This presentation explores the left-tail of daily stock returns since 1950. It investigates whether the Cauchy distribution is an appropriate one to fit this tail as suggested by Benoit Mandelbrot. It also investigates the consequences of using the Normal distribution within a Value-at-Risk type model.
How the Option Market deal with Fat Tail? Gaetan Lion
This is an investigation on how the Option Market deal with the Fat Tail issue. This analysis is focused on Put options on the S&P 500 index with a term around 9 to 12 months.
Theoretical probability distributions: Binomial, Poisson,
Normal and Exponential and also includes, discrete probability distributions, continuous probability distribution, random variables, sample problems
This presentation explores the left-tail of daily stock returns since 1950. It investigates whether the Cauchy distribution is an appropriate one to fit this tail as suggested by Benoit Mandelbrot. It also investigates the consequences of using the Normal distribution within a Value-at-Risk type model.
How the Option Market deal with Fat Tail? Gaetan Lion
This is an investigation on how the Option Market deal with the Fat Tail issue. This analysis is focused on Put options on the S&P 500 index with a term around 9 to 12 months.
Theoretical probability distributions: Binomial, Poisson,
Normal and Exponential and also includes, discrete probability distributions, continuous probability distribution, random variables, sample problems
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A paper by Thomas J. Linsmeier and Neil D. Pearson. This paper is a self-contained introduction to the concept and methodology of “value at risk”. It explains the concept of
value at risk, and then describes in detail the three methods for computing it: historical simulation;
the variance-covariance method; and Monte Carlo or stochastic simulation. It also discusses the
advantages and disadvantages of the three methods for computing value at risk.
This discusses the topics under Estimating Market Risk Measures: An introduction and Overview by Kevin Dowd
It is part of the FRM Part 2 curriculum under the Market Risk section.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
A paper by Thomas J. Linsmeier and Neil D. Pearson. This paper is a self-contained introduction to the concept and methodology of “value at risk”. It explains the concept of
value at risk, and then describes in detail the three methods for computing it: historical simulation;
the variance-covariance method; and Monte Carlo or stochastic simulation. It also discusses the
advantages and disadvantages of the three methods for computing value at risk.
This discusses the topics under Estimating Market Risk Measures: An introduction and Overview by Kevin Dowd
It is part of the FRM Part 2 curriculum under the Market Risk section.
In this slide, variables types, probability theory behind the algorithms and its uses including distribution is explained. Also theorems like bayes theorem is also explained.
My presentation from the recent RIMS Atlanta Educational Conference. The slides cover the most common biases we naturally inject into strategic decision making and risk assessment. In some cases awareness alone will serve as mitigation but the slides cover some direct response tactics as well.
A General Manger of Harley-Davidson has to decide on the size of a.docxevonnehoggarth79783
A General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed the choices to two: large facility or small facility. The company has collected information on the payoffs. It now has to decide which option is the best using probability analysis, the decision tree model, and expected monetary value.
Options:
Facility
Demand Options
Probability
Actions
Expected Payoffs
Large
Low Demand
0.4
Do Nothing
($10)
Low Demand
0.4
Reduce Prices
$50
High Demand
0.6
$70
Small
Low Demand
0.4
$40
High Demand
0.6
Do Nothing
$40
High Demand
0.6
Overtime
$50
High Demand
0.6
Expand
$55
Determination of chance probability and respective payoffs:
Build Small:
Low Demand
0.4($40)=$16
High Demand
0.6($55)=$33
Build Large:
Low Demand
0.4($50)=$20
High Demand
0.6($70)=$42
Determination of Expected Value of each alternative
Build Small: $16+$33=$49
Build Large: $20+$42=$62
Click here for the Statistical Terms review sheet.
Submit your conclusion in a Word document to the M4: Assignment 2 Dropbox byWednesday, November 18, 2015.
A General Manger of Harley
-
Davidson has to decide on the size of a new facility. The GM has narrowed
the choices to two: large facility or small facility. The company has collected information on the payoffs. It
now has to decide which option is the best u
sing probability analysis, the decision tree model, and
expected monetary value.
Options:
Facility
Demand
Options
Probability
Actions
Expected
Payoffs
Large
Low Demand
0.4
Do Nothing
($10)
Low Demand
0.4
Reduce Prices
$50
High Demand
0.6
$70
Small
Low Demand
0.4
$40
High Demand
0.6
Do Nothing
$40
High Demand
0.6
Overtime
$50
High Demand
0.6
Expand
$55
A General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed
the choices to two: large facility or small facility. The company has collected information on the payoffs. It
now has to decide which option is the best using probability analysis, the decision tree model, and
expected monetary value.
Options:
Facility
Demand
Options
Probability Actions
Expected
Payoffs
Large Low Demand 0.4 Do Nothing ($10)
Low Demand 0.4 Reduce Prices $50
High Demand 0.6
$70
Small Low Demand 0.4
$40
High Demand 0.6 Do Nothing $40
High Demand 0.6 Overtime $50
High Demand 0.6 Expand $55
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a .
PAGE 1 Chapter 5 Normal Probability Distributions .docxgerardkortney
PAGE 1
Chapter 5: Normal Probability Distributions
Section 5.1: Intro to Normal Distributions and the Standard Normal Distributions
Objectives:
Normal Distribution Properties
Use z-scores to Calculate Area Under the Standard Normal Curve (using StatCrunch or Calculator)
Discuss Unusual Values
In this section we will revisit histograms which can be estimated with normal (symmetric, bell-shaped) curves. From
Test 1 remember that normal curves have z-scores (for any data value) and areas under the curve (one way: Empirical
Rule). Now we will use these normal curves to find probabilities (areas) and z-scores for any data value. Why do we
need to study this? Eventually we will use these probabilities and z-scores to make decisions.
By using the normal distribution curve, we are treating the data as a continuous random variable that has its own
continuous probability distribution. (Remember that any probability distribution has two properties: all probabilities
are between 0 and 1 and the sum of the probabilities is 1.) **Probabilities = Areas under the curve**
Ex: Consider the normal distribution curves below. Which normal curve has the greatest mean? Which normal curve has
the greatest standard deviation?
Note: Every normal distribution can be transformed into the Standard Normal Distribution (the distribution for z-
scores). This means we will use the z-score formula to transform any data value into a “measure of position” with the
formula:
data value mean
standard deviation
z
PAGE 2
**All probability calculations will be done with either StatCrunch or the TI 83/84 calculator. You do NOT need to learn
how to read the Standard Normal Table.**
**Also < and are treated the same as well as > and for any continuous probability distribution.**
Ex: Confirm that the area to the left of z = 1.15 is 0.8749. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, enter inequality symbol and z-score, Compute
TI-83/84: 2nd VARS normalcdf( -1000000000 Comma 1.15 Comma 0 Comma 1 enter
P(z 1.15) = 0.8749
Ex: Confirm that the cumulative area that corresponds to z = -0.24 is 0.4052. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, Standard, enter inequality symbol and z-score, Compute
TI-83/84: 2nd VARS normalcdf( -1000000000 Comma -0.24 Comma 0 Comma 1 enter
P(z -0.24) = 0.4052
PAGE 3
Ex: Find the area to right of each z-score. Hint: Use the fact that the total area (probability) is 1. **Label the z-score and
the area.**
a) b)
P(z 1.15) = _________________ P(z -0.24) = _________________
Ex: Find the shaded area. **Label the z-score and the area.**
StatCrunch: Stat menu, Calculators, Normal, Stand.
Types of Probability Distributions - Statistics IIRupak Roy
Get to know in detail the definitions of the types of probability distributions from binomial, poison, hypergeometric, negative binomial to continuous distribution like t-distribution and much more.
Let me know if anything is required. Ping me at google #bobrupakroy