A Numerical Method for Pricing Discrete Double Barrier Option by Legendre Multiwavelet

In this Article, a fast numerical numerical algorithm for pricing discrete double barrier option is presented. According to Black-Scholes model, the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution. These recursive solutions are approximated by using Legendre multiwavelets as orthonormal basis functions and expressed in operational matrix form. The most important feature of this method is that its CPU time is nearly invariant when monitoring dates increase. Besides, the rate of convergence of presented algorithm was obtained. The numerical results verify the validity and efficiency of the numerical method

Measuring Modularity in Open Source Code Bases

Modularity of an open source software code base has been associated with growth of the software development community, the incentives for voluntary code contribution, and a reduction in the number of users who take code without contributing back to the community. As a theoretical construct, modularity links OSS to other domains of research, including organization theory, the economics of industry structure, and new product development. However, measuring the modularity of an OSS design has proven difficult, especially for large and complex systems. In this article, we describe some preliminary results of recent research at Carleton University that examines the evolving modularity of large-scale software systems. We describe a measurement method and a new modularity metric for comparing code bases of different size, introduce an open source toolkit that implements this method and metric, and provide an analysis of the evolution of the Apache Tomcat application server as an illustrative example of the insights gained from this approach. Although these results are preliminary, they open the door to further cross-discipline research that quantitatively links the concerns of business managers, entrepreneurs, policy-makers, and open source software developers

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.In this paper we explore the numerical diffusion introduced by two nonstandard finite difference schemes applied to the Black-Scholes partial differential equation for pricing discontinuous payoff and low volatility options. Discontinuities in the initial conditions require applying nonstandard non-oscillating finite difference schemes such as the exponentially fitted finite difference schemes suggested by D. Duffy and the Crank-Nicolson variant scheme of Milev-Tagliani. We present a short survey of these two schemes, investigate the origin of the respective artificial numerical diffusion and demonstrate how it could be diminished