Instructor: Jianfeng Zhang, KAP 248E, (213)740-9805, jianfenz@usc.edu dornsife.usc.edu/jianfeng-zhang/
Grader: Tianle Liu, tianleli@usc.edu
Time and location: WF 2:00 – 3:15pm, KAP156
Office hours: W 11:30am-1pm, F 9am-10:30am, in KAP 248E, or by appointment
Textbooks: (Either Bjork’s book or Shreve’s two books)
- Arbitrage Theory in Continuous Time, 3rd edition by Tomas Bjork, Oxford University Press, 2009
- Stochastic calculus for finance. I. The binomial asset pricing model, by Shreve, Springer 2004
- Stochastic calculus for finance. II. Continuous-time models, by Shreve, Springer 2004
Prerequisites: Math 530A (or approval by the instructor)
Exam Dates:
Midterm Exam: March 14, Friday, in class
Final Exam: Take home exam
Course Contents:
This course is the second part of a two-semester sequence, which provides the mathematical theory and probabilistic tools for modeling and analyzing security markets. In this semester, we shall introduce some more advanced topics, including: interest rate models; credit risk models; and stochastic optimization.
I will use my own lecture notes. The textbooks serve as main reference books, and additional reading materials will be recommended. Here is a tentative schedule (subject to change):
Chapter 3. The Black-Scholes-Merton Theory
3.4 American options
3.5 Nonlinear models
Chapter 4. Interest rate models
4.1 Interest rates
4.2 Short rate models
4.3 Forward rate models
4.4. Financial derivatives
4.5 OIS discounting
Chapter 5. Credit risk models
5.1. Structural models
5.2 Reduced form models
5.3. Examples
5.4 Pricing derivatives in reduced form models
5.5 Correlated defaults
Chapter 6. Stochastic optimization
6.1. Introduction
6.2 Dynamic programming and HJB equations
6.3. Stochastic maximum principle
6.4 Closed loop controls and weak formulation
6.5 Pricing derivatives in incomplete markets
Grading and Examination Policies
30% of the grade will be based on homework assignments, 30% on the midterm exam, and 40% on the final exam.
The 75 minutes Midterm Exam will be given in regular class time. The exam is open book, open notes, but non-cooperative. The final exam will be a take home exam. You will have two weeks to finish it.
Homework problems will be assigned weekly. You are permitted and even encouraged to discuss homework problems with classmates. However, you are not permitted to copy solutions from others.
Feedback and Questions
It is extremely important for me to get feedback and questions, both inside and outside class. You are very welcome to visit me during my office hours, and/or make appointments to see me at other time.
Statement for Students with Disabilities
USC welcomes students with disabilities into all of the University’s educational programs. The Office of Student Accessibility Services (OSAS) is responsible for the determination of appropriate accommodations for students who encounter disability-related barriers. Once a student has completed the OSAS process (registration, initial appointment, and submitted documentation) and accommodations are determined to be reasonable and appropriate, a Letter of Accommodation (LOA) will be available to generate for each course. The LOA must be given to each course instructor by the student and followed up with a discussion. This should be done as early in the semester as possible as accommodations are not retroactive. More information can be found at osas.usc.edu. You may contact OSAS at (213) 740-0776 or via email at osasfrontdesk@usc.edu.
Statement on Academic Integrity
The University of Southern California is foremost a learning community committed to fostering successful scholars and researchers dedicated to the pursuit of knowledge and the transmission of ideas. Academic misconduct is in contrast to the university’s mission to educate students through a broad array of first-rank academic, professional, and extracurricular programs and includes any act of dishonesty in the submission of academic work (either in draft or final form).
This course will follow the expectations for academic integrity as stated in the USC Student Handbook. All students are expected to submit assignments that are original work and prepared specifically for the course/section in this academic term. You may not submit work written by others or “recycle” work prepared for other courses without obtaining written permission from the instructor(s). Students suspected of engaging in academic misconduct will be reported to the Office of Academic Integrity.
Other violations of academic misconduct include, but are not limited to, cheating, plagiarism, fabrication (e.g., falsifying data), knowingly assisting others in acts of academic dishonesty, and any act that gains or is intended to gain an unfair academic advantage.
Academic dishonesty has a far-reaching impact and is considered a serious offense against the university. Violations will result in a grade penalty, such as a failing grade on the assignment or in the course, and disciplinary action from the university itself, such as suspension or even expulsion.
For more information about academic integrity see the student handbook or the Office of Academic Integrity’s website, and university policies on Research and Scholarship Misconduct.
Please ask your instructor if you are unsure what constitutes unauthorized assistance on an exam or assignment or what information requires citation and/or attribution.