FinM 345/STAT 390 Stochastic Calculus
Autumn 2009
Mondays, 6:30-9:30PM, Kent 120, Chicago;
Mondays, 7:30-10:30 pm, UBS, Stamford;
Tuesdays, 7:30-10:30 am, Spring, Singapore
Visiting Professor Floyd B. Hanson
(hanson at math dot uchicago dot edu)
30 November 2009
- Instructor: Floyd B. Hanson (hanson at math at uchicago dot edu).
- Office Hour: Monday, time (5PM?), FinMath Lounge/Lab E7;
weeks 3 & 4 in Singapore.
- Webpages:
- Chicago Teaching Assistants:
- Sunil Kumar (sunil at uchicago dot edu).
- Dan Wang (danwang at uchicago dot edu).
- Jin Zhang (jzhang26 at uchicago dot edu).
- Ting Zhang (tingzhang at uchicago dot edu).
- Office Hours: 5:30 to 6:30 on Friday at E117
- Review Sessions: TBA
- Singapore Teaching Assistants:
- Wei Khing For (weikhing at uchicago dot edu).
- Sanjeet Singh (sanjeet at uchicago dot edu).
- Ronnie Thomas (ronniethomas at uchicago dot edu).
- Office Hours: Thursdays from 6:00pm - 7:00pm
- Review Sessions: TBA
- UBS Stamford CT Teaching Assistant:
- Manuel Zamfir (t-9manue at uchicago dot edu).
- Office Hour: TBA
- Review Session: TBA
- Class Webpage (tentative):
- Texts:
- Primary Text: FINM 345 Lecture Notes, Autumn 2009,
usually each lecture is
posted on Chalk before each lecture;
FINM 331 Lecture Notes:
- Optionally recommended:
- Optional:
- Steven E. Shreve Stochastic Calculus for Finance II: Continuous-Time Models,
Springer Finance, April 2008. (This is the Carnegie Mellon
Computational Finance course, but is more abstract and much
less applied, primarily about diffusions, getting to jumps much later in the book; however, this book is often used in the
Financial Mathematics courses here.)
- Recommended Computational System: MATLAB;
- Desmond J. Higham and Nicolas J. Higham,
MATLAB Guide, SIAM Books,
2nd Edition, 2005,
Order Code OT92.
(Comments: There is a 30% discount with SIAM student membership, but you can get a
complimentary membership
if sponsored by a SIAM member. This is probably the best
mathematical MATLAB book.)
- Also, R, S and Excel are acceptable for assignments, but you are on your own.
- Grading:
- Homework:
- There will be about 8-10 graded homework sets, and perhaps several
projects:
- A student may consult with other student about the ideas involved,
but submitted homework must be the individual student's
own work and expression.
- Nearly identical solutions, i.e., copies, will receive discounted grades with divided credit as if one problem.
- Codes and/or worksheets need to be submitted with computational solutions.
- Graphs should be professionally done with titles,
axes labels and short description or caption.
- Homework submitted via Chalk should have a unique name,
e.g., <CNETusername>_HW<N>.pdf, where
is the homework number.
- Exams: There will be a final exam,
take-home:
- Final Grade: The grade will be based upon an
average of homework and final exam scores,
weighted to reflect the number of points involved, i.e., homework
will substantially count.
Course Outline (tentative)
(Comments: This will be a more applied course than in the
past, starting from
stochastic differentials and stochastic integrals,
as in the regular calculus, except with basic probabilities,
then building up to stochastic differential equations and
their solutions,
eventually leading to financial applications and some
useful abstract notions in stochastic calculus.
Knowledge of basic probability is assumed, but you can
review background preliminaries from online sources
given below.)
- Introduction to Stochastic Diffusion and Jump Processes:
Basic properties of Poisson and
Wiener stochastic processes. Based on the calculus model,
differential and incremental models are discussed.
The continuous Wiener processes model the background or central part of
of financial distributions, while the Poisson jump process models
the extreme, long tail behavior of crashes and bubbles of
financial distributions. ... 1-2 Lectures
- Stochastic Integration for Stochastic Differential Equations:
While the stochastic
differentials and increments are useful in developing stochastic
models and numerically simulating solutions, stochastic
integration is important for getting explicit solutions or
more manageable forms. ... 1 Lecture
- Elementary Stochastic Differential Equations (SDEs):
The stochastic chain rules for jump-diffusions with simple
Poisson jump processes, starting from diffusion chain rules
to jump chain rules to jump-diffusion chain rules. Time-varying
coefficients are also considered. ... 2 Lectures
- Stochastic Differential Equations for General
Jump-Diffusions:
Stochastic differential equations with compound Poisson
processes, i.e., including randomly distributed jump-amplitudes,
state-time dependent coefficients, multi-dimensional SDEs,
Martingales and finite rate Levy jump-diffusion formulations. ... 2-3 Lectures
- Applications to Financial Engineering:
Generalized Black-Scholes-Merton option pricing analysis,
option pricing for jump-diffusions and stochastic volatility,
using risk-neutral measures; also the important
event Greenspan process. Of course, financial models
and motivations will be used throughout the course.
... 1-2 Lectures
- Time Series Introduction and the relationship
to SDE models: Time series models such as the
discrete AR (autoregressive), MA (moving average),
ARMA (combined), and ARCH (conditional "volatility")
models, as time allows. ... 1-2 Lectures
Prerequisite Knowledge:
- Introductory Probability: see for instance,
- Very Basic MATLAB:
- The
MATLAB Student Version comes with the statistics
and other toolboxes. However, MATLAB will be introduced in the
course as examples and demonstration codes will be given in
the lectures as well as posted online. Heavily rely on
MATLAB Help Windows.
- See also Hanson's
Online MATLAB Programs mentioned above.
- See also Professor
Nygaard's review sessions on various topics, in particular
on statistics.
Some Related Resources of the Instructor and Prior FinM 345:
Web Source: http://www.math.uchicago.edu/~hanson/finm345a09.html
Email Comments or Questions to
fhanson at math dot uchicago dot edu )