to us. To study how people interact with these spreadsheets in case they are leaked, we posted unique links pointing to the spreadsheets on a popular paste site. We then monitored activity in the accounts for 72 days, and observed 165 accesses in total. We were able to observe interesting modifications to these spreadsheets performed by illicit accesses. For instance, we observed deletion of some fake bank account information, in addition to insults and warnings that some visitors entered in some of the spreadsheets. Our preliminary results show that our system can be used to shed light on cybercriminal behavior with regards to leaked online documents

Some error estimates for the lumped mass finite element method for a parabolic problem

We study the spatially semidiscrete lumped mass method for the model homogeneous heat equation with homogeneous Dirichlet boundary conditions. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method whereas nonsmooth initial data estimates require special assumptions on the triangulation. We also discuss the application to time discretization by the backward Euler and Crank-Nicolson methods