Syllabus

314-398-3186 (cell)

Washington University Olin School

Mathematics is the language of modern financial economics, and finance makes extensive use of mathematical tools commonly used in Economics and Engineering. This course is intended to provide students with an introduction (or review) of these tools.

This course is for first-year MSF students in the Corporate Finance track, and there is no formal prerequisite beyond being in this track. As in most quantitative courses, students with the strongest math backgrounds will breeze through most easily. Mastering the material in this course will make subsequent courses and career easier.

Please do not get behind in this course! The lectures will make use of tools developed in previous lectures and will make links to earlier topics. This is good reinforcement for students who are keeping up, but it can be a problem for a student who gets behind. If you are starting to get behind, please seek help before it becomes a big problem. You can obtain help from me, the TAs, or your friends.

**Feedback** Some of these materials are new this year,
so I am especially grateful for any feedback.
A good job of pointing out any problems with the course so I can make
it better will increase your grade at the margin.

**Organization of the course** The course will
be in a traditional lecture format, with problem sets and a final
exam.

**Course Requirements**
Grades will be based
70% on the final exam and 30% on the problem sets. Class
participation may change a grade near a cutoff, as may useful
feedback on the course materials.
Understandably, job search or other obligations may
occasionally conflict with class. It is your responsibility to
find out from your classmates what you miss when you are
absent.

**Problem Sets** The problem sets are available
on my web page or through Blackboard (which also points at the
web page). Problem sets have several parts. The normal parts
without any special label are required for all students. The
"extra for experts" parts go beyond the regular course material
for students who find the class easy.
The "challengers" are very tough questions
intended to be hard for even the very best students.

**Rules for Problem Sets** Students are permitted
to get help from anyone for the normal and extra-for-experts parts
of the homework, but students are required to do their own write-ups.
The challenger questions are
strictly individual efforts. All homeworks and related programs
should be handed in through Blackboard by the date listed on the
course materials page.

**Final Exam** The final exam will be held Thursday,
October 20, 2:30-4:00 PM, location TBA.
This will be a closed-book exam, and no portable electronic devices
such as calculators and cell phones,
or written or printed information you bring with you
can be used in the exam. (Unfortunately, many portable electronic
devices can store information and can be used for communications, so
allowing students to use them makes cheating too easy.)
Usually, my exams are straightforward
and if you have done the homeworks yourself, go to the lectures,
and study the slides, you should do well. If you
miss the exam for whatever reason or you need to take the exam at
another time, let me know in advance and I will
substitute an oral exam. This avoids even the appearance that someone
may have access to exam questions or answers in advance. This is
also ``incentive compatible'' because most students do not like oral
exams and will avoid missing the exam without a good reason.

**Course materials** Course materials include
slides and problem sets that are available on the web. Instead of a
text, there are links to web sites that have useful supplemental
materials and some optional books are on reserve. There is no separate
packet.

**Transparencies** The lectures will be based
on transparency slides that are available on the Web.
You will probably want to print a paper copy of the slides before
each class for cross-reference during class, for study, and for
taking notes on. The slides are available from Blackboard or
my teaching page on the WEB: http://dybfin.wustl.edu/teaching/ or http://phildybvig.com/teaching/. (Actually the Blackboard page is a link to my web page.)
Many of the slides were created by Yajun Wang (a brilliant finance PhD student
who finished recently and is now teaching at the University of Maryland), and they do an excellent job of teaching the material
in a straigthforward way. I have also created a number of slides myself,
and in places I have revised her slides to suit our class.
I also invite you to visit my home page and research page:
http://dybfin.wustl.edu/.

**Textbooks** I am not assigning any textbooks this year,
and I will rely more on web-based materials. In case you like learning from
books, I am placing several books on reserve that can give you an
alternative lens on the materials.
If you are going to buy one book, it should be Mathematics
for Economists, 1994, by Carl Simon and Lawrence Blume. The other
two books I am putting on reserve are
Probability and Statistics, 2002, by
DeGroot and Schervish, and
Numerical Methods for Engineers, by Steven Chapra
and Raymond Canale. This last book is for people who want to go beyond
the class and learn about numerical methods for some things we do
analytically in the class.

**Topics** We cover many topics that are essential for
working with sophisticated financial models. Here is an approximate
outline:

- probability and statistics, part 1 (2 lectures). Discrete random variables, mean, variance, standard deviation, skewness, kurtosis, general moments, and linear regression.
- calculus review (1 lecture). Derivatives, integrals, fundamental theorem of calculus, l'H\^opital's rule, and Taylor series
- probability and statistics, part 2 (1 lecture). Continuous random variables, probability density function, cumulative distribution function, moment generating function, joint distribution, univariate and bivariate normal distribution, independence.
- vectors and matrices (2 lectures). Matrix notation and conventions, matrix inverse and solving linear equations, symmetric matrices, definiteness, and eigenvalues and eigenvectors.
- multivariable calculus (1 lecture). Matrix representation of derivatives, gradients, and Jacobians, the chain rule in multivariate calculus, and change of measure in integrals.
- optimization (1 lectures). First- and second-order conditions and Kuhn-Tucker conditions.
- ordinary differential equations (2 lectures). First- and second order linear ordinary differential equations.
- probability theory (2 lectures). Random variables, probability density functions, expectations, variance and covariance, bivariate normal distribution, exponential distribution. Tie-ins to previous subjects: mean and covariance matrices, portfolio optimization.
- X-treme review (2 lectures)

**Readings** The lectures and slides are self-contained, so
it is not necessary to do any additional readings. If you want to do some
readings to get another perspective, here
are recommendations about how to
time them with the lectures. In most cases, there is a lot information
in the text that we don't need in the course, and there is some
information in the course not covered in the book. SB, CC, and DS are the
three optional textbooks given above: Simon and Blume, Chapra and Canale,
and DeGroot and Schervish. OTG-ML is Matlab's Optimization Toolbox User's Guide. D is Paul Dawkins' online
class notes on differential equations:http://tutorial.math.lamar.edu/terms.aspx.

Here is a set of reading suggestions with approximate schedule:

main topic | date(s) | readings |
---|---|---|

probability and statistics, part 1 | Sept 6 and 8 | DS ch 3, 4, and 5 |

calculus review probability and statidstics, part 2 | Sept 13 and 15 | SB ch 2, 3, 4, 5, A2, A4 |

DS ch 3, 5.6, and 5.7 | ||

vectors and matrices eigenvalues and eigenvectors | Sept 20 and 22 | SB ch. 7, 8, and 9 |

SB ch. 23 | ||

multivariate calculus optimization | Sept 27 and 29 | SB ch. 14, 16.1, and 16.2 |

SB ch. 17, 18, and 19 | ||

ordinary differential equations | Oct 4 and 6 | D pp. 20-33, 102-121, 137-155, and 340-344 |

X-treme review | Oct 11 and 13 | N/A |

**Additional resources on the web** (coming soon)

**Teaching Assistance** We will be assisted by
Chen "Tracy" Li and Matt Templemire. They are both third-semester MSF
students. Their and my contact information:

Chen "Tracy" Li | 314-757-3607 | |

Matt Templemire | 573-291-3067 | |

Phil Dybvig | 314-398-3196 |

**About you** In addition to enrolling through
the proper authorities, please send me an e-mail with the
following information:

- name
- program and year in program (probably first-year corporate-finance-track MSF)
- your background in finance and mathematics
- telephone number(s)
- any other information you care to add

**About me** Many years ago, I was a tenured full
professor at Yale, and I came to Wash U in 1988 in the hope of
building a top finance group, which we have done. More
information on me is in the chatty blurb at
http://dybfin.wustl.edu/misc/about.html or in my vitae at
http://dybfin.wustl.edu/misc/vitae.html.

**Integrity** Students are expected to conform
to the Olin School's Code of Conduct and Code of Professional
Conduct. If I learn about a violation, I will report it (with
some sadness and a strong sense of duty).

**Summary** I invite you to join me in
exploring some mathematical tools that are useful for finance.