# 46-944: Stochastic Calculus for Finance 1 Spring 2019

Instructor Gautam Iyer.   WEH 6121.   gi1242+944@cmu.edu. TTh 2:45--4:15PM in POS 145 (Pittsburgh), telecast in TPR NY1 (New York) I will lecture from New York on Tue 1/22, and Th 2/21. Tue 10:00--11:00pm (Pittsburgh only) Tue 12:00--1:00pm (On Zoom, NY students only, on request). (For Zoom office hours, please email me at least two hours before the start of office hours. Download and install Zoom, and you will then be added to a conference on Zoom during office hours.) David Itkin.  WEH 7211.   ditkin@andrew.cmu.edu. Wed 4:30--5:30 (Pittsburgh) Wed 2:30--3:30 (On Canvas, NY students only, on request) (For Canvas office hours, please email the person conducting the office hours at least two hours before the start of office hours. You will then be added to a conference on Canvas during office hours.) Fri 12:30--2:00pm in POS 145 (Pittsburgh), telecast in TPR NY1 (New York). Thursdays, at 2:44:59PM. (Late homework policy) Thu, Feb 7, in class Wed, Mar 6, 5:30PM--8:30PM in POS 145/146 Wed, Mar 20, 5:00pm--8:00pm (room TBA) mscf-944 (for course announcements and discussion. Please subscribe to this list.) Class discussion board here. Grades etc. are available here. (Current students only). Videos of lectures and recitations are available here. (Current students only).

## Course Description

The first half of this course introduces martingales, Brownian motion, Itô integrals and Itô’s formula, in both the uni-variate and multi-variate case. This is done within the context of the Black-Scholes option pricing model and includes a detailed examination of this model. The second half of the introduces exponential martingales and the Girsanov theorem. This is done in the context of risk neutral measures and the fundamental theorems of asset pricing.

### References

• Brief lecture notes. (A tablet friendly version is here, and the full TeX source is here.)
Note: I am currently (Spring 2019) updating these notes. While the bulk of the matter and later parts of the notes should be largely unchanged, the first few chapters will be changed as the semester progresses. If you want to be notified of changes, you should create an account on GitLab, and watch the repository gi1242/cmu-mscf-944.
• Stochastic Calculus for Finance II by Steven Shreve. (We will cover roughly the first five chapters.)

## Class Policies

### Lectures

• If you must sleep, don’t snore!
• Be courteous when you use mobile devices.

### Homework

• Homework is due at the beginning of class on the due date.
• Late homework policy: Homework turned in within 48 hours of the deadline will be accepted.
• Late homework turned in within the first 24 hours of the deadline will receive a 10% penalty. In particular, homework turned in even one nanosecond after class starts, will receive this penalty.
• Late homework turned in within the next 24 hours will receive a 25% penalty.
• Homework more than 48 hours late will not be accepted.
• To account for unusual circumstances, your lowest homework will not count towards your grade.
• I will only consider making exceptions to the late homework policy for unexpected severe emergencies that require your absence for more than 12 days. Following MSCF policy, I will not make exceptions on account of job interviews or career fares.
• Solutions will usually be posted 48 hours after the homework deadline. Due to holidays or exams solutions to some assignments might post earlier. In this case, you will be notified of this in advance, and late homework will not be accepted after solutions have been posted.
• Your homework must be uploaded as a PDF on Canvas. If you use pencil and paper to write your homework, then you must scan and upload it. Please ensure your scans are a high quality PDF, as photos of your homework will not be accepted.
• You may collaborate on the homework, however, you may only turn in solutions which you fully understand and have written up independently. Violation of this policy will be treated seriously according to procedures in the MSCF student handbook.

### Exams

• No notes, calculators, computational aids, or internet enabled devices are allowed during exams.
• You may not give or receive assistance during exams.
• Violation of these policies will be treated seriously according to procedures in the MSCF student handbook.
• If you earn a C+ or lower, and have at least a 70% average on the homework, you may take the makeup final. Your performance on the makeup final can not reduce your grade, and can only increase your grade in the course by at most a full letter, up to a maximum of B–.
• Explicitly, if $F$, $M$, and $H$ are your numerical grades on the final, midterm, and homework respectively, then your overall grade $G$ will be computed by