FINE ART, IMAGINATION, AND LITERACY

Farshid Maghami Asl

Description

• mémoire
• expression écrite - matière potentielle : children
• cours - matière potentielle : today
• expression écrite
• cours - matière potentielle : curriculums

FINE ART, IMAGINATION, AND LITERACY Catherine Read, Simon Fraser University ABSTRACT Participation in various parallel forms of expression that integrate art, imagination, and language create a solid foundation for excellence in literacy. Fine art is a language and a means of expression in itself, and many parallels exist between the developmental processes of creating art and writing. Participation in the arts can provide students with the opportunity to exercise and expand their imaginations, which ultimately provides valuable experiences that are transferable into reading and writing skills.

• literary capabilities
• development of creativity
• drawings
• things
• brain
• art
• visual arts
• children
• skills
• language

Sujets

• Mémoire
• Children
• Steele
• Fine art
• Sheridan
• Greene
• Éducation

Informations

• Publié par: mevang
• Nombre de lectures: 19
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Lecture 1. 1
Financial Econometrics and Statistical
Arbitrage
Master of Science Program in Mathematical Finance
New York University
Lecture 1: Basics on Time Series Analysis
Fall 2005
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
Lecture 1. 2Administrative Details
• Instructors: Farshid Maghami ASL and Lee Maclin
• Email: [e-mail]
•Course Web sites:
– Blackboard
– http://homepages.nyu.edu/~fma1
• Teaching Assistant: Junyoep Park
• Email: [e-mail]
• Office Hours: Mondays 5-7 pm
• Office Location: WWH 606
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
1Lecture 1. 3Administrative Details (cont.)
Time: Mondays, 7:10 – 9 pm
First Class: September 12, 2005, Last Class: December 12, 2005. There will be no class on
Columbus Day (October 10, 2005). We will make it up on Wednesday 11/23/05.
Homework and Exam:
• There will be six homework sets which will be assigned every other week.
Students must write up and turn in their solutions individually within one week.
• Computer assignments can be solved by C/C++/C#, MATLAB, R. For other tools,
please coordinate with the TA or the instructor.
• There will be one final exam (no mid-term).
• Final grade will be evaluated based on homework solutions (30%) and the final
exam (70%).
• Lecture Notes and Homework will be posted on the course website as they
become available
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
Lecture 1. 4Administrative Details (cont.)
Textbooks: Lectures are drawn from many sources including the
following books:
1. Alexander, C. “Market Models,” John Wiley and Sons, 2001
2. Brockwell, P.J., Davis, R.A., “Introduction to Time Series and
Forecasting,” Springer
3. Javaheri, A. “Inside Volatility Arbitrage : The Secrets of Skewness”
Wiley
4. Tsay, R. S., “Analysis of Financial Time Series,” Wiley, 2002
5. Wilmott, P. “Derivatives: The Theory and Practice of Financial
Engineering,” Wiley Frontiers in Finance Series
6. Pandit S.M., Wu S.M., “Time Series and System Analysis with
Applications.” Krieger Publishing, Malabar, FL, 2001
7. Hamilton J. D. “Time Series Analysis.” Princeton University Press, 1994
A number of research articles will be posted on the course webpage.
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
2Lecture 1. 5Expected Background
• Prior knowledge of Linear Algebra, Probability and
Statistics is required
• I assume you have taken the following courses:
– Derivative Securities
– Continuous Time Finance
– Scientific Computing / Computing for Finance
• Programming in C/C++ or MATLAB/R is required
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
Lecture 1. 6What is Statistical Arbitrage?
• Arbitrage is a riskless profit. “Arbitrage Strategy” is a
trading strategy that locks in a riskless profit.
Strategies and Implementation Process
(Cointegration based pairs trading, Volatility trading, …)
Financial Econometrics
(Time Series Review and Volatility modeling)
• Statistical Arbitrage covers any trading strategy which
uses statistical tools and time series analysis to identify
approximate arbitrage opportunities while evaluating the
risks inherent in the trades considering the transaction
costs and other practical aspects.
Market Microstructur Theory
(Transaction costs and Optimal Control, Algorithmic Trading,…)
Risk Management
(Practical Risk Measurement and Management Technics)
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
3Lecture 1. 7Course Outline
• Financial Econometrics (8 weeks)
– Time Series Models Review and Analysis
– Volatility and Correlation Models in Financial Systems
– Calibration and Estimation Methods
• Cointegration and Market Microstructure in Practice (3 weeks)
– C and Pairs Trading
– Transaction Costs, and Market Friction
– Trade Execution Strategies
• Practical Simulation and Risk Management (1 week)
• More on Trading Strategies (1-2 week)
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
Lecture 1. 8Typical Behavior of Financial Assets
12000
10000
8000
6000
4000
2000
0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Time in days from 1/1/1975 to 07/30/2005
• The unpredictability inherent in asset prices is the main feature of financial
modeling.
• Because there is so much randomness, any mathematical model of a financial
asset must acknowledge the randomness and have a probabilistic foundation.
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
4
Dow Jones IndexLecture 1. 9Introduction to Financial Modeling
• There are three general types of analysis used in finance and trading
1. Fundamental Analysis
2. Technical Analysis
3. Quantitative Analysis
• Return in financial assets
By return we mean the percentage growth in the value of an asset,
together with accumulated dividends, over some period:
+ accumulated cashflowsChange in value of the asset
Return =
Original value of the asset
• Denoting the asset value on the i-th day by Si, the return from day i
to day i+1 is given by
S − Si+1 iR =i
Si
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
Lecture 1. 10Introduction to Financial Modeling
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Time in days from 1/1/1975 to 07/30/2005
• Supposing that we believe that the empirical returns are close enough to
Normal for this to be a good approximation.
• For start, we write the returns as a random variable drawn from a Normal
distribution with a known, constant, non-zero mean and a known, constant,
1 2− φ1non-zero standard deviation: 2N (0,1) = e
2π
S − Si+1 iR = = mean + standard deviation x φi
Si
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
5
Difference of the Log Trans form of Dow Jones IndexLecture 1. 11Introduction to Financial Modeling
S − Si+1 iR = = mean + standard deviation x φi
Si
• Time scale δt
Mean return over Standard deviation over
period δt is period δt is
1/ 2µδt σδt
S − Si+1 i 1/ 2R = = µδt +σδt ×φi
Si δX
And in the limit δt 0
dStR = = µdt +σdX t
St
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
Lecture 1. 12Basic Review
STOCHASTIC PROCESS:
A stochastic process is a collection of random variables {X (ω), t ∈τ } defined on a t
probability space (Ω , F , P ).
ωFor a fixed , a realization of stochastic process is a function of time (t).
4
x 10
1.3
1.2
1.1
1
ω 0.9State 5
5
State 4
4
100State 3
3 80
State 2 60
2 40
20State 1
1 0Ω
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
6
Time
TimeLecture 1. 13Simulation of a Stochastic Process
4
x 10
1.6
1.4
1.2
1
0.8
0.6
200
150 100
80100
60
50 40
20
0 0
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
Lecture 1. 14Definition
Time Series:
A time series is a stochastic process where τ is a set of discrete points in
time. In other words, it is a discrete time, continuous state process.
In this course we consider τ = { all integers}
3
Xk
2
1
0
-1
-2
X1 X2 X3 …
-3
-4
0 5 10 15 20 25 30 35 40
k
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
7Lecture 1. 15Goals of Studying Time Series
1- Forecasting
We want to forecast distributions
12000
10000
8000
6000
4000
2000
0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Time in days from 1/1/1975 to 07/30/2005
2- Understanding the statistical characteristics and building
trading strategies based on them
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
Lecture 1. 16Basic Review
An Example of a Time Series:
10
Xk 8
6
4
2
0
-2
-4
-6
-8
k
-1 0
0 1000 200 0 30 00 4 000 5000 6000 7000
10 10 10 10
8 8 8 8Xk
6 6 Xk 6 Xk
6 Xk
4 4 4 4
2 2 2 2
0 0
0 0
-2 -2 -2 -2
-4 -4 -4 -4
-6
-6 -6 -6
-8 -8 -8
-8Xk-1 Xk-2 Xk-3 Xk-10
-10 -10 -10
-10 -8 -6 -4 -2 0 2 4 6 8 10 -10
-10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10
Auto-Regression as a Dynamic System?Xk= ϕ 1 Xk-1+ ϕ 2 Xk-2+…+ek We will get back to this
Farshid Magami Asl G63.2707 - Financial Econometrics and Statistical Arbitrage
8
Dow Jones IndexLecture 1. 17Definition
Autocovariance Function:
Let {Xt} be a time series. The autocovariance function of process {Xt} for all
integers r and s is:
γ (r, s) = cov(X , X )X r s
γ (r, s) = E[(X − E(X ))(X − E(X ))]
X r r s s
γ (r, s) = E[X X − X E(X ) − X E(X ) + E(X )E(X )]X r s r s s r r s
γ (r,s) = E(X X ) − E(X )E(X ) − E(X )E(X ) + E(X