FE610 Stochastic Calculus for Financial Engineers
Course Catalog Description
Introduction
Campus  Fall  Spring  Summer 

On Campus  X  X  
Web Campus  X  X  X 
Instructors
Professor  Office  

Thomas Lonon

tlonon@stevens.edu  Zoom, accessed through Canvas 
More Information
Course Description
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 Financial Engineering.
Prerequisites: Background in probability and applied mathematics
Course Outcomes
At the end of this course, students will be able to:
1. Classify stochastic processes as martingales, Markov, or both/neither
2. Simplify stochastic (Ito) integrals
3. Determine the differentials of functions of stochastic processes
4. Change probability measures to facilitate pricing of derivatives
5. Solve stochastic differential equations through transformations to partial differential equations.
Course Resources
Textbook
Stochastic Calculus for Finance vol II, by Steven E. Shreve, Springer Finance, 2004, ISBN13: 9780387401010 (vol II).
Additional References
Stochastic Calculus for Finance vol I, by Steven E. Shreve, Springer Finance, 2004, ISBN13: 9780387249681 (vol I).
Introduction to Probability Models, 10th edition, by Sheldon M. Ross, Academic Press, 2009, ISBN10: 0123756863, ISBN13: 9780123756862.
Probability and Random Processes, by Geoffrey Grimmett and David Stirzaker, Oxford University Press 2001.
Stochastic Integration and Differential Equations, by Philip E. Protter, Springer 2005. ISBN13: 9783642055607
Stochastic Differential Equation, by Bernt Oksendal, 6th edition, 2010, ISBN10: 3540047581, ISBN13: 9783540047582
Introduction to the Mathematics of Financial Derivatives, by by Salih N Neftci, 2nd ed, Associated Press, 2000, ISBN 0125153929.
Grading
Grading Policies
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.
Extra Credit
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.
Lecture Outline
Topic  Reading  

Week 1  Probability review: Random variables and vectors. Stochastic processes.  Ch. 1 and 2 
Week 2  Random walk. Brownian motion.  Ch. 3 
Week 3  Markov Property, Reflection Principle and Passage Times  Ch. 3 
Week 4  Stochastic Calculus(Integrands)  Ch. 4 
Week 5  Ito lemma and applications  Ch. 4 
Week 6  BlackScholesMerton Model  Ch. 4 
Week 7  Multivariable Stochastic Calculus  Ch. 4 
Week 8  Midterm  
Week 9  RiskNeutral Measure and Girsanov  Ch. 5 
Week 10  Multidimensional Stock Model  Ch. 5 
Week 11  PDE's and SDE's  Ch. 6 
Week 12  Poisson Processes and Jump Diffusion  Ch. 11 
Week 13  Exotic Options  Ch. 7 
Week 14  Review & Catchup 