IE 446/546
Introduction to Continuous Time Finance
Spring 2009
Instructor:
M. C. Pinar
Room:
305
Office Hours:
Wednesdays 3:30-5:30 pm.
Textbooks
and Recommended Resources:
Recommended Reading:
Arbitrage Theory in Continuous Time by T. Björk, Oxford
University Press, second edition, 2004.
The course is intended as an introduction to the modern techniques of
mathematical finance. There is no text book, but the
book by Björk is useful. Lectures are based on the instructor's notes. No
prerequisites, except some familiarity with calculus, linear algebra, probability and
optimization, are assumed.
Course Contents:
Introduction
to the Wiener Process (week 1)
Basic numerics
to simulate stochastic differential equations(weeks 2-3)
Binomial lattice
models (week 4)
Stochastic
calculus and Ito Formula (week 5),
The Black-Scholes equation (week 6)
Applications of Black-Scholes to defaultable bonds and midterm exam (week 7)
The Fokker-Planck Equation (week 8)
The Feynman-Kac formula (week 9)
The Kolmogorov Backward Equation (week 10)
Proof of the Ito Integral (week 11)
Proof of the Ito Integral (week 12)
The Laplace Transform and first passage times of Brownian motion (week 13)
Valuation of American Perpetual Warrant (week 14)
Policy on Homework and Exams
Your success
in the course depends greatly on doing the homework exercises on your
own.
I will
distribute the hw questions in class.
Late hws will
not be accepted.
Cheating in
homework and exams has serious consequences. Therefore, all work
submitted should reflect your own effort.