Probabilistic Aspects of Financial Modeling
MATH5110/6010, Spring semester, 2019
Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall.
Office Hours: Fri 2:30-3:30pm, other time by appointment.
Class meeting: MWF 12:20pm - 1:15pm, 816 Swift Hall.
Textbook
- Lecture slides updated at Blackboard. No textbook required.
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. For Black-Scholes model, however, background on stochastic calculus and stochastic differential equations will be sketched and the analysis of the Black-Scholes model will focus on formal computation only.
Grades
- MATH6010 students: homework (25%) + quiz (25%) + midterm (25%) + final (25%).
- MATH5010 students:: homework (25%) + 2 $\times$ max(quiz,midterm) (50%) + final (25%).
Tentative Schedule
Homeworks will be posted at Blackboard.
- Week 1 (Jan 14): Review of probability.
- Week 2 (Jan 21): No class on MLK, Monday (Jan 21).
- Week 3 (Jan 28): Binomial model. Portfolio, path-space point of view. HW1 due Mon, Q1 Fri.
- Week 4 (Feb 4): Martingale, risk-neutral probability measure, no arbitrage for binomial model.
- Week 5 (Feb 11): Options pricing HW2 due Wed.
- Week 6 (Feb 18): Replicating portfolio Q2 Mon.
- Week 7 (Feb 25):
- Week 8 (Mar 4):
Brownian motion. HW3 due Mon, Q3 Fri.
- Week 9 (Mar 11): Midterm Wed.
- Week 10 (Mar 18): Spring Break.
- Week 11 (Mar 25): Stochastic calculus. HW4 due Fri.
- Week 12 (Apr 1): Q4 Wed.
- Week 13 (Apr 8):
- Week 14 (Apr 15): Black-Scholes model. HW5 due Mon, Q5 Fri.
- Week 15 (Apr 22):
- Week 16 (Apr 29): Final Exam.