FE543 Introduction to Stochastic Calculus for Finance
Course Catalog Description
Introduction
Campus  Fall  Spring  Summer 

On Campus  X  X  
Web Campus  X 
Instructors
Professor  Office  

Thomas Lonon

tlonon@stevens.edu  Virtual 
More Information
Course Description
This course is designed for advanced undergraduate students and masters students in Financial Engineering. The goal is to learn the foundation on which Finance is built upon. The students are supposed to have a strong background in applied mathematics (analysis and calculus) and probability at an undergraduate level. Any student who does not already have this previous knowledge will have much greater difficulty learning the material.
Course Resources
Textbook
Stochastic Calculus for Finance vol I and II, by Steven E. Shreve, Springer Finance, 2004, ISBN13: 9780387249681 (vol I) and 9780387401010 (vol II).
Additional References
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 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
There will be around 5 homework assignments throughout the semester. Collaboration is encouraged as it can be helpful to understand some of these concepts. Do not confuse collaboration for academic misconduct. Attempt each problem on your own before seeking help from another person. Make sure that you understand the entire assignment that you turn in, and could reproduce the work or solve a similar problem. Do not think that you can simply copy another person's assignment and expect to understand the material. Late homework will be accepted under the following policy. If the homework is turned in within one week of the original due date, it will receive 2/3 (two third) of its score, going down by a third each week it is late. The homework assignments will have a very firm deadline, of 11:55 PM on the due date. When I say this is a firm date, I mean that if homework is submitted online at 11:56 PM, its late, no exceptions. Plan ahead and submit your homework early to avoid problems due to internet or computer issues.
ExamsThere will be one midterm and one final exam given in the class. If you miss an exam, you must provide a written explanation signed by proper authorities in order to be allowed the chance to take a replacement exam. The midterm and final exam are closed book, but each student can bring one handwritten page of notes to the midterm and two handwritten pages of notes to the final. Calculators are permitted and encouraged, but cell phones and notebook computers are not allowed.
 The final grade in the class will be determined in the following manner:
 20% Homeworks
 30% Midterm
 50% Final Exam
Lecture Outline
Topic  Reading  

Week 1  One Period BAPM  Ch. 1 in vol. I 
Week 2  Multiperiod Model and FPS  Ch. 1 and 2 in vol. I 
Week 3  Expectation in BAPM  Ch. 2 in vol. I 
Week 4  Martingales and Markov  Ch. 2 in vol. I 
Week 5  Stopping Times and RW  Ch. 4 & 5 in vol. I 
Week 6  SSRW and BM  Ch. 3 in vol. II 
Week 7  Quadratic Variation and MP  Ch. 3 in vol. II 
Week 8  Midterm  
Week 9  Reflection Prop. and Cont. Passage Times  Ch. 3 in vol. II 
Week 10  Stochastic Calculus Integrands  Ch. 4 in vol. II 
Week 11  Ito’s Formula  Ch. 4 in vol. II 
Week 12  BlackScholes and Levy  Ch. 4 in vol. II 
Week 13  Change of Measure  Ch. 5 in vol. II 
Week 14  Review & Catchup 