Math 590 Financial Engineering
or Mathematics of Stock Markets
Fall 1996
Syllabus
Time Table:
Time=11MWF Room=316TH Call=61738 Instructor=Lipton
Outline:
This is an introduction into a rapidly developing area of mathematics
known as financial engineering. Recent advances in understanding the
behavior of the bond and stock markets will be described from a
mathematical viewpoint. Modern financial instruments and mathematical
methods of their valuation will be discussed in detail. Hands on
experience in numerical methods will be provided.
Instructor:
Alexander Lipton (Lifschitz), 728 SEO, 996-4609, alexli@uic.edu
Office Hours:
M, W, F 12PM or by appointment
Instructor Web Page: http://www.math.uic.edu/~hanson/lipton.index.html
Prerequisites:
Graduate standing and Math 481 Applied Partial Differential Equations
and MCS 471 Numerical Analysis or consent of the instructor
Grading:
Grade will be based on homework and computer problems to be distributed
during the semester; there will be no exams
Texts:
- P.W. Wilmott, S. Howison, J. Dewynne,
The Mathematics of Financial Derivatives: a Student Introduction,
Cambridge Univ Press, 1995
- J. Hull, Options, Futures, and Other Derivative Securities,
Prentice-Hall, 1993.
- G.D. Smith, Numerical Solution of Partial Differential Equations,
3rd edition, Oxford Univ Press, 1985.
- A.J. Davies, The Finite Element Method: A First Approach,
Oxford Univ Press, 1986.
List of Topics:
- Numerical Methods for Parabolic PDEs: review of finite difference
methods, explicit methods, Crank-Nicolson implicit method,
consistency, stability, convergence, Fourier stability methods,
alternating directions implicit method, higher
level schemes, nonlinear equations, predictor corrector methods,
trees, lattice methods, Monte-Carlo methods, computer problems, 12 hours
- Stochastic Processes: basic concepts, elements of random
analysis, infinite-dimensional distributions, martingales, Markov
processes with discrete time, Marcov processes with continuous
time, stochastic equations and diffusion, computer problems, 12 hours.
- Financial Derivatives: overview of stock and bond markets,
the Black-Scholes models, risk neutral pricing,
basic options, European, American, Asian, barrier, and exotic
options, free-boundary versus fixed-boundary problems, interest
rate derivatives, computer problems, 15 hours.
- Special topics: implied volatilities, the volatility smile,
chaos, nonlinear dynamics and neural networks, computer problems,
6 hours.
Web Source: http://www.math.uic.edu/~hanson/math590f96syllabus.html