Math 586
Computational Finance
University of Illinois at Chicago
Spring 2012

Professor David Nicholls

1219 Science and Engineering Offices (SEO)
(312) 413-1641
nicholls@math.uic.edu
http://www.math.uic.edu/~nicholls/math586_spring10/index.html

Lecture (Taft Hall 320): MWF 10:00 am - 10:50 am

Office Hours (1219 SEO):

Mondays, 1:00 pm - 2:00 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.
Higham & Higham, MATLAB Guide, Second Edition.

Grading:

Homeworks: 60%
HW 1 due Friday, February 3 by 2pm
HW 2 due Friday, February 24 by 2pm Monday, February 27 by 2pm [NEW DUE DATE]
HW 3 due Friday, March 16 by 2pm
HW 4 due Friday, April 13 by 2pm Monday, April 16 by 2pm [NEW DUE DATE]
Final Project: 40%

Tentative Schedule (WHD = "Wilmott, Howison, & Dewynne", H = "Higham", BR = "Baxter & Rennie"):

Week	Day	Date	Topics	HW Number (due-date)	HW Problems
1	Mon Wed Fri	1/9 1/11 1/13	Introduction. (WHD 1.1) What is an Option? Types of Options. (WHD 1.2-1.5) Forwards, Futures, Interest Rates. (WHD 1.6-1.7)	#1 (2/3)
2	Mon Wed Fri	1/16 (M.L.K. Day) 1/18 1/20	NO CLASS Asset Price Model. Ito's Lemma. (WHD 2.1-2.3) Elimination of Randomness. (WHD 2.4)	#1 (2/3)	Chap 2: #1
3	Mon Wed Fri	1/23 1/25 1/27	Black-Scholes Analysis (WHD Chap 3) PDEs. Diffusion Equation (WHD 4.1, 4.2) Initial/Boundary Conditions (WHD 4.3)	#1 (2/3)	Chap 3: #2, #3 Chap 4: #1
4	Mon Wed Fri	1/30 2/1 2/3 [HW 1 due]	Similarity Solutions (WHD 5.1-5.3) NO CLASS Black-Scholes formula derived. (WHD 5.4)	#2 (2/24)	Chap 5: #2, #3
5	Mon Wed Fri	2/6 2/8 2/10	Black-Scholes formula derived. (WHD 5.4) Finite Differences 1 (WHD Chap 8) Finite Differences 2 (WHD Chap 8)	#2 (2/24)	FD problems
6	Mon Wed Fri	2/13 2/15 2/17	Finite Differences 3 (WHD Chap 8) Finite Differences 4 (WHD Chap 8) Finite Differences 5 (WHD Chap 8)	#2 (2/24)
7	Mon Wed Fri	2/20 2/22 2/24	Finite Differences 6 (WHD Chap 8) Finite Differences 7 (WHD Chap 8) Finite Differences 8 (WHD Chap 8)	#3 (3/16)	HW 3 Problems
8	Mon Wed Fri	2/27 [HW 2 due] 2/29 3/2	Finite Differences 9 (WHD Chap 8) Volatility: Solving Nonlinear Equations (H Chap 13) Implied Volatility (H Chap 14)	#3 (3/16)
9	Mon Wed Fri	3/5 3/7 3/9	Historical Volatility (H Chap 20) American Options. Obstacle Problem. (WHD 7.1-7.3) American Put. Linear Complementary Problems. (WHD 7.4-7.6)	#3 (3/16)
10	Mon Wed Fri	3/12 3/14 3/16 [HW 3 due]	LCPs (WHD 7.6) LCPs (WHD 7.6) Finite Differences for Obstacle Problems (WHD Chap 9)	#4 (4/13)	HW 4 Problems B&R Chapter 2
11	Mon-Fri	3/19-3/23	SPRING BREAK
12	Mon Wed Fri	3/26 3/28 3/30	Finite Differences for Americans (WHD Chap 9) Parable of the Bookmaker (BR 0) Expectation and Arbitrage Pricing (BR 1)	#4 (4/13)
13	Mon Wed Fri	4/2 4/4 4/6	Binomial Branch Model (BR 2.1) Binomial Tree Model (BR 2.2) Option Price Formula (BR 2.4)	#4 (4/13)
14	Mon Wed Fri	4/9 4/11 4/13 [HW 4 due]	The Binomial Method The Binomial Method for Americans NO CLASS
15	Mon Wed Fri	4/16 [HW 4 due] 4/18 4/20	Monte Carlo Monte Carlo (Antithetic Variates) Monte Carlo (Control Variates)
16	Mon	4/23-4/27	FINAL PRESENTATIONS

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