Probabilistic Aspects of Financial Modeling

MATH5110/6010, Spring semester, 2021

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: French Hall 4302.
Office Hours: by appointment.
Class meeting: synchronous online lectures, Wed 3:35pm-4:30pm, two more pre-recorded lectures per week. All lectures will be available via Canvas.

Textbook

Course description

This course covers two fundamental probabilistic models in mathematical finance: the (discrete-time) binomial model and the (continuous-time) Black-Scholes model. The financial applications serve as the motivation of studying these two models mathematically, but are not the focus on this course. The two models themselves exhibit appealing properties and hence deserve further investigation from probabilistic point of view alone. Our treatment of binomial model will be self-contained, illustrating the role of martingales. For Black-Scholes model, however, we shall spend most of the time on the basics of Brownian motions (staring from random walks), stochastic calculus and very briefly stochastic differential equations (with occasional sketched proofs only). The presentation of the Black-Scholes model will be based on formal calculation only.

No prior knowledge on finance is required. The course would be helpful to students interested in stochastic modeling in general.

If you find the course materials interesting and are looking for an opportunity for capstone projects, please read here first.

Grades

Letter grades: A(90%), A-(85%), B+(80%), B(75%), B-(70%), C+(65%), C(60%), C-(55%).

Tentative Schedule

There will be 7 homework sets, to be posted at Canvas. All exams are take-home.