Instructor: Jianfeng Zhang, KAP 248E, (213)740-9805, jianfenz@usc.edu     dornsife.usc.edu/jianfeng-zhang/

Grader: Jayson Grassi, grassi@usc.edu

Time and location: WF 2:00 – 3:15pm, THH 208

Office hours: WF 12:30-2:00pm at KAP 248E, or by appointment

Textbooks and Reference Books: (Buy either Bjork’s book or Shreve’s two books, the others are optional)

  • 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
  • Introduction to the Economics and Mathematics of Financial Markets, By Cvitanic and Zapatero, MIT Press, 2004

Prerequisites: High level of undergraduate probability theory (e.g. Math 407) is required. Some knowledge on stochastic processes, partial differential equations and financial derivatives (e.g. options) will be very helpful.

Exam Dates:

Midterm Exam: October 16, Wednesday

Final Exam: 12/13, Friday, 2:00pm-4:00pm

Course Content: 

This course is the first 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 focus on the basic materials, and more advanced topics will be provided next semester in 530B.  We will start with the discrete time option pricing and hedging theory, which covers most financial topics we are interested in but requires only elementary probability theory. We next introduce the basic theory of Stochastic Calculus, for which the discrete time model also provides the perfect motivation. Finally we study the continuous time option pricing and hedging theory, in particular the Black Scholes model.

Some important financial concepts include: contingent claims, self-financing portfolios, hedging strategy, risk neutral measure, arbitrage free markets, complete and incomplete markets, American type options. Some topics of Stochastic Calculus are: Brownian Motion, filtration, stochastic integration, Ito’s formula, Girsanov transformation, martingales, martingale representation theorem, stochastic differential equations, and possibly some basic materials of backward stochastic differential equations.

I will use my own lecture notes. The textbooks and the reference books serve as main reference books.

Grading and Examination Policies 

30% of the grade will be based on homework assignments, 25% on the midterm exam, and 45% on the final exam. The grade cutoffs will be decided after the final exam, based on the students’ overall achievements.

The 75 minutes Midterm Exam will be given in regular class time. The Final Exam will be comprehensive, with an emphasis on the materials covered after the Midterm Exam. All exams are closed book, but students are allowed to bring one formual sheet.

Homework problems will be assigned biweekly. No late homework will be accepted, but missed homework with valid reasons can be excused. 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 

Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me (or to TA) as early in the semester as possible. DSP is located in GFS 120. Its phone number is (213) 740-0776 and website is: https://dsp.usc.edu.

Statement on Academic Integrity 

USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect one’s own academic work from misuse by others as well as to avoid using another’s work as one’s own. All students are expected to understand and abide by these principles. Scampus, the Student Guidebook, contains the Student Conduct Code and the recommended sanctions: https://policy.usc.edu/student/scampus/. Students will be referred to the Office of Student Judicial Affairs and Community Standards for further review, should there be any suspicion of academic dishonesty. The Review process can be found at: https://sjacs.usc.edu/students/.