Homework #1, ORF 505
Assigned on Sept 20; Due Sept 27, 2016
1. Consider n realizations, x1 , x2 , , xn of the uniform distributed random variable X
Unif(a, b).
(i) Show that E[X] =
a+b
2 ,
E[X 2 ] =
a2 +ab+b2
.
3
(ii) Use the Method of Moments to estimat
ECO 465/FIN 522 - Assignment 3 Solutions
Christian Wolf
Question 1
Lets start by computing the corresponding instantaneous rates. We have
erBrazil = 1.22
which gives
rBrazil = 0.1989
and
erU S = 1.02
which gives
rU S = 0.0198
Lets now compute the swap pay
FIN / ORF 505
Thursday October 9, 2014
FIRST MIDTERM
Closed book, and anything with a switch ON/OFF should be turned OFF!
No unjustified answer will be given credit, even if the answer is correct.
The problems are (and some of the questions within the
Homework #5, ORF 505
Assigned on October 18; Due October 25, 2016
1. Let us assume that X1 and X2 are two positive random variables which we assume to be
independent and having the same distribution.
(i) Say why the expectation
E
n
X1 o
X1 + X2
exists.
(i
Homework #6, ORF 505
Assigned on November 8; Due November 15, 2016
1. The centroid of data (x1 , y1 ), (x2 , y2 ), (xn , yn ) is the point (
x, y) with coordinates given
by
m
m
1X
1X
xj ,
y =
yj .
x
=
n
n
j=1
j=1
In this problem we shall perform an orthog
Springer Texts in Statistics
Ren Carmona
Statistical
Analysis of
Financial Data
in R
Second Edition
Springer Texts in Statistics
Series Editors:
G. Casella
R. DeVeaux
S.E. Fienberg
I. Olkin
For further volumes:
http:/www.springer.com/series/417
Rene Carmo
Homework #3, ORF 505
Assigned on October 4; Due October 11, 2016
1. Consider the Gumbel distribution with parameters m and :
F (x) = Gm,=0 (x) = exp[e
xm
],
x R.
(i) Find the formula for the quantile function Q(p) = F 1 (p).
(ii) Write the R function that
Homework #2, ORF 505
Assigned on Sept 27; Due October 4, 2016
1. (i) Use the R command rnorm to simulate n = 10, 000 samples for two standard normal
random variables X and Y . Construct the vector Z = X 2 + Y 2 , draw its histogram
and its kernel density
PRINCETON UNIVERSITY
BENDHEIM CENTER FOR FINANCE
Professor Wei Xiong
Fall
2016
ECO 465/FIN 522
Assignment 2 (Due on Oct 6)
1. Suppose the current value of the S&P 500 index is 1000, the future value of the dividends
over the next six months will be $20 an