Instructor: Jianfeng Zhang, DRB 228, (213)740-9805    jianfenz@usc.edu     http://almaak.usc.edu/~jianfenz
Time and location: MWF 10:00pm – 10:50pm, KAP 163.
Office hours: M 1-2 (Math Center), W 1-2 (DRB 228), F 2-3 (DRB 228)

Textbook:

  • Arbitrage Theory in Continuous Time, second edition by Tomas Bjork, Oxford University Press, 2004

    Reference Books:

  • Introduction to the Economics and Mathematics of Financial Markets, By Cvitanic and Zapatero, MIT Prss, 2004
  • 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: Stochastic Processes (e.g. Math 506) and some basic knowledge on financial derivatives (in particular options)

    Exam Dates:

  • Midterm Exam: 3/2, Friday
  • Final Exam: 5/7, Monday, 8:00am-10:00pm

Course Content: 
This course provides mathematical theory and probabilistic tools for modeling and analyzing security markets. A very brief review of stochastic integrals, Ito’s rule and Girsanov theorem will be given. The main topics are discrete and continuous time option pricing theory, and term structure of interest rate models. We will study several models in detail: binomial model, Black-Scholes model, and Heath-Jarrow-Morton model etc. Some important concepts include: contingent claims, self-financing portfolios, risk neutral measure, arbitrage free markets, complete and incomplete markets. We will study the two fundamental theorems in option pricing theory, and introduce the two representations of the fair option price – as an expected value and as a solution to a Partial Differential Equation of Feynman-Kac type. European type options, American type options and various exotic options will be introduced, and the change of numeraire technique will be used. If time permits, we will introduce some extensions and/or recent developments on the subject.

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 by the instructor after the final exam, based on the students’ overall achievements.

The one hour 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 sheet of formulas.

Homework problems will be assigned in lectures, and collected weekly. 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.