Welcome to Mathematical Methods For
Quantitative Finance.
For this first video, I'm just going to do
a
quick overview of what you can expect
during this course.
So, I'm your instructor Kjell Konis.
First name rhymes with cello, so cello
without the o.
For evaluation for this course, this is
something
I can't do really well in a massive
setting.
So what I've come up with are discussion
questions.
And so, at the end of each video, there
will be a discussion question.
It should be something that if you've
understood the
video that you'll be able to answer just
within a few minutes.
And then you're encouraged to share your
solution on on the forum.
And so hopefully, sort of just
organically,
there'll be some correct crowd sourced
solutions.
And additionally, there'll be weekly
homework assignments.
And these will be something, these will be
more difficult problems.
So the idea will be that you watch all of
the
videos for one particular week, and then
you
should be able to do the homework
assignment.
It should take you probably 3 or 4 hours,
about
the same amount of time as the videos take
to watch.
And then there will be a due date for
these
homework assignments, and after the due
date, I will post solutions.
And again, because it's a mathematics
course, it's going
to be something that's difficult for me to
actually grade.
So, you'll be expected
to just go through the solutions and grade
yourself.
And then one last thing I, I want to
mention
at the very beginning, is Wolfram/Alpha,
this is a website.
It's a lot like Google, except
it's for asking and answering mathematics
questions.
A lot of what would normally be in a first
year calculus
course or a first year linear algebra
course is some rote memorization.
So there're just certain functions where
you
have to memorize this is the derivative
of that.
I don't really want to concentrate so much
on just having you memorize things like
this.
So you can, and there are a lot of tools
on line now.
So my favorite right now is Wolfram Alpha.
And so, for simple functions, things like
sine, cosine, logarithm, you can
just ask Wolfram Alpha, and just type into
the, into the search bar.
You know, what is the derivative of the
logarithm and it'll think for
a couple seconds, and it'll give you the
answer.
So what the course is going to cover.
So, the numbers on the left here, these
correspond to the weeks of the course.
So this will be an eight week course.
The first week is going to be a review of
limits and derivatives.
The second week will be integration.
So, this is going to be essentially a two
week review
of what you would normally learn in a
first year calculus course.
And then, we'll move onto partial
derivatives.
And so, partial derivative is something
you
can take using the same techniques that
we'll cover in week one, but it's defined
for a function of several variables.
And then multiple integrals, week 4, is
the same idea except for integration.
So, it's basically how you can make sense
of integrals of functions that take
several variables.
And the reason these topics are, are sort
of divided into two
bunch, bunches, so we have one through
four and then five through eight.
What I'm really aiming for with the first
four weeks is I want, I
want you to be able to take
the derivatives of the Black Shoal's
pricing formula.
And since this is a math class, really
what I'm
going to be focusing on is the mathematics
of this.
So, the Black Shoals formula is just
function of many variables.
And so, if you understand the, the
concepts
that are, that we're going to cover in
these
first 4 weeks, then you're going to be
able
to take the derivative of the Black Shoals
formula.
And these derivatives are something that's
commonly known as the Greeks.
The second set of lectures is going to be
on linear algebra, Legrange
multipliers and numerical methods.
And the,
the problem I'm looking at in this second
set of the course
is something called minimum variance
portfolio.
And so it'll turn out is, when we look at
linear algebra,
we're really going to be concerning
ourselves
with solving systems of linear equations.
Lagrange multipliers is going to give us
the
tools we need to calculate the minimum.
So we want to find a portfolio of assets
that has the minimum variance.
And then it's going to turn out that when
we use this Lagrange multiplier approach,
it's going to give us a system of linear
equations that need to be solved.
So, we'll have done that already in weeks
five and six.
And then finally in week 8, I'm going to
start using something called the R
Environment for Statistical Computing.
It's, software program
for working with vectors and matrices, and
also, for it's also a programming
language.
It's something very similar to MATLAB, if
you already have some experience with
that.
And we'll actually try and solve some
problems using a computer to do that.
So there's one recommended textbook for
this
course, it's Primer for the Mathematics
of Financial Engineering by Dan Stefanica.
This is a very a much more general book
than, than this course will be.
So this book contains several mathematical
topics as
well as the financial applications of
those topics.
I'm going to just choose a few of the
mathematical topics and
I'm going to focus much more on just the
mathematics and not so much
on the, on the financial applications.
And the idea being that after you do this
course, you'll be a lot ready, better
prepared to go on to a course where
they're going to focus more on the
finance.
And it'll be sort of like you, you sort of
learn one thing first and then the other.
And the idea being that will be a bit
easier for you
than trying to learn both the mathematics
and the finance in tandem.
And one thing that's nice about this
course,
is there's also a solutions manual which
has detailed
solutions for all of the homework
assignments in this book.
And so, I, I recommend if you, if you can
get your
hands on the textbook, that you also try
and get the solutions manual.
And then on your own time, try and work
through some of the, the exercises in in
the textbook.
And then use the solutions manual to make
sure that
you're using the right approach and
getting the right answer.
And the last recommended book that I
wanted to mention.
So this is the first year calculus book
that they use at the University of
Washington.
And so that's why I've put it on this
slide and have a picture of it.
But really any first year calculus book
will be
sufficient, and this one is over a
thousand pages long.
And really what you're looking for is just
sort of and encyclopedia of calculus.
So that when you have questions,
you have somewhere to go and look it up.
So, Calculus, Early Transcendentals by
James Stewart.
pretty much any edition would be
sufficient,
or any other first year calculus book.
But if you get your hands on a book like
that, that is going
to be a valuable resource for doing some
of the exercises in this class.
Okay?
So that's all I have for the introduction,
and
I hope you enjoy the rest of the course.