Review of modern numerical methods for a simple vanilla option pricing problem

Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better

The utilization of coffee waste into fired clay brick

The rapid growth of coffee industry is accompanied by a staggering increase in the amount of agriculture waste produced. In coffee producing countries, coffee wastes constitute a source of severe contamination and a serious environmental problem. In this study, the investigation on the possibility to utilize the coffee waste (CW) incorporated into the fired clay brick was carried out. The main purpose of this study is to determine the physical, mechanical properties and leach ability test of bricks incorporated with different percentages of CW. In this methodology, control brick (CB) and three different percentages of coffee waste brick (CWB) (1%, 3% and 5%) were manufactured and fired at 1050 °C. Physical and mechanical properties including shrinkage, density and compressive strength were reported and discussed. Additionally, leaching of heavy metals from manufactured clay brick was tested by using Toxicity Characteristics Leaching Procedure (TCLP). The results reported that with the incorporation of CW, the shrinkage increased linearly but still comply with minimum standard below 8% and good quality of brick was manufactured. Meanwhile, the results showed that density value decreased up to 30% from the normal brick with increased percentages of CW. The decreased compressive strength value of all the manufactured brick is still complies with minimum standard. On the other hand, heavy metals concentration leach out from different percentages of coffee waste brick is not exceeding the limit of 5 mg/L allowed by United States Environmental Protection Agency (USEPA). As a conclusion, the incorporation of CW into fired clay brick gives some advantages to the brick properties and also provides alternative solution on disposing the CW. In addition, the CW could also be a potential of low cost waste additive for the production of a brick

The Phase Diagram of Scalar Field Theory on the Fuzzy Disc

Using a recently developed bootstrapping method, we compute the phase diagram of scalar field theory on the fuzzy disc with quartic even potential. We find three distinct phases with second and third order phase transitions between them. In particular, we find that the second order phase transition happens approximately at a fixed ratio of the two coupling constants defining the potential. We compute this ratio analytically in the limit of large coupling constants. Our results qualitatively agree with previously obtained numerical results.Comment: 1+17 pages, v2: typos fixed, published versio

Time-delayed models of gene regulatory networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternativemodelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems