Fall 2012 MATH 180 Introduction to Financial Mathematics

TTh 11-12:15. Room 380-380Y.

Instructor:

Isabelle Camilier

Room 383 FF (math building)

Email: camilier (at) stanford (dot) edu

Please put 'MATH 180 your request' in the object of your email.

Office hours:

Wednesdays 2:30-4:15 pm and Thursdays 2:15-3:15 pm, or by appointment (email me).

Course Assistant:

Xiaodong Li

Email: xdli1985 (at) stanford (dot) edu

Office hours: Monday, Tuesday, Thursday 1:00-2:00 pm.

Room: 380T.

Syllabus

Financial derivatives: contracts and options. Arbitrage, interest rate, and discounted value. Geometric random walk and Brownian motion as models of risky assets. Self-financing replicating portfolio. Black-Scholes pricing of European options. Implied volatility.

Prerequisites: At least one probability class. You should be familiar with random variables: discrete random variables (such as binomial random variables), continuous random variables (especially Gaussian random variables, we use them all the time). You should be able to compute expectations and Laplace transforms.

Corequisites: 151 or STATS 116 . It is also a good idea to take at least one PDE class (Math 131 for instance)

Assignments

Homework (20 %) . 6 problem sets. Lowest score dropped. Weekly homework will be posted by Thursday night and will be due in the class on Thursday the following week. No late homework. Individual solutions must be submitted.

Midterm exam (30%) in class. Thursday October 25. During class time (11 a.m-12:15pm).

Final exam (50%) in class on Thursday December 13, 3:30 pm-6:30 pm.

Textbooks (optional)

• Arbitrage Theory in Continuous time by Bjork.
• Options, Futures and other derivatives by Hull

Handouts (lecture notes) will be posted on Coursework.

Weeks 1-2 Introduction.

Weeks 2-4 Discrete time finance.

Weeks 5-10 Continuous time finance.

Schedule

	Topics	Additional reading?
Tu 09/25	Introduction. Definitions.	Hull 1
Th 09/27	Derivatives, forward contracts, call and put options	Hull 1, 9.1-9.4
Tu 10/02	Arbitrage, call-put parity	Hull 4.2, 10,11
Th 10/04	Discrete time models. One step model.
Tu 10/09	Two steps model (and option pricing).	Hull 12, 20.1,20.2
Th 10/11	Two steps model (and option pricing). Martingales. HW1 due
Tu 10/16	Discrete time n steps models (binomial trees).
Th 10/18	Pricing American options. HW2 due
Tu 10/23	Convergence towards continuous time models. Midterm review.
Th 10/27	Midterm exam
Tu 10/30	Continuous time models.
Th 11/01	Gaussian random variables. Brownian motion, stochastic processes.	Hull 13
Tu 11/06	Ito formula. HW3 due.
Th 11/08	Pricing options in continuous time models. Black-Scholes PDE.	Hull 14
Tu 11/13	Black-Scholes formula.
Th 11/15	Greeks. Volatility. HW4 due	Hull 18
Thanksgiving break
Tu 11/27	Introduction to Monte-Carlo methods.
Th 11/29	Solving the Black-Scholes PDE. HW5 due
Tu 12/04	Additional topics: implied volatility, stochastic volatility, options with dividends.
Th 12/06	Review. HW6 due.
Thursday, December 13	Final exam