CS476/676 PDE Slides I
Peter Forsyth
University of Waterloo
Winter 2016
1 / 118
Outline
Introduction
Discretizations
American Options
Discrete Dividends
Parisian Options
2 / 118
Why Use Numerical PDE Methods?
Analytic solutions:
Only simple cases, e.g. no
CS 476 - CS 676 Course Outline
Numeric Computation for Financial Modelling
Objectives
To provide students an overview of modern numerical algorithms for use in financial applications.
References
Tools for Computational Finance, R. Seydel (2002) Springer.
Winter 2014
TABLE OF CONTENTS
CS 476 (Winter 2014 - 1141)
Numerical Computation for Financial Modeling
Prof. P.A. Forsyth
University of Waterloo
LATEXer: W. KONG
http:/wwkong.github.io
Last Revision: April 30, 2014
Table of Contents
1 Introduction
1.1 Fin
CS 487/687 / CM 730: Intro. to Symbolic Comp.
Winter 2016: A. Storjohann
CS 487/687 / CM 730: Assignment #1
Assignment 1 Page 1
Due: January 28, 2016 at 11:59pm
1. (Continued fractions) Let K be a field, and f1 , . . . , f` K. Then
1
f1 +
f2 +
1
f`1 +
1
f
CS 487/687 / CM 730: Intro. to Symbolic Comp.
CS 487: Assignment #2
Winter 2016: A. Storjohann
Assignment 2 Page 1
Due: Monday, February 22, 2016 at 11:59pm
Note: Questions 1.(b), 3.(a)-(d) and 5.(a)-(d) require you to submit Maple code. E-mail a single
p
CS 489: Complexity of Computational Problems
Problem Set 2
Due on: February 10, 2016
The five problems on this assignment are worth 10 marks each. Remember to acknowledge all collaborations and external sources used in the
completion of the assignment. (I
CS 489: Complexity of Computational Problems
Problem Set 4
Due on: March 16, 2016
The five problems on this assignment are worth 10 marks each. Remember to acknowledge all collaborations and external sources used in the
completion of the assignment. (If y
Optimal Trade Execution:
Do you know what your broker is doing?
Peter Forsyth1
Stephen Tse1 Yuying Li1
S. Kennedy2
H. Windcliff2
1 Cheriton
School of Computer Science
University of Waterloo
2 Morgan
Stanley
New York
Waterloo, Winter 2016
1 / 32
The Basic
Jump Diffusion
Peter Forsyth and Ken Vetzal
University of Waterloo
Winter 2016
1 / 30
Outline
Introduction
Numerical Techniques
Examples
2 / 30
Jump Diffusion
Geometric Brownian motion not a perfect model of stock
prices
GBM plus jumps leads to a better m
CS476 W16
American Options under Regime Switching
Peter Forsyth
University of Waterloo
Cheriton School of Computer Science
CS476/676 Winter 2016
1 / 40
CS476 W16
Outline
Regime Switching Examples
HJB Equation
Direct Control vs. Penalty
Iterative Methods
N
Lecture 1
Long Term Asset Allocation for the Patient
Investor
Peter Forsyth1
1 Cheriton
School of Computer Science
University of Waterloo
CS476/676
Winter 2016
1 / 43
Lecture 1
The Basic Problem
Suppose you are saving for retirement (i.e. 20 years away)
W
Bankers, Bonuses and Busts
Peter Forsyth1
1 Cheriton
School of Computer Science
University of Waterloo
Winter 2016
1 / 42
Market-Meltdown 2008-9
It is commonly believed that poor modelling of financial derivatives
caused the market meltdown of 2008-9.
Sho
Lecture 3
Long Term Asset Allocation:
HJB Equation Formulation and Solution
Peter Forsyth1
1 Cheriton
School of Computer Science
University of Waterloo
CS476/676
Winter 2016
1 / 39
Lecture 3
Outline
1
Dynamic mean variance
Embedding result
Equivalence to
CS 489: Complexity of Computational Problems
Problem Set 3
Due on: March 2, 2016
The two problems on this assignment are worth 10 marks each. Remember to acknowledge all collaborations and external sources used in the
completion of the assignment. (If you
CS 489: Complexity of Computational Problems
Problem Set 5
Due on: March 30, 2016
The five problems on this assignment are worth 10 marks each. Remember to acknowledge all collaborations and external sources used in the
completion of the assignment. (If y
CS 489: Complexity of Computational Problems
Problem Set 1
Due on: January 27, 2016
The five problems on this assignment are worth 10 marks each. Remember to acknowledge all collaborations and external sources used in the
completion of the assignment. See
CS 487/787 / CM 730: Intro. to Symbolic Comp.
CS 487: Assignment #3
Winter 2016: A. Storjohann
Assignment 3 Page 1
Due: Mon Mar 14, 2016 at 11:59pm
1. Consider the following polynomial from Z[x, y].
f = 3 x2 y + 54 y2 x 6 x2 + 18 y2 216 x 72
Considering f
CD 321.7125, lo
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