> ## Content Index > Fetch the complete content index at: https://fsc.stevens.edu/llms.txt > Use this file to discover other available public pages before exploring further. # FE610 Stochastic Calculus for Financial Engineers - URL: https://fsc.stevens.edu/fe610-stochastic-calculus-for-financial-engineers/ - Published: 2019-07-18T20:39:08.000Z - Updated: 2026-10-30T21:40:24.000Z - Author: hfsladmin - Tags: Courses, #Import 2025-11-08 22:14 Course Catalog Description # Introduction This course is designed for masters students in Financial Engineering. The goal is to learn the foundation on which Finance and Financial Engineering 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. | Campus | Fall | Spring | Summer | | ---------- | ---- | ------ | ------ | | On Campus | X | X | | | Web Campus | X | X | X | Instructors | Professor | Email | Office | | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------ | ---------- | | [Thomas Lonon](https://web.stevens.edu/facultyprofile/?id=2040&ref=fsc.stevens.edu "Thomas Lonon") ![](https://fsc.stevens.edu/content/images/2019/10/Thomas_Lonon.jpg) | tlonon@stevens.edu | Babbio 544 | 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**: Knowledge of Calculus and Probability # 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, ISBN-13: 978-0387401010 (vol II). # Additional References *Stochastic Calculus for Finance vol I*, by Steven E. Shreve, Springer Finance, 2004, ISBN-13: 978-0387249681 (vol I). *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 Integration and Differential Equations*, by Philip E. Protter, Springer 2005\. ISBN-13: 9783642055607 *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 The final grade in the class will be determined in the following manner: - 5% Attendence - 10% Homeworks - 30% Basic Skill Assessment - 25% Midterm - 30% 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. **Extensions and Re-submits** It is my policy to never give a student an extension after a deadline is missed. You know before you actually miss a deadline that you will miss the deadline. If you reach out to me before an assignment is due and let me know why you will miss the deadline, if its a valid reason (and this does not have to include medical issues, I realize that sometimes life just gets in the way) I have no problem providing an extension if necessary. I will under very rare circumstances allow a student to re-submit an assignment that has already been submitted, but it is my policy to not allow a re-submit of an assignment once it has been graded. Once the assignment has been graded, you now possess much better information than the average student and it is therefore unfair to the others in the class to allow this. **Extra Credit** The recommended problems on the homeworks and possibly an extra problem on the exams will be the only sources 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 | Black-Scholes-Merton Model | Ch. 4 | | Week 7 | Multivariable Stochastic Calculus | Ch. 4 | | Week 8 | Midterm | | | Week 9 | Risk-Neutral 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 & Catch-up | |