Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2015
Small project
Let matrix A Rnn . As A use the Vandermonde matrix, V (dened as
Vi,j = xnj , i, j = 1, ., n), xi [0, 1] equidistantly distributed.
i
Note: use Matlab commands V=vander(x), where x=linspace(0,1,n).
1. Find how its condition number (V ) depend
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2015
Warmup Homework: Vectorization
Generate the vector y = sin(x2 ) for x [0, ] in three ways:
a) sequential, using a forloop, for example:
h = /n; f or i = 0 : h : , y(i) = sin(i); end
b) the same as in a) preceded by the initialization of y, i.e. setting
y
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2015
Project 1 Mathematics 512
Instructor: Ricardo Mancera
Spring 2016
Due date: Friday, Jan 22
1.
a) Use the random number generator
generate 10000 uniformly distributed random numbers on
with
and plot the histogram.
b) Generate 10000 uniformly distributed di
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2015
Project 2 Mathematics 512
Instructor: Ricardo Mancera
Spring 2015
Due date: Wed, Feb 04
1.
Let
matrix
be a Gaussian random vector having the following mean
:
and variancecovariance
a) Using the Cholesky decomposition of the variancecovariance matrix and
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2015
Project 6 Mathematics 512
Instructor: Ricardo Mancera
Spring 2015
Due date : Fr, April 24
1. VAR
(Historical Approach)
Consider a portfolio that consists of the following assets:
US$100.000 in S&P 500 index
US$100.000 in Nasdaq composite index
US$100.000
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2015
Project 4 Mathematics 512
Instructor: Ricardo Mancera
Due date: TBA
Spring 2015
1.
Consider the stock AMZN that does not pay dividends.
a) Estimate the historical volatility
using the closing prices of the past 12 months. ( you may find this data at
yahoo
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2015
Project 3 Mathematics 512
Instructor: Ricardo Mancera
Due date: TBA
Spring 2015
1.
a) Estimate the following expected value :
where
is a Wiener process.
b) Use a variance reduction technique (Antithetic or Control ) to compute the expected value in part a
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2015
Project 5 Mathematics 512
Instructor: Ricardo Mancera
Spring 2015
Due date : Fr, March 27
1.
For this project we are required to price a 5 month American put option when the stock price
strike price
, the riskfree interest rate
and the volatility
, the
a