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Prob & Stat for Engineers

by: Danny Conn

Prob & Stat for Engineers STAT 3128

Danny Conn
GPA 3.64

Zongwu Cai

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Zongwu Cai
Class Notes
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This 4 page Class Notes was uploaded by Danny Conn on Sunday October 25, 2015. The Class Notes belongs to STAT 3128 at University of North Carolina - Charlotte taught by Zongwu Cai in Fall. Since its upload, it has received 29 views. For similar materials see /class/229023/stat-3128-university-of-north-carolina-charlotte in Statistics at University of North Carolina - Charlotte.


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Date Created: 10/25/15
Rmetrics An Environment for Teaching Financial Engineering and Computational Finance R Rmetrics Built 20110059 Diethelm Wu39rtz Institute for Theoretical Physics Swiss Federal Institute of Technology ET H Zu39rich Rmetrics is a collection of several hundreds of functions which may be useful for teaching quotFinancial Engineeringquot and quotComputational Finance This R port was initiated 1999 as an outcome of my lectures held on topics in econophysics at ET H Zu39rich The family of the Rmetrics packages includes currently six members dealing with the following subjects fBusics Markets Basic Statistics Date and Time fSeries The Dynamical Process Behind Financial Markets llultivur Multivariate Data Analysis fEn remes Beyond the Sample Dealing with Extreme Values f0pti0ns 7 The Valuation of Options and fPory olio Portfolio Selection and Optimization fBasics The package fBasics covers the manage ment of economic and nancial market data Included are functions to download eco nomic indicators and financial market data from the Internet Distribution functions relevant in nance are added like the asym metric stable the hyperbolic and the inverse normal gaussian distribution function to compute densities probabilities quantiles and random deviates Estimators to t the distributional parameters are also available Some additional hypothesis tests for the A A A 0 J and other stylized facts of nancial time series can also be found in this package Furthermore for date and time management a holiday database for all ecclesiastical and public holidays in the G7 countries and Switzerland is provided together with a data base of daylight saving times for nancial centers around the world Special calendar management functions were implemented to create easily business calendars for ex changes A collection of functions for ltering and outlier detection of high fre quency foreign exchange data records collected from Reuters data feed can also be found together with functions for de volatilization and deseasonalization of the data A S4 quottimeDatequot class is included for managing date and time around the globe for any nancial center The concept allows for dealing with time zones day light saving time and holiday calendars independent of the date and time specifications of the ope rating system implemented on your com puter This is an important issue especially for R running under Microsoft39s Windows operating system The time zone concept is replaced by the quotFinancial Centerquot concept The nancial center speci es where you are living and working With the speci cation of the nancial center the system knows what rules for day light saving times should be applied or what is your holiday calendar So one can distinguish between Frankfurt and Zurich which both belong to the same time zone but differed in DST changes in the eighties and have different holiday calendars Another important feature is the fact that Rmetrics uses internally the ISO 8601 standard for date and time notations The S4 quottimeSeriesquot class manages regular and irregular time series objects Dates and times are implemented as quottimeDatequot ob jects Included are functions and methods for the generation representation and mathe matical manipulation of time series objects Series This package covers topics from the eld of nancial time series analysis including A G CH long memory modelling and chaotic time series analysis This libra ry tries to bring together the content of existing Rpackages with additional new functionality on a common platform The collection comes with functions for simu lations parameter estimation diagnostic analysis and hypothesis testing of nancial time series The tests include methods for testing unit roots independence normality of the distribution trend stationary and neglected nonlinearities In addition func tions for testing for higher serial corre lations for heteroskedasticity for autocor relations of disturbances for linearity and functional relations are provided Further more distribution functions for GARCH modelling like the normalized Studentt and the GED together with their skewed versions have been added which require for their computation Heaviside and related func tions The demonstration directory includes also a R interface for the GarchOx software package fMultivar This library deals mainly with multivariate aspects of time series analysis Offered are algorithms for regression analysis including neural network modelling with feedforward networks Furthermore functions for sytem equation modelling are available Technical analysis and benchmarking is another major issue of this package The collection offers a set of the most common technical indicators together with functions for charting and benchmark measurements For the technical analysis of markets several trading func tions are implemented and also tools are availalble for a rolling market analysis A matrix addon with many functions which allow an easy use of matrix manipulations is also part of this package This addon includes functions to generate several kind of standard matrixes to extract subsets of a matrix and some function from linear alge bra This matrix addon is thought to be used to manipulate easily the data of multivariate time series objects fExtremes This package covers topics from the eld what is known as extreme value theory The package has functions for the exploratory data analysis of extreme values in insurance economics and nance applications In cluded are plot functions for empirical distri butions quantile plots graphs exploring the properties of exceedences over a threshold plots for meansum ratio and for the development of records Furthermore func tions for preprocessing data for extreme value analysis are available offering tools to separate data beyond a threshold value to compute blockwise data like block maxima and to decluster point process data One major aspect of this package is to brin together the content of the already existing Rpackages evir and ismev with additional new functionality for nancial engineers on a common platform investigating uctu ations of maxima extremes via point pro cesses and the extremal index Options This package covers the valuation of options including topics like the basics of option pricing in the framework of Black and Scholes including almost 100 functions for exotic options pricing including the Heston Nandi option pricing approach mastering stochastic volatility and Monte Carlo simu lations together with generators for low discrepancy sequences Beside the Black and Scholes option pricing formulas func tions to valuate other plain vanilla options on commodities and futures and function to approximate American options are available Some binomial tree models are also imple mented The exotic options part comes with a large number of functions to valuate mul tiple exercise options multiple asset options lookback options barrier options binary op tions Asian options and currency translated options Parts for a new additional chapter on exponential Brownian motion including functions dealing with moment matching methods PDE solvers Laplace inversion methods and spectral expansion approaches for option are already present They include additional distribution functions moment statistics and specical mathematical func tions like the gamma and the con uent hy pergeometric functions fPortfolio This library has just been started The topics cover multivariate distributions assets modelling drawdown statistics valueat risk modelling Markowitz portfolios two assets The multivariate distribution func tions allow to compute multivariate densities and probabilities from skew normal and skew Studentt distribution functions Furthermore multivariate random daviates can be generated and for multivariate data the parameters of the underlying distribution can be estimated by the maximum log likelihood estimation The functions for assets modelling can be used togenerate multivariate art cial data sets of assets which t the parameters to a multivariate normal skew normal or skew Studentt distribution Included in the library are also functions to compute some benchmark sta tistics In addition a function is provided which allows for the selection and clustering of individual assets from portfolios using hierarchical and kmeans clustering approa ches Tools are provided to evaluate dtaw down statistics Availalble are functions for the density distribution function and random number generation for the maxi mum drawdown distribution In addition the expectation of drawdowns for Brownian motion can be computed ValueatRisk Modelling is another topic which is consider in this library ValueatRisk and related risk measures for a portfolio of assets can be evaluated A group of functions is dedicated to the Markowitz portfolio optimization problem Functions for the computation of the efficient frontier for the market line for the tangency portfolio and for Monte Carlo simulations are part of the library Analytical formulas for the Markowitz and for the Condition VaR Portfolio approach are implemented Outlook A further packages is under current The library fBonds is just at the beginning and deals with bond arithmetic with yield curve modelling with interest rate instruments and with replicating portfolios Summary Rmetrics is a collection of R functions having its source in algorithms and functions written by many authors The aim is to bring the software together under a common plat form and to make it public available for teaching nancial engineering and compu tational nance The packages are docu mented in User Guides and Reference Guides currently about 800 pages The most recent source packages of Rmetrics and the compiled Windows bi naries can be obtained from the Rmetrics Server The reason is that I develop Rmetrics under MS Windows XP since in the nancial community Windows is the mostly used operating system Stable source packages for Linux and binaries for Mac OSX and MS Windows are downloadable from the CRAN Server In addition Debian packages for Rmetrics are also available and they are part of the KnoppiX Qantian CD Acknowledgement Many thanks to the members of the R development team for their support and continuous help to all the authors who made their programs and Rpackages available under the GNU General Public License so that they could be used or included to Rmetrics and to Dirk Eddelbuettel for creating the Debian Packages and including Rmetrics to the Quantian CD References RCRAN Server cranrprojectorg Debian Server wwwdebianorg KnoppiX Server wwwknoppixorg Quantian Server www guantian org Rmetrics Server wwwrmetricsorg


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