FE620 Pricing and Hedging -TEST
Course Catalog Description
This course provides the mathematical foundation for understanding modern financial theory. It includes topics such
as basic probability, random variables, discrete continous distributions, random processes, Brownian motion, and an
introduction to Ito’s calculus. Applications to financial instruments are discussed throughout the course.
This course is designed for first year graduate students in Financial Engineering. The goal is to learn the
foundation on which Financial engineering is built upon. It is highly recommended that students have a strong
background in applied mathematics (analysis) and probability. This is a core course for all programs in
Prerequisites: Background in probability and applied mathematics
At the end of this course, students will be able to:
- classify stochastic processes as martingales, Markov, or both/neither
- simplify stochastic (Ito) integrals
- determine the differentials of functions of stochastic processes
- change probability measures to facilitate pricing of derivatives
- solve stochastic differential equations through transformations to partial differential equations.
Stochastic Calculus for Finance vol II, by Steven E. Shreve, Springer Finance, 2004, ISBN-13:
978-0387401010 (vol II).
Stochastic Calculus for
Finance vol I, by Steven E. Shreve, Springer Finance, 2004, ISBN-13: 978-0387249681 (vol
Probability Models, 10th edition, by Sheldon M. Ross, Academic Press, 2009, ISBN-10:
0123756863, ISBN-13: 978-0123756862.
Probability and Random
Processes, by Geoffrey Grimmett and David Stirzaker, Oxford University Press
and Differential Equations, by Philip E. Protter, Springer 2005. ISBN-13:
Differential Equation, by Bernt Oksendal, 6th edition, 2010, ISBN-10: 3540047581, ISBN-13:
Introduction to the
Mathematics of Financial Derivatives, by by Salih N Neftci, 2nd ed, Associated Press, 2000, ISBN 0125153929.
The final grade in the class will be determined in the following manner:
- 20% Homeworks
- 30% Midterm
- 50% Final Exam
Please note that your grade will be determined solely on the work you present over the course of the semester.
No consideration such as your need for a better grade will be considered.
Possibly on the exams, there will be the occasional extra credit problem. This is the only source of extra
credit for the course. There are no "extra assignments" that students can do to raise their average outside of
the ones assigned. There are no exceptions, don't even bother coming to me and asking about extra work and the
end of the semester, as I will only direct your attention to this part of the syllabus.
||Probability review: Random variables and vectors. Stochastic
||Ch. 1 and 2
||Random walk. Brownian motion.
||Markov Property, Reflection Principle and Passage Times
||Ito lemma and applications
||Multivariable Stochastic Calculus
||Risk-Neutral Measure and Girsanov
||Multidimensional Stock Model
||PDE's and SDE's
||Poisson Processes and Jump Diffusion
||Review & Catch-up