Mathematics 383, Actuarial Models II, Fall 2010

Illinois State University – Mathematics Department

Instructors

Classes Meet

Tuesdays and Thursdays 4:00-5:50 p.m. (with a ten minute break), in Stevenson Hall, room 120.

Office Hours

Office hours will be held Tuesdays and Thursdays 3:00-3:50 p.m., in Stevenson Hall room 313G, by Dr. Krzysztof Ostaszewski. Please ask for an appointment at other times.

Textbooks

Notes for all topics with practice exercises will be posted as links next to dates of classes, see below, in the schedule of classes.

• Derivatives Markets, Second Edition, by McDonald, R.L., Addison-Wesley, Pearson Education, 2006.
The following (downloadable as PDFs) study notes from the Society of Actuaries are also useful:

• Multi-State Transition Models with Actuarial Applications by J. Daniel. This is a reference on Markov Processes.

• Poisson Processes (and mixture distributions), by J. Daniel. This is a reference on Poisson Processes.

• Exam MFE syllabus for the Fall 2010 examination session.• Exam MFE Tables.
• Some Remarks on “Derivatives Markets”, by E. Shiu.
• “Derivatives Markets,” Errata, by R. McDonald.
• Exam MFE Sample Questions and Solutions.
• May 2009 SOA Exam MFE/CAS Exam 3 and Solutions.
• May 2007 SOA Exam MFE and Solutions.

Objective

The objective of this class is to help you learn about Poisson and Markov stochastic processes and mathematical models utilized in financial economics.These actuarial models form a key part of modern actuarial science. We will cover the entire contents of the Course MFE/3F professional actuarial examination, and the portion on Poisson and Markov processes from the Course MLC professional actuarial examination. For students interested in taking those examinations:

• Registration form for the Fall 2010 Course MLC and Course MFE professional actuarial examinations.

Grading

There will be a total of five tests. Any of the comprehensive tests (as indicated in the schedule) can count as a final. Because there will be so many opportunities for testing and only the best four test scores will affect the class grade, no make-up tests will be offered. The final will count as 40% of your grade, and the best two of the remaining tests will count as 30% of your grade each. You will also receive up to 10% extra credit for the best of the remaining tests. The grading scale for undergraduate students will be as follows: 90% or better — A, 80% to 90% — B, 70% to 80% — C, 60% to 70% — D, below 60% — F. The grading scale for graduate students will be the same, but their score in the class will be multiplied by the factor of 0.9, to account for increased expectations of them, as they receive graduate credit for the class.

Important dates

Illinois State University withdrawal information for the Fall 2010 semester is given at this web site: http://www.registrar.ilstu.edu/registration/withdrawal/fall.shtml.

Disability concerns

Illinois State University provides a welcoming atmosphere for individuals with disabilities by assisting each in functioning independently within the University community and providing equal access and opportunity in accomplishing educational, professional and personal goals. Disability Concerns, a unit of the Student Affairs Division,  is the designated office to provide approved accommodation services for students, faculty, staff, and guests with disabilities. Disability Concerns obtains and maintains documentation of disability, certifies eligibility for services, determines reasonable accommodations, and develops plans for providing such accommodations. This is accomplished in a confidential manner to ensure equal opportunity for participation in all courses, programs, activities and employment offered by Illinois State. Please contact the Disability Concerns in Fell Hall room 350, tel.  309-438-5853 (Voice), 309-438-8620 (TTY) if you have needs that can be accommodate by that office.

Schedule of classes

• Tuesday, August 24, 2010. Parity and Other Option Relationships (Derivatives Markets, Chapter 9).
• Thursday, August 26, 2010. Parity and Other Option Relationships (Derivatives Markets, Chapter 9).
• Tuesday, August 31, 2010. Parity and Other Option Relationships (Derivatives Markets, Chapter 9). Additional study material: Put-call parity charts.
• Thursday, September 2, 2010. Binomial Option Pricing I (Derivatives Markets, Chapter 10). Class taught by Mr. Ken Williams.
• Tuesday, September 7, 2010. Binomial Option Pricing I (Derivatives Markets, Chapter 10). Class taught by Mr. Ken Williams.
• Thursday, September 9, 2010. Binomial Option Pricing II (Derivatives Markets, Chapter 11). Class taught by Mr. Ken Williams.
• Tuesday, September 14, 2010. Binomial Option Pricing II (Derivatives Markets, Chapter 11). Class taught by Mr. Ken Williams.
• Thursday, September 16, 2010. The Black Scholes Formula (Derivatives Markets, Chapter 12).
• Tuesday, September 21, 2010. The Black Scholes Formula (Derivatives Markets, Chapter 12).
• Thursday, September 23, 2010.Test No. 1, on the material covered through September 21, 2010.
• Tuesday, September 28, 2010. Market-Making and Delta-Hedging (Derivatives Markets, Chapter 13). Class taught by Mr. Ken Williams.
• Thursday, September 30, 2010. Market-Making and Delta-Hedging (Derivatives Markets, Chapter 13). Class taught by Mr. Ken Williams.
• Tuesday, October 5. 2010.  Exotic Options (Derivatives Markets, Chapter 14). Class taught by Mr. Ken Williams.
• Thursday, October 7, 2010.  Exotic Options (Derivatives Markets, Chapter 14). Class taught by Mr. Ken Williams.
• Tuesday, October 12, 2010. The Lognormal distribution (Derivatives Markets, Chapter 18). Monte Carlo Valuation (Derivatives Markets, Chapter 19).
• Thursday, October 14, 2010. Test No. 2, on the material covered through October 14, 2010.
• Tuesday, October 19, 2010. Brownian Motion and Ito’s Lemma (Derivatives Markets, Chapter 20).
• Thursday, October 21, 2010. Brownian Motion and Ito’s Lemma (Derivatives Markets, Chapter 20).
• Tuesday, October 26, 2010. The Black-Scholes Equation (Derivatives Markets, Chapter 21).
• Thursday, October 28, 2010. The Black-Scholes Equation (Derivatives Markets, Chapter 21).
• Tuesday, November 2. 2010. Exotic Options II (Derivatives Markets, Chapter 22). Volatility (Derivatives Markets, Chapter 23).
• Thursday, November 4. 2010. Interest Rate Models (Derivatives Markets, Chapter 24).
• Tuesday, November 9, 2010. Interest Rate Models (Derivatives Markets, Chapter 24).
  • Some additional Course MFE/3F exercises.
• Thursday, November 11, 2010. Poisson Processes. Class taught by Mr. Ken Williams.
• Tuesday, November 16, 2010. Poisson Processes. Class taught by Mr. Ken Williams.
• Thursday, November 18, 2010. Poisson Processes. Class taught by Mr. Ken Williams.
• Tuesday, November 30, 2010. Markov Processes.
• Thursday, December 2, 2010. Markov Processes.
• Tuesday, December 7, 2010. Test No. 3, comprehensive.
• Thursday, December 9, 2010. Test No. 4, comprehensive.
• Friday, December 17, 2010. 10:00 a.m. — 12:00 a.m. Test No. 5, comprehensive.

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All information contained here is, to our best knowledge, correct, but it is merely a representation, and should not be considered to be any form of professional advice. This electronic publication should not be misconstrued as the official position of Illinois State University, or its Department of Mathematics. We are glad to provide as much information as possible here, but we kindly ask that in any decision related to matters listed here you seek additional counsel and information. Comments on this Home Page are welcome and should be sent to Dr. Krzysztof Ostaszewski  at his e-mail address: krzysio@ilstu.edu.