University of Connecticut

Financial Mathematics I

Math 365

Fall 2003

Classes: MW: 4:30 – 5:45                                   Instructor: James G. Bridgeman, FSA

MSB 118                                                MSB408

Office Hours: M:   3:30 –  4:30                           860-486-8382

W:  1:00 –   2:30                          bridgeman@math.uconn.edu

F:10:00 – 11:00                          instructor's web site

Or by appointment                       course web site

Context for the Course

Required for the Professional Master’s degree in Applied Financial Mathematics

Partial preparation for SOA/CAS course 2 examination on Interest Theory, Economics and Finance

(Next scheduled for Wednesday November 5, 2003)

# Specific Course Content

Theory of interest in both discrete and continuous time including annuity functions, cash flow valuation, and determination of yield rates.  Concepts and skills to apply the theory to financial transactions and instruments including loans, mortgages, bonds and other securities and to financial analysis including capitalization, amortization and depreciation, return on investment, and portfolio performance.

# Required Text

Kellison, The Theory of Interest (2nd ed.), Irwin/McGraw-Hill 1991

# Supplemental Material (not required)

Averbach & Vance, Theory of Interest Study Manual

London, ACTEX Study Manual for Exam 2 (Interest Theory)

Parmenter, Theory of Interest and Life Contingencies, with Pension Applications (3rd ed.)

Society of Actuaries, Study Note Package for course 2 examination

ACTEX/Mad River Books (distributor), Study Manuals and related materials for course 2 examination

Week of

Topic(s)

# Chapter

Aug. 25

Need for a theory, interest & discount, present & accumulated values, nominal rates

Ch.1.1-1.8

Sept. 1

Force of interest, varying interest rates

Ch.1.9-1.11

Sept. 8

Calculation, equations of value, problem-solving

Ch.2.1-2.8

Sept. 15

Basic annuities & perpetuities

Ch.3.1-3.5

Sept. 22

Annuity problem-solving

Ch.3.6-3.9*

Sept. 29

Annuity payment frequency

Ch.4.1-4.5

Oct. 6

Varying annuities

Ch.4.6-4.9*

Oct. 13

Exact measurement of interest rates and returns; mid-term exam (Oct. 15)

Ch.5.1-5.4

Oct. 20

Approximate measurement of interest rates and returns, investment year methods

Basic amortization schedules

Ch.5.5-5.7

6.1-6.3

Oct. 27

Complex amortization schedules and sinking funds

Ch.6.4-6.6

Nov. 3

Basic bond pricing & amortization (no new material on Nov. 5)

Ch.7.1-7.4*

Nov. 10

Complex bond pricing, other securities

Ch.7.5-7.7,

7.10-7.11*

Nov. 17

Mortgages, loan disclosures, approximate methods

Ch.8.1-8.4*

Dec. 1

Depreciation, capitalization, short sales, review

Ch.8.5-8.7

Dec. 8

Final Exam

All

* Sections 3.6, 3.7, 4.8, 7.1, 7.2, 7.5 thru 7.7, 7.10, 7.11, and 8.1 thru 8.4 are not part of the SOA/CAS

Exam syllabus but are included in the Math 285Q/365 syllabus and may be tested on the Mid-Term Exam

or Final Exam for the course.  While not directly required for the Society Exam, they do exercise skills

helpful for success on it.  They provide useful perspective for financial practitioners and/or illustrate

applications of the subject.

Projects                                                  20%

4 Take-home Quizzes                           20%

Mid-term Exam                                      25%

Final Exam                                             35%

## Projects

(1) Form teams of three students each to make an oral presentation to me of the proof of the Black-Scholes option-value formula from Appendix X (see Sec. 10.5 also.)  Will be scheduled Dec. 1 – 12.

(2) Each student prepare a paper selected from among the following topics.  The paper should demonstrate understanding of all important concepts within the topic, as presented in the text or other reference, and include sufficient detail to demonstrate that you have mastered the mathematics involved:

(a) An alternative way (i.e. different than Appendix X) to look at and prove the Black-Scholes option-value formula (see me for some references).

(b) Applications of the yield rate concept (sections 5.8 thru 5.9 of the text)

(c) Generalizations of the amortization concept (sections 6.7 & 6.8 of the text)

(d) Drivers of the interest rate (sections 9.1 thru 9.5 of the text)

(e) Components of the interest rate (sections 9.4 thru 9.6 of the text)

(f) Duration and immunization of interest rate risk (sections 9.8 & 9.9)

(g) Immunization and matching of interest rate risk (sections 9.9 & 9.10, including references to 9.8)

(h) Full immunization of interest rate risk (section 9.9 & appendix VIII, including references to 9.8)

(i) Stochastic models of the interest rate (sections 10.1 thru 10.3)

Start thinking about your selection now and let me know in writing by Oct. 27 what topic you have selected.

(3) Correct a set of quiz papers from the class, including pointing out the specific error when an answer is wrong,

Both the syllabus and the grading plan are subject to change with appropriate advance notice to the class