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

Spring 2014
MATH512 Spring 2017
Financial Informatics and Simulation
Lecture 1: Introduction
TingKam Leonard Wong
Department of Mathematics, University of Southern California
January 9, 2017
1 / 12
Instructor
I
I
I
I
I
TingKam Leonard Wong
http:/wwwbcf.usc.edu/~ti
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 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 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 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 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
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
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 2014
MATH 512
Financial Informatics and Simulation
Spring 2017
Instructor: Leonard Wong
Time and Location: MWF 11:0011:50pm, VKC 152
Email: [email protected]
Office Hours: W 13pm, KAP 406H, or by appointment
Teaching Assistant: TBA
Overview
This is an intensive
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2014
MATH512 Spring 2017
Assignment 1
Due: January 27, 2017
The first two problems are standard and straightforward, but the first also invites you to think about the
behaviors of heavytailed distributions. Problems 3 and 4 challenge your probabilistic intuit
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2014
MATH512 Spring 2017
Assignment 5
Due: March 24, 2017
In this problem set we will work with the research and algorithm environments of Quantopian. It is
lighter than the previous assignments so that you have some time to catch up with Python/Quantopian and
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2014
MATH512 Spring 2017
Financial Informatics and Simulation
Lecture 2: Random Number Generation
TingKam Leonard Wong
Department of Mathematics, University of Southern California
January 11, 2017
1 / 20
Readings
I Sections 2.12.3 of Glasserman
For more detai
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2014
MATH512
Spring 2017
6. Brownian motion and geometric Brownian motion
TingKam Leonard Wong
Department of Mathematics, University of Southern California
January 23, 2017
1 / 18
Brownian motion
The 1dimensional standard Brownian motion (aka Wiener
process)
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2014
MATH512 Spring 2017
Financial Informatics and Simulation
Lecture 3: <random>
TingKam Leonard Wong
Department of Mathematics, University of Southern California
January 13, 2017
1 / 11
Introduction
To use the random number generation facilities in C+, we
i
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2014
MATH512
Spring 2017
5. Designing and implementing a class
TingKam Leonard Wong
Department of Mathematics, University of Southern California
January 18, 2017
1 / 11
Introduction
Taken from The C+ Programming Language (Fourth Edition)
by Byjarne Stroustrup
Financial Informatics and Simulation (Computer Labs and Practitioner Seminar)
MATH 512

Spring 2014
MATH512
Spring 2017
4. Multivariate Normal and Cholesky Decomposition
TingKam Leonard Wong
Department of Mathematics, University of Southern California
January 18, 2017
1 / 16
Multivariate normal distribution
Let d 1 be the dimension. A ddimensional mul
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