Math 586
Computational Finance
University of Illinois at Chicago
Spring 2013

Professor David Nicholls

1219 Science and Engineering Offices (SEO)
(312) 413-1641
nicholls@math.uic.edu
http://www.math.uic.edu/~nicholls/math586_spring13/index.html

Lecture (Lincoln Hall 104): MWF 9:00 am - 9:50 am

Office Hours (1219 SEO):

Mondays, 2:00 pm - 3:00 pm
by appointment

Textbook:

Wilmott, Howison, & Dewynne, The Mathematics of Financial Derivatives: A Student Introduction.

Other References:

Higham, An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation.
Higham's Book Web-Site
Baxter & Rennie, Financial Calculus : An Introduction to Derivative Pricing.
Hull, Options, Futures, and Other Derivatives, Sixth Edition.
Brandimarte, Numerical Methods in Finance and Economics: A MATLAB-Based Introduction, Second Edition.
Seydel, Tools for Computational Finance.
Kwok, Mathematical Models of Financial Derivatives, Second Edition.
Wang, Monte Carlo Simulation with Applications to Finance.
Higham & Higham, MATLAB Guide, Second Edition.

Grading:

Homeworks: 60%
HW 1 due Friday, February 8 by 2pm
HW 2 due Friday, March 1 March 8 by 2pm
HW 3 due Friday, March 22 April 5 by 2pm
HW 4 due Friday, April 19 by 2pm
Final Project: 40%

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	1/14 1/16 1/18	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	Lecture 1 Lecture 2 Lecture 3
2	Mon Wed Fri	1/21 1/23 1/25	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	Lecture 4 Lecture 5
3	Mon Wed Fri	1/28 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	Lecture 6 Lecture 7 Lecture 8
4	Mon Wed Fri	2/4 2/6 2/8	WHD (4): Heat Equation WHD (4): Fundamental Solutions, Delta Functions WHD (5): Black-Scholes solution derived	Lecture 9 Lecture 10 Lecture 11
5	Mon Wed Fri	2/11 2/13 2/15	WHD (8): Finite Difference Methods (TFSC, TBSC) WHD (8): Solving tridiagonal systems, Crank-Nicolson Consistency, Stability, and Convergence of FD Schemes	Lecture 12 Lecture 13 Lecture 14
6	Mon Wed Fri	2/18 2/20 2/22	Von Neumann Stability Analysis, Crank-Nicolson WHD (7): American Options WHD (7): Obstacle Problem as an LCP	Lecture 15 Lecture 16 Lecture 17
7	Mon Wed Fri	2/25 2/27 3/1	NW (12, 16): Constrained Optimization J (1): Introduction to the Finite Element Method no class	Lecture 18 Lecture 19
8	Mon Wed Fri	3/4 3/6 3/8	J (1): FEM Error Estimate J (1): FEM for Poisson J (1, 8): FEM with Neumann BCs; FEM for Heat Equation	Lecture 20 Lecture 21 Lecture 22
9	Mon Wed Fri	3/11 3/13 3/15	FEM for Variational Inequalities VIs and LCPs BR (0, 1): Parable of the Bookmaker, Arbitrage Pricing of Forwards	Lecture 23 Lecture 24 Lecture 25
10	Mon Wed Fri	3/18 3/20 3/22	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	Lecture 26 Lecture 27 Lecture 28
11	Mon-Fri	3/25-3/29	SPRING BREAK
12	Mon Wed Fri	4/1 4/3 4/5	BR (2): Binomial Representation Theorem and Self-Financing Portfolios H (16): The Binomial Method Binomial Method as a Finite Difference Method	Lecture 29 Lecture 30 Lecture 31
13	Mon Wed Fri	4/8 4/10 4/12	Nine Ways to Program the Binomial Method H (12, 15): Introduction to the Monte Carlo Method H (21): Monte Carlo: Antithetic Variates	Lecture 31 (above) Lecture 32 Lecture 33
14	Mon Wed Fri	4/15 4/17 4/19	H (22): Monte Carlo: Control Variates H (20): Historical Volatility no class	Lecture 34 Lecture 35
15	Mon Wed Fri	4/22 4/24 4/26	no class W (6.3): Stratified Sampling W (7.1): Importance Sampling	Lecture 36 Lecture 37
16	Mon-Fri	4/29-5/3	FINAL PRESENTATIONS

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