Modeling, Simulation, and Applications of Fractional Partial Differential Equations

The Black-Scholes model is commonly used to track the price of European options with respect to maturity in many financial markets. This model degenerates into a partial differential equation that relates the European-style option price to the underlying price and time of expiry. Black-Scholes assumes that underlying prices satisfy a geometric Brownian motion. After the U.S. stock market crash of 1987, this assumption becomes inaccurate as it fails to represent the behavior of S&P 500 European vanilla option prices. Specifically, under the measure of moneyness, the volatility smirk does not flatten out and the resulting conditional return distribution does not converge to normality. Recent academic literature have proposed readjusted financial models to account for the shortcomings of Black-Scholes, none which successfully have combined infinite return moments and finite price moments. To reduce the effects of these consequences and to incorporate the additional moment conditions, we assume that the underlying satisfy a Levy −stable motion. Under this assumption, we will derive the Finite Moment Log Stable (FMLS) model and its respective fractional partial differential equation counterpart. Then, we will solve the Black-Scholes equation under FMLS by using the standard finite difference method and a finite volume scheme that significantly reduces the computational and storage cost in comparison. Lastly, we will perform a numerical simulation of our methods by using recent financial data in the S&P 500 market acquired within a one-year time frame to compare the performance of these methods

The Relation Between Corporate Social Responsibility Disclosure and Financial Performance: Evidence from the Commercial Banking Industry

The purpose of this paper is to extend previous research on the relationship between corporate social responsibility disclosure and financial performance. Increase level of CSR disclosure can improve a firm‘s credibility but it can also incur extra cost and reduce firm‘s profit. The unique contribution of this study is the empirical analysis of this relation on a sample of international commercial banks, supplemented by ranking and deciles comparisons. Our findings show that no definitive relationship exists, neither positive nor negative, between CSR disclosure and financial performance in commercial banks

Gamma Rays from Ultra-High Energy Cosmic Rays in Cygnus A

Ultra-high energy cosmic rays (UHECRs) accelerated in the jets of active galactic nuclei can accumulate in high magnetic field, ~100 kpc-scale regions surrounding powerful radio galaxies. Photohadronic processes involving UHECRs and photons of the extragalactic background light make ultra-relativistic electrons and positrons that initiate electromagnetic cascades, leading to the production of a gamma-ray synchrotron halo. We calculate the halo emission in the case of Cygnus A and show that it should be detectable with the Fermi Gamma ray Space Telescope and possibly detectable with ground-based gamma-ray telescopes if radio galaxies are the sources of UHECRs.Comment: 9 pages, 2 figures, extended calculations, added references; ApJL, in pres

Media And Information Literacy Curriculum For Teachers

Fulltext in: http://unesdoc.unesco.org/images/0019/001929/192971e.pd