Potential barrier of Graphene edges

We calculated row resolved density of states, charge distribution and work function of graphene's zigzag and armchair edge (either clean or terminated alternatively with H, O or OH group). The zigzag edge saturated via OH group has the lowest work function of 3.76 eV, while the zigzag edge terminated via O has the highest work function of 7.74 eV. The angle-dependent potential barrier on the edge is fitted to a multi-pole model and is explained by the charge distribution.Comment: 16 pages, 8 figures. Copyright (2011) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. This article appeared in (J. Appl. Phys. 109 (2011) 114308) and may be found at (http://link.aip.org/link/?JAP/109/114308

Statistical Analysis of Short-time Option Prices Based on a Levy Model

The Black-Scholes model has been widely used to find the prices of option, while several generalizations have been made due to its limitation. In this thesis, we consider one of the generalizations---the exponential Levy model with a mixture of CGMY process and Brownian motion. We state the main results of the first-, second- and third-order expansions for close-to-the-money call option prices under this model. Using importance sampling based on Monte Carlo method, a dataset of call option prices can be simulated. Comparing the simulated true prices with the three different order approximations, we find that the higher-order approximation is more accurate than the lower-order in most cases, which can be used for calibrating the parameters in the model. In order to verify these results, we use call option prices obtained from the Standard & Poor\u27s 500 index options. The third-order approximation of this real dataset is not as accurate as before