Math 215/Econ 225: MATHEMATICAL FINANCE (Petters)
This course is ideal for students who want a rigorous introduction to
finance.
The course covers three fundamental topics every modeler in finance
should know: security price modeling, portfolio theory, and
financial derivatives (see below for the course Outline).
We shall dissect financial models by isolating their
central assumptions and conceptual
building blocks, showing rigorously how their governing
equations and relations are derived, and weighing critically
their strengths and weaknesses.
Prerequisites: Math 103, 104, and 135 (or Stat 104), or consent of instructor.
No course on finance is required.
Required Text:
-
A. O. Petters and X. Dong,
Mathematical Finance with Applications: Securities, Portfolios, and Derivatives.
The course will be based on a draft of this text in preparation.
Supplemental Readings:
- Portfolio Theory and Capital Market Theory
-
M. Capinski and T. Zastawniak,
Mathematics for Finance
(Springer, Berlin, 2003)
-
D. Luenberger,
Investment Science
(Oxford University Press, Oxford, 1998)
-
J. Ingersoll, Jr.,
Theory of Financial Decision Making
(Rowman \& Littlefield, Savage, 1987)
- Derivatives
-
J. Hull,
Options, Futures, and Other Derivatives,
(Pearson Prentice Hall, Upper Saddle River, 2009)
-
R. McDonald,
Derivative Markets,
Second Edition
(Addison-Wesley, Boston, 2006)
-
S. Ross,
An Elementary Introduction to Mathematical Finance,
Second Edition
(Cambridge U. Press, Cambridge, 2003)
-
P. Wilmott, S. Hawison, and J. Dewynne,
The Mathematics of Financial Derivatives
(Cambridge U. Press, Cambridge, 1995)
Instructor:
Arlie Petters:
- Office: 208 Physics Bldg
- Phone: (919) 660-2812
- Office Hours: Mondays, 11:30 am - 1:30 pm; otherwise, by appointment
- Email:
arlie.petters@duke.edu
Graders: TBA
COURSE OUTLINE (tentative):
I. Non-Risky Securities
- Simple and compound Interest
- Annuities
- Applications
II. Portfolio Theory
- Markowitz theory
- Expected utility maximization
- Capital market theory
III. Risky Securities
- Return rates and volatility
- Discrete-time models: binomial trees
- Continuous-time models: geometric Brownian motion
IV. Stochastic Calculus
- Random walks
- Brownian motion
- Stochastic Differential Equations and Ito's Formula
V. Derivative Pricing
- Options: general theory
- Black-Scholes pricing: binomial approach
- Black-Scholes pricing: risk-neutral approach
- Black-Scholes pricing: p.d.e. approach
- Corporate Applications
Grading (approximate):
- Homework: 70%
- Final (comprehensive): 30%