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 8604868382
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)
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.
Kellison, The Theory of Interest (2nd ed.), Irwin/McGrawHill 1991
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 (3^{rd} 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
Outline & Intended Pace 


Week of 
Topic(s) 
Chapter 

Aug. 25 
Need for a theory, interest & discount, present & accumulated values, nominal rates 
Ch.1.11.8 

Sept. 1 
Force of interest, varying interest rates 
Ch.1.91.11 

Sept. 8 
Calculation, equations of value, problemsolving 
Ch.2.12.8 

Sept. 15 
Basic annuities & perpetuities 
Ch.3.13.5 

Sept. 22 
Annuity problemsolving 
Ch.3.63.9* 

Sept. 29 
Annuity payment frequency 
Ch.4.14.5 

Oct. 6 
Varying annuities 
Ch.4.64.9* 

Oct. 13 
Exact measurement of interest rates and returns; midterm exam (Oct. 15) 
Ch.5.15.4 

Oct. 20 
Approximate measurement of interest rates and returns, investment year methods Basic amortization schedules 
Ch.5.55.7 6.16.3 

Oct. 27 
Complex amortization schedules and sinking funds 
Ch.6.46.6 

Nov. 3 
Basic bond pricing & amortization (no new material on Nov. 5) 
Ch.7.17.4* 

Nov. 10 
Complex bond pricing, other securities 
Ch.7.57.7, 7.107.11* 

Nov. 17 
Mortgages, loan disclosures, approximate methods 
Ch.8.18.4* 

Dec. 1 
Depreciation, capitalization, short sales, review 
Ch.8.58.7 

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 MidTerm 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 Takehome Quizzes 20%
Midterm Exam 25%
Final Exam 35%
(1) Form teams of three students each to make an oral presentation to me of the proof of the BlackScholes optionvalue 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 BlackScholes optionvalue 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