MATH 6910 - Stochastic Calculus in Finance
This course will introduce the basic ideas and methods of stochastic
calculus and will apply these methods to financial models, particularly the
pricing and hedging of derivative securities. We will start by introducing the
concepts of arbitrage, hedging and risk-neutral pricing in a discrete-time
setting, and will then move to more sophisticated continuous-time models. Along
the way we will cover the following mathematical topics: Brownian Motion,
Stochastic Integrals, Ito's Formula, Martingales, and Girsanov transformations.
Prerequisites: A solid knowledge of calculus and
basic probability theory (random variables, expectation, variance, etc.) will be
assumed. The necessary concepts from measure theory and stochastic processes will be
introduced as they are needed.
Text: Steven E. Shreve, Stochastic Calculus for
Finance II: Continuous-Time Models, Springer.
Instructor: Hanna Jankowski
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Office: N621B Ross
FINAL: Thursday, May
14th, 7pm-10pm, VH3009.
Monday, May 11th, 2-3 pm, in my office.
Wednesday, May 13th, 5-7pm, in Ross N638.
Thursday, May 14th, 3-5pm, in my office.
N.B. Please note that I am away starting May 18th.
- [May 13] I have marked the third assignment. For those of you with
a mailbox in Ross, I've put your there. I will bring the remaining to
the office hours today. All left over will be placed in an envelope for
you to pick up outside my door.
- [May 13] I have just posted
partial solutions to the third assignment. Please take a look at these!
- [May 12] I get a lot of questions about this one: my
current version of the exam is 9 questions, of which you have to
do 8. I say "current version" because I'm still fiddling with
- [May 11] Here (new) and here (midterm) are the complete aid sheets for the
exam (thanks to Pavan and Cartland for their contributions). Typos on the
midterm version have been corrected, but not on the scanned version above.
Let me know if you see any typos in the new addition. FYI - I didn't put
any Ito formula stuff on there, because I think it's too important to not
be committed to memory. Also, I didn't put on any formulas for dX_t,
d(D_tX_t), d(D_tS_t), ... I think that you should know dX_t from memory,
and all the others can be derived, so you don't need them. If I remember,
I will try to re-scan these on the good scanner when I have some spare
time, so that you have a version that prints better.
28] In the L9 notes, pages 6 and 7 should be
- [April 26] Here is your aid sheet
from the midterm. I will provide this with your final as well.
Suggestions (please, more detailed than last time) for the final
are due no later than 3pm on Monday, May 11th.
- [March 31] A conditional probability problem.
- [March 22] In the next problem set I ask you to do some
simulations (they help), using R. If you're not very
familiar with computers, or would just like some more info on
what R can do, here
is a step-by-step guide.
You can access the discussion forum here. All
students enrolled in the class should be able to have access. My hope is that the forum will be used to discuss homework/assignment
problems or class concepts. I will try to check the forum every other day or so to answer
To access the forum you will need an AML account. Instructions should be there (in
the link) on how to get one. If you have trouble, let me know.
This is the first time that I'm using MOODLE at York, so there will probably be a short
period of time before I am fully familiar with the system and how best to use it for our
needs. I expect that there will be an adjustment period for us all. For now, if you have
questions about how to use the forum, you can send me an e-mail and I'll try to answer it.
- [Assignment 1] [partial
solutions] Due Monday, April
- Q6(d): the second distribution mu_2 should have mean theta_2 (and
- Q5: the sigma algebra in the math display should be called G, and not
- Q8(b): F_n is the sigma algebra generated by X_1 through X_n, that is
F_n=sigma(X_1, ... , X_n). The sigma is missing in the type up.
- [Assignment 2] Due Monday, April
- [Assignment 3] [partial
solutions]Due Monday, May
11th by noon.