Math 215/Econ 225, MATHEMATICAL FINANCE (Petters)
Introduction to the basic concepts and mathematical models
used for personal finance, portfolio theory,
security price behavior, and option pricing.
Prerequisites: Math 103,104, and 135 (or Stat 104), or consent of instructor.
No course on finance is required.
Text:
-
X. Dong and A. O. Petters,
Mathematical Finance I
The course will be based on a draft of this text in preparation.
Supplemental Reading:
-
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: Tues, 11:30am - 1:30 pm
- Email:
petters@math.duke.edu
Grader:
Jingyuan Wu
- Email:
jw62@duke.edu
COURSE OUTLINE (tentative):
I. Personal Finance
- Interest Rates
- Annuities
- Applications
II. Portfolio Theory
- Mean-variance analysis and the efficient frontier
- Capital market theory
- Expected utility maximization
III. Modeling Security Price Behavior
- Return rates and volatility
- Binomial models of security prices
- Geometric Brownian motion property of security prices
IV. Stochastic Calculus
- Random walks
- Brownian motion
- Ito's Formula and stochastic differential equations
V. Option Pricing
- Call and put Options
- The Black-Scholes equation
- The Black-Scholes option pricing formula
Grading (approximate):
- Homework: 70%
- Final (Comprehensive): 30%