This is the sequel to Stat 39000/Math 34500. We cover topics in the theory of stochastic calculus and the pricing and hedging of derivative securities, including

• risk neutral measures for general numeraires
• hedging strategies for exotic options
• incompleteness: discontinuity, untraded processes, and statistical uncertainty

The course is offered in collaboration by the Department of Statistics and the master's program in Mathematical Finance. Stat 39000-39100 are part of the Statistics and Finance program. MathFin34500-34600 are part of the Master's program in Financial Mathematics. There will be weekly homework assignments, and midterm and final exams. The course assistants will conduct weekly help sessions on Friday afternoons.

Exams:

• Midterm: Wednesday, February 6, 6:00--7:30 p.m. (Eckhart 133)
• Final: Wednesday, March 13, 6:00--9:00 p.m. (Eckhart 133)

Prerequisites:

• Stat 391: Stat 390 or consent of instructor (enforced)
• Math 346: Math 345, and enrollment in (or permission from) the Financial Mathematics Program

Texts:

• Required:
• Musiela, M., and Rutkowski, M. (1997). Martingale methods in financial modelling. Springer.
• I. Karatzas and S.E. Shreve (1991). Brownian Motion and Stochastic Calculus. Springer-Verlag.
• I. Karatzas and S.E. Shreve (1998). Methods of Mathematical Finance. Springer-Verlag.

 

• Additional papers will be handed out during the course.