FE543 Introduction to Stochastic Calculus for Finance

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Course Catalog Description

Introduction

This course introduces the stochastic calculus to students of nance and nancial engineering. The course deals with Markov chains, Poisson processes, random walks, Brownian motion, asset prices as processes, limits of stochastic sequences, Ito sums and integral, fundamental models in modern nance, price dynamics and elementary examples of stochastic differential equations.
Campus Fall Spring Summer
On Campus X X
Web Campus

Instructors

Professor Email Office
Papa Ndiaye
Papa.Ndiaye@stevens.edu Altorfer 311



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, ISBN-13: 978-0387249681 (vol I) and 978-0387401010 (vol II).


Additional References

Introduction to 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 2001.



Stochastic Differential Equation, by Bernt Oksendal, 6th edition, 2010, ISBN-10: 3540047581, ISBN-13: 978-3540047582


Introduction to the Mathematics of Financial Derivatives, by by Salih N Neftci, 2nd ed, Associated Press, 2000, ISBN 0125153929



Grading

Grading Policies

Homework

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 a 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.

Exams

There 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 hand written page of notes to the midterm and two hand written 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 Black-Scholes and Levy Ch. 4 in vol. II
Week 13 Change of Measure Ch. 5 in vol. II
Week 14 Review & Catch-up