Actuarial Science Program
DEPARTMENT OF MATHEMATICS
Math 476 / 567
Actuarial Risk Theory
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Fall,
2009 |
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103
Talbot Lab |
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374 Altgeld Hall |
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8:00-9:20
am TuTh |
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Phone: 244-1739 |
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Office
Hours: 3-4 pm Tues, 2-4 pm
Wed, or by appointment |
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E-mail: |
Required Text: Derivatives Markets (DM) by McDonald (2nd Edition)
Class Summaries (including Assignment Postings): See Below
Course Overview
This course covers several important and
interesting actuarial topics in the areas of stochastic processes, risk,
and financial
economics. The course will largely focus on the mathematics and
economics underlying the pricing of financial options. As part of this focus,
we will discuss stochastic processes, which involve the evolution of random
variables over time; in particular, we will explore Brownian motion as a
modeling framework for financial and economic processes. Ultimately, this leads
to ideas and techniques critical for understanding advanced actuarial and
financial risk management material, such as the Black-Scholes
option pricing model, and delta-hedging. Other important topics covered in the
course include stochastic simulation of economic and financial variables, and
the modeling of interest rates.
Overall, our goal is to explore the material
relevant to professional actuarial Exam 3F/MFE.
Accessibility
Statement
To
insure that disability-related concerns are properly addressed throughout the
semester, students with disabilities who require reasonable accommodations to
participate in this class are asked to contact me within the first two weeks of
class.
Honors
Projects
For
those involved in a Campus or College honors program, such as James Scholar,
you are welcomed to perform an honors project in association with this class.
Such a project would involve an opportunity for undergraduate research relevant
to actuarial science. Please let Prof. Gorvett know of your interest in the
first few weeks of the class.
Grading
Course grades will be
determined based on the following weights:
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Homework assignments |
20 % |
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In-class/other
assignments |
5 % |
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Group Project |
10 % |
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Exams 1 and 2 |
40 % (20% each) |
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Final Exam |
25 % |
Exams may not be made up
or taken at different times, except in extremis. In general, the grade
weight for a missed exam (provided there is a valid excuse) will accrue equally
to any remaining exams. A missed in-class or homework assignment may
not be made up; however, the lowest homework score, and the lowest two
in-class assignment scores, will be dropped when determining those parts of
your grade. Class attendance is expected; serious attendance problems may
result in a grade lower than that indicated by the weighting system above.
Please note that the
final exam schedule is prescribed by the university; in general, instructors
are not permitted to change the final exam timing of their courses.
Graduate
students taking this class for four hours of credit will be required to
complete one additional project. Performance on this project may impact the
overall grade.
Key Dates
The following are key
dates associated with this course:
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First day of class |
Tuesday, Aug. 25 |
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Exam 1 |
Thursday, Sep. 24 |
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Exam 2 |
Thursday, Oct. 29 |
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Last day of class |
Tuesday, Dec. 8 |
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Final exam (Exam 3) |
8 am, Wednesday, Dec.
16 |
In most non-exam weeks,
there will be a homework assignment and one or more short in-class assignments.
In addition, practicing actuaries will occasionally be invited to give guest
presentations to the class during the semester.
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Sep. 17, 2009 |
Registration Deadline
for Exam 3L (Casualty Actuarial Society) in Oct. 2009 |
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Sep. 24, 2009 |
Registration Deadline
for: -Exam 4/C in Nov. 2009 -Exam 3F/MFE in Nov.
2009 -Exam MLC in Nov. 2009 |
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Oct. 8, 2009 |
Registration Deadline
for Exam 1/P in Nov. 2009 |
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Oct. 22, 2009 |
Registration Deadline
for Exam 2/FM in Dec. 2009 |
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Oct. 27, 2009 |
Exam 3L (Casualty
Actuarial Society) |
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Nov. 2, 2009 |
Exam 3F/MFE |
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Nov. 3, 2009 |
Exam MLC (Society of
Actuaries) |
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Nov. 3-9, 2009 |
Exam 4/C (CBT) |
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Nov. 18-30, 2009 |
Exam 1/P (CBT) |
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Dec. 1-8, 2009 |
Exam 2/FM (CBT) |
Class Summaries
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Date |
General Topic |
Specific Class Topics |
Assignments |
Textbook |
Other Items / Links |
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Aug 25 |
Introduction and
motivation. |
Review of syllabus. Motivation via
mathematical and financial context. |
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Aug 27 |
Options |
Financial background. Call and put options. Put-call parity. |
DM, |
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Sep 1 |
Option pricing theory |
Binomial option
pricing. Portfolio replication. Arbitrage
opportunities. |
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DM, |
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Sep 3 |
Option pricing theory
(cont.) |
Binomial option
pricing (cont.). Risk-neutral pricing. Risk-neutral
probabilities. |
DM, |
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Sep 8 |
Option pricing theory (cont.) |
Mathematical
structure: delta and B. Constructing binomial
trees. |
DM, |
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Sep 10 |
Option pricing theory (cont.) |
Multiperiod binomial trees. American options. |
DM, |
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Sep 15 |
Option pricing theory
(cont.) |
Real probabilities. Real stock and option
rates of return. |
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DM, |
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Sep 17 |
Black-Scholes Model |
Historical volatility. Black-Scholes formula. |
DM, |
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Sep 22 |
Review for Exam # 1 |
Will go over Old Exam
in class. |
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Sep 24 |
Exam # 1 |
314 Altgeld Hall. Regular class time. One 3-inch-by-5-inch notecard allowed. Any type of calculator
allowed. |
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Sep 29 |
Convexity |
Passed back and went
over Exam # 1. Laws of convexity. |
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DM, |
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Oct 1 |
Option Greeks |
Option greeks. Delta gamma
approximation. |
DM, |
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Oct 6 |
Brownian Motion |
Old exam problems on
option Greeks. Wiener processes. |
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DM, |
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Oct 8 |
Brownian Motion
(cont.) |
Arithmetic Brownian
motion. Geometric Brownian
motion. |
DM, |
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Oct 13 |
Lognormality |
Lognormal distribution
and probabilities. |
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DM, |
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Oct 15 |
Ito Lemma |
Background. Theory. Applications. |
DM, |
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Oct 20 |
Ito Lemma (cont.) |
More Ito applications. Sharpe ratio. |
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DM, |
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Oct 22 |
Ito Lemma (cont.) |
Old and sample MFE
exam problems. |
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DM, |
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Oct 27 |
Review
for Exam # 2 |
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Oct 29 |
Exam # 2 |
314 Altgeld Hall. Regular class time. One 3-inch-by-5-inch notecard allowed. Any type of calculator
allowed. |
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Nov 3 |
Exam # 2 Solutions |
Handed back and went
over Exam # 2. |
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Nov 5 |
Simulation |
Inverse transform
method. |
DM, |
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Nov 10 |
Exotic Options |
Simulation examples. Introduction to exotic
options. |
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DM, |
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Nov 12 |
Exotic Options (cont.) |
Barrier, lookback, Asian, etc options. |
DM, |
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Nov 17 |
Interest Rate Modeling |
Finished exotic
options. Interest rate movie. Historical interest
rate characteristics. |
DM, |
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Nov 19 |
No Class |
Work on class group
project. Possibly attend Math
490 presentation at 9:30 am. |
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Dec 1 |
Interest Rate Modeling
(cont.) |
Vasicek model. CIR model. |
DM, |
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Dec 3 |
Interest Rate Modeling
(cont.) |
CIR model. Binomial interest rate
models. |
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DM, |
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Dec 8 |
Interest Rate Modeling
(cont.) |
Binomial interest rate
models. |
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DM, |
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Dec 16 |
Final Exam |
8-11 am. 180 Bevier Hall. One 3-inch-by-5-inch notecard allowed. Any type of calculator
allowed. |
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