In this paper we discuss how to price American, European and Asian options using a geometric Brownian motion model for stock price. We investigate the analytic solution for Black-Scholes differential equation for European options and consider numerical methods for approximating the price of other types of options. These numerical methods include Monte Carlo, binomial trees, trinomial trees and finite difference methods. We conclude our discussion with an investigation of how these methods perform with respect to the changes in different Greeks. Further analysing how the value of a certain Greeks affect the price of a given option.
A survey from the perspective of a 25 year High School Science teacher on how Calculus is relevant to the high school science classroom, supported by CCSSM and NGSS.
📖 The classic and complete guide written in Traditional Chinese to help you get started on your journey with LaTeX: 《大家來學 LaTeX》.
此倉庫託管著李果正(Edward G.J. Lee)先生於 2004 年接受中華民國行政院研考會委辦的「政府機關資料文件交換之電子檔案格式應用研究」計畫補助所撰寫的《大家來學 LaTeX》原始程式代碼。
https://github.com/TeX-tw/LaTeX123/tree/legacy
GNU Free Documentation License version 1.2
As LED systems have been evolving today in a
great number of niche applications including
automotive lighting, water purification, and skin
imaging etc., extensive studies of scientists and
engineers in the field have been constantly
looking for ways to reduce generated heat loads
and maximize the light output to reach the highest
efficiency ratios. While the current systems
developed over the last years achieved to reach
even a 40% LED light efficiency, a higher portion
of the electrical input energy of LEDs is still
produced as heat and it hinders their development
potential. In addition, the compact size of the LED
systems poses some challenges to the reliable
characterization of their performance at low
uncertainties. Especially, the performance
considerations associated with thermal loads over
a limited size of LED chips require the effective
characterization of these systems for various
operational conditions. One of the techniques
used for this purpose is that an LED package is
characterized by a decrease in forward voltage
with increasing junction temperature. As LEDs are
operated at higher junction temperatures, the
amount and quality of the light deteriorates
significantly, and the less efficient use of the LEDs
results in additional operating costs and reduced
lifetime of LEDs. In fact, accurate identification of
thermal behavior of LED packages is one of the
essential tasks towards improving the design of
LED systems. If thermal characterization of LEDs
is accurately done, performance parameters of
LED packages are more reliably optimized to yield
the highest possible performance ratios. Thus,
this study focused on the design and
manufacturing of a thermally improved and fully
operational rapid temperature controllable
chamber in which calibration and test phases of
junction temperature measurements are
sensitively conducted under a low uncertainty.
Mete Muslu
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