Math 586
Computational Finance
University of Illinois at Chicago
Spring 2018

Professor David Nicholls

1219 Science and Engineering Offices (SEO)
(312) 413-1641
davidn@uic.edu
http://www.math.uic.edu/~nicholls/math586_spring18/index.html

Lecture (Lincoln Hall 304): MWF 9:00 am - 9:50 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 (Finance):

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.

Other References (Numerical Methods):

Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Second Edition.
Nocedal & Wright, Numerical Optimization, Second Edition.
Higham & Higham, MATLAB Guide, Second Edition.

Grading:

Homeworks: 100%
HW 1 due Friday, February 9 by 2pm
HW 2 due Friday, March 2 by 2pm
HW 3 due Friday, March 23 by 2pm
HW 4 due Friday, April 27 by 2pm

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	1/15 1/17 1/19	M.L.K. Day [no class] H (1): What is an Option? H (2, 3): Option Valuation Preliminaries and Random Variables
2	Mon Wed Fri	1/22 1/24 1/26	H (4, 5, 6): Computer Simulation, Asset Price Movement and Model H (5, 6, 7, 8): Asset Price Model and Black-Scholes PDE H (8, 10): Black-Scholes PDE, The Greeks
3	Mon Wed Fri	1/29 1/31 2/2	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	2/5 2/7 2/9 [HW 1]	WHD (4): Heat Equation WHD (4): Fundamental Solutions, Delta Functions WHD (5): Black-Scholes solution derived
5	Mon Wed Fri	2/12 2/14 2/16	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	2/19 2/21 2/23	Von Neumann Stability Analysis, Crank-Nicolson WHD (7): American Options WHD (7): American Options
7	Mon Wed Fri	2/26 2/28 3/2 [HW 2]	WHD (7): Obstacle Problem as an LCP NW (12, 16): Constrained Optimization J (1): Introduction to the Finite Element Method
8	Mon Wed Fri	3/5 3/7 3/9	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	3/12 3/14 3/16	FEM for Variational Inequalities VIs and LCPs BR (0, 1): Parable of the Bookmaker, Arbitrage Pricing of Forwards
10	Mon Wed Fri	3/19 3/21 3/23 [HW 3]	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	3/26-3/30	SPRING BREAK
12	Mon Wed Fri	4/2 4/4 4/6	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	4/9 4/11 4/13	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	4/16 4/18 4/20	H (22): Monte Carlo: Control Variates H (20): Historical Volatility
15	Mon Wed Fri	4/23 4/25 4/27 [HW 4]	W (6.3): Stratified Sampling W (7.1): Importance Sampling
16	Mon Wed Frid	4/30 5/2 5/4	TBA TBA TBA

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