FE 610 - Stochastic Calculus for Financial Engineers

FE 610 - Stochastic Calculus for Financial Engineers

Prof. Steve Yang
Stevens Institute of Technology
Spring Semester 2013

Instructor: Steve Yang, Babbio 536, steve.yang@stevens.edu

Class Time: Lectures on Thursdays 03:00PM-5:30PM (01-14-2013 – 05-15-2013)

Class Room: Edwin A. Stevens Hall 230

Office Hours: Wednesdays 11:00AM-12:00PM at Babbio 536

Prerequisites: N/A

Topics: This course provides the mathematical foundation for understanding modern financial theory. It includes topics, such as, basic probability theory, random variables, discrete and continuous distributions, Martingale processes, Brownian motion, stochastic integration and Ito process and calculus. Applications to financial concepts and instruments are discussed throughout the course.

Textbook:

· "Introduction to the Mathemtics of Financial Derivatives" by Salih N Neftci, 2nd ed, AP ISBN 0125153929 [REQUIRED]

· "Stochastic Calculus and Financial Applications", by J. Michael Steele, Springer 2000, ISBN-10: 0387950168, ISBN-13: 978-0387950167 [OPTIONAL]

· "Financial Calculus" by Martin Baxter and Andrew Rennie, Cambridge University Press, 1999. ISBN 0 521 55289 3. [OPTIONAL]

Lecture Outline:

Week	Topic(s)	Reading(s)	HW
1	Financial Derivatives	S. N. Neftci [1]
2	Introduction to the Arbitrage Theorem	S. N. Neftci [2]	HW1
3	Calculus in Deterministic and Stochastic Environment	S. N. Neftci [3]
4	Pricing Derivatives	S. N. Neftci [4]	HW2
5	Review of Probability Theory	S. N. Neftci [5]
6	Martingales and Martingale Representations	S. N. Neftci [6]	HW3
7	Differentiation in Stochastic Processes	S. N. Neftci [7]
8	Midterm Exam		EXAM-I
9	The Wiener Process and Rare Events	S. N. Neftci [8]
10	Integration in Stochastic Environments	S. N. Neftci [9]
11	Ito’s Lemma and Process	S. N. Neftci [10]	HW4
12	Stochastic Differential Equations	S. N. Neftci [11]
13	Partial Differential Equations	S. N. Neftci [12]
14	The Black-Scholes PDE	S. N. Neftci [13]	HW5
15	Equivalent Martingale Measures and Applications	S. N. Neftci [14, 15]
16	Final Exam		EXAM-II

Exams and Grades:

Assignment	Grade Percentage
Homework Assignments	40%
Midterm Exam	30%
Final Exam	30%
Total Grade	100%

Exams: Two Exams. (Midterm) EXAM I: March 7 - (Thursday). (Final) EXAM II May 9 - (Thursday).

Exam Honor Policy: You are not allowed to discuss any of the exam questions with one another or to show any of your solutions. The work must be done independently and pledged.

Homework: There will be 5 homework assignments (approx every 2-3 weeks).

Homework Honor Policy: You are allowed to discuss the problems between yourselves, but once you begin writing up your solution, you must do so independently, and cannot show one another any parts of your written solutions. The HW is to be pledged (that it adheres to this).

Your solutions to the homework and exam problems have to be typed (written legibly) and uploaded to the Moodle course website in one single PDF file (no other file format will be accepted). Any changes to the course schedule or due date of assignments will be announced through the course website announcement system. If you have problem to save your files to PDF, please let me know.

To understand the course material and get a good grade, you need to invest a substantial amount of time reading the required chapters and working on the assignments. Each homework assignment will contain 3-5 problems, and will be posted on the class website. No late homework will be accepted under any circumstances.

Attendance: Attendance will be taken randomly (e.g., 6-7 times during the semester) and will determine "which direction" the resulting grade will “fall”, for those grades which are borderline (e.g., between B+ or A-).