18.440  Probability & Random Variables

Another practice final

I just added the Fall 2012 final exam (along with the solution set) to the course web page, so you have one more practice exam that you can take. This exam together with the posted spring 2011 final exam should give you a pretty good sense of what our final exam will be like.

I'd also like to point out that the document linked to by the label "Practice Final Problems" has some problems that are more difficult and time-consuming than what would appear on an actual final exam (these are "practice problems" but are not problems from actual final exams), including a couple of problems on risk neutral probability that go beyond what we covered in class.

Best,

Scott

Announced on 17 May 2014  3:03  p.m. by Scott Roger Sheffield

Office hours today, Th 5/15, 3-5pm, E17-301W

Announced on 15 May 2014  10:59  a.m. by Dimiter Valentinov Ostrev

Thanks!

Many thanks for taking the class and doing probability with me for the last few months. A couple of final remarks:

1. The department has asked me to personally encourage you to submit online course evaluations. So please consider yourselves thus encouraged. I will make sure to read everything you write and consider your suggestions.

2. I have office hours today from 4 to 6 today as usual.

3. I'll try to be responsive to Piazza over the next few days, in case there are any questions that come up while you are working through practice problems. Of course, you are also very welcome to answer questions for your classmates.

Best,

Scott

Announced on 14 May 2014  12:25  p.m. by Scott Roger Sheffield

problem set solutions in "Materials"

All ten sets of solutions for the problem sets are now available on Stellar under the "Materials" tab.

Best,

Scott

P.S. Less relevantly, the "Materials" section contains a few of those silly songs, which you are welcome use the next time you find yourself leading mathematically precocious third graders in singing time. This could happen sooner than you think. The silly love song written from my hard-to-focus-on-class undergraduate days is here:

https://dl.dropboxusercontent.com/u/3925161/Math%20Major%20in%20Love%20Mix1.mp3

Announced on 12 May 2014  9:34  a.m. by Scott Roger Sheffield

final two non-review lectures

Yesterday's lecture on martingales and tomorrow's lecture on risk neutral probability are the only two lectures in the course that cover material that is not in the textbook. All of the material you need to know for the exam on these topics is contained in the lecture slides and in the short "martingale note" linked to from the course web page.

The material you are required to know about martingales is the following:

1. The definition of a martingale.
2. The definition of a stopping time.
3. The statement of the optional stopping theorem.

You can evaluate your mastery of these concepts by trying the practice exam problems, the problem set problems, and the martingale note problems.

The material you are required to know about risk neutral probability is the following:

1. Definition of risk neutral probability.
2. Relationship of risk neutral probability distribution of an asset price to the price of an "derivative" whose value is a function of that asset price.
3. How to compute the expectation of e^X if X is normal.
4. How to compute the expectation of 1_{X > a}e^X if X is normal. Here 1_{X > a} is the indicator random variable equal to 1 if X>a and 0 otherwise.

The last two items are simple mathematical ideas that come up in the derivation of Black-Scholes that you will work through on your problem set. You definitely do not need to memorize the Black Scholes formula. You are free to use Wikipedia or other sources for help if you get stuck on the Black Scholes portion of the problem set due Friday.

Best,

Scott

Announced on 06 May 2014  2:40  p.m. by Scott Roger Sheffield