Math 215/Econ 225, MATHEMATICAL FINANCE (Petters)
Rigorous introduction to the basic concepts and mathematical models
for 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:
-
A. O. Petters,
Mathematical Finance: A One Semester Course
This is a text in preparation. The course will be based on a draft that
will be available at the start of classes.
Instructor:
Arlie O. PETTERS:
- Office: 230 Physics Bldg
- Phone: (919) 660-2812
- Office Hours:
- Email:
petters@math.duke.edu
Grader:
- Email:
COURSE OUTLINE (tentative):
I. Introduction
- Securities
- Securities Markets
- Review of Probability Theory
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):
- Homeworks: 70%
- Take Home Final (comprehensive): 30%
Assignments: