This paper examines a class of barrier options, multi-step which can have any finite number barriers level. We obtain general, explicit expression for option prices this type under the Black–Scholes model by deriving reflection principle, that is, boundary-crossing probability Brownian motion. Multi-step options are not only useful in they handle different levels and time steps but also approxi...

Two trials were conducted to study the effect of multi-steps phase-feeding (PF) program on growth performance of broiler chickens from 1 to 24 and 1 to 39 d of age. The control group was the nutrient recommendation of Aviagen (2019) with a three-step PF program (1-10, 11-24 and 25-39 d of age). In the first trial, the control group was compared with an eight-step PF program (PF8), and in the se...

I n this paper, we specify that the GARCH(1,1) model has strong forecasting volatility and its usage under the truncated standard normal distribution (TSND) is more suitable than when it is under the normal and student-t distributions. On the contrary, no comparison was tried between the forecasting performance of volatility of the daily return series using the multi-step ahead forec...

The detectability of planetesimal impacts on imaged exoplanets can be measured using Jupiter during the 1994 comet Shoemaker-Levy 9 events as a proxy. By integrating the whole planet flux with and without impact spots, the effect of the impacts at wavelengths from 2 4 μm is revealed. Jupiter’s reflected light spectrum in the near-infrared is dominated by its methane opacity including a deep ban...

In this paper, a new algorithm to solve the discrete logarithm problem is presented which is similar to the usual baby-step giant-step algorithm. Our algorithm exploits the order of the discrete logarithm in the multiplicative group of a finite field. Using randomization with parallelized collision search, our algorithm indicates some weakness in NIST curves over prime fields which are consider...