Math 215/Econ 225: MATHEMATICAL FINANCE (Petters)
This course is ideal for students who want a rigorous introduction to
quantitative finance, will become quants or traders at an investment bank, or
will interact with quants at an investment firm.
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. The ranges of validity of the models
in real-world settings are also investigated.
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,
Applied Mathematical Finance I.
The course will be based on a draft of this text in preparation.
Supplemental Readings:
-
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: Mon, 10:00 am - 12:00 pm
- Email:
petters@math.duke.edu
Graders:
COURSE OUTLINE (tentative):
I. Non-Risky Securities
- Securities
- Interest rates
- Annuities
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
- 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
Grading (approximate):
- Homework: 70%
- Final (comprehensive): 30%