Math 586
Computational Finance
University of Illinois at Chicago
Spring 2014


Professor David Nicholls

1219 Science and Engineering Offices (SEO)
(312) 413-1641
nicholls@math.uic.edu
http://www.math.uic.edu/~nicholls/math586_spring14/index.html

Lecture (Taft Hall 300...for now...): MWF 10:00 am - 10:50 am

Office Hours (1219 SEO):

Textbook:

Other References (Finance):
Other References (Numerical Methods):

Grading:
Tentative Schedule (WHD = "Wilmott, Howison, & Dewynne", H = "Higham", BR = "Baxter & Rennie", NW = "Nocedal & Wright", J = "Johnson", W = "Wang"):

Week
Day
Date
Topics
Lecture
1
Mon
Wed
Fri
1/13
1/15
1/17
H (1): What is an Option?
H (2, 3):  Option Valuation Preliminaries and Random Variables
H (4, 5, 6): Computer Simulation, Asset Price Movement and Model

2
Mon
Wed
Fri
1/20
1/22
1/24
M.L.K. Day [no class]
H (5, 6, 7, 8): Asset Price Model and Black-Scholes PDE
H (8, 10): Black-Scholes PDE, The Greeks

3
Mon
Wed
Fri
1/27
1/29
1/31
H (13, 14): Solving Nonlinear Equations, Implied Volatility
WHD (2, 3): Asset Price Random Walks, Black-Scholes PDE
WHD (3, 4): American Options, First-Order PDE

4
Mon
Wed
Fri
2/3
2/5
2/7 [HW 1]
WHD (4): Heat Equation
WHD (4): Fundamental Solutions, Delta Functions
WHD (5): Black-Scholes solution derived

5
Mon
Wed
Fri
2/10
2/12
2/14
WHD (8): Finite Difference Methods (TFSC, TBSC)
WHD (8): Solving tridiagonal systems, Crank-Nicolson
Consistency, Stability, and Convergence of FD Schemes

6
Mon
Wed
Fri
2/17
2/19
2/21
no class
Von Neumann Stability Analysis, Crank-Nicolson
WHD (7): American Options

7
Mon
Wed
Fri
2/24
2/26
2/28
WHD (7): Obstacle Problem as an LCP
NW (12, 16): Constrained Optimization
J (1): Introduction to the Finite Element Method

8
Mon
Wed
Fri
3/3
3/5
3/7
J (1): FEM Error Estimate
J (1): FEM for Poisson
J (1, 8): FEM with Neumann BCs; FEM for Heat Equation

9
Mon
Wed
Fri
3/10
3/12
3/14
FEM for Variational Inequalities
VIs and LCPs
BR (0, 1): Parable of the Bookmaker, Arbitrage Pricing of Forwards

10
Mon
Wed
Fri
3/17
3/19
3/21
BR (2): Binomial Tree: One time-tick
BR (2): Binomial Tree: Many time-ticks and a Worked Example
BR (2): Definitions for the Binomial Representation Theorem

11
Mon-Fri
3/24-3/28
SPRING BREAK

12
Mon
Wed
Fri
3/31
4/2
4/4
BR (2): Binomial Representation Theorem and Self-Financing Portfolios
H (16): The Binomial Method
Binomial Method as a Finite Difference Method

13
Mon
Wed
Fri
4/7
4/9
4/11
Nine Ways to Program the Binomial Method
H (12, 15): Introduction to the Monte Carlo Method
H (21): Monte Carlo: Antithetic Variates

14
Mon
Wed
Fri
4/14
4/16
4/18
H (22): Monte Carlo: Control Variates
H (20): Historical Volatility

15
Mon
Wed
Fri
4/21
4/23
4/25
W (6.3): Stratified Sampling
W (7.1): Importance Sampling


16
Mon-Fri
4/29-5/3
FINAL PRESENTATIONS


MATLAB Primer:
primer35.pdf
Information Page: PDF
MATLAB Codes for Heat Equation: heat.m