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# Applied Mathematics & Statistics

#### AMS 318, Financial Mathematics

Catalog Description: Accumulation functions, yield rates, annuities, loan repayment, term structure of interest rates/spot rates/forward rates, options, duration/convexity.  This course follows the syllabus for Financial Mathematics (FM) Exam of the Society of Actuaries and prepares students to pass the FM Exam.

PrerequisiteAMS 310

Course offered in Summer, Fall and Spring only. 3 credits.

Textbook: Mathematical Interest Theory, 2nd Edition by J. Daniel and L. Vaaler, Pearson
ISBN# 978-0-8-8385754-0

Actuarial Exam: The material in this course is the basis of the second actuarial exam, Exam FM, of the  Society of Actuaries . For more details about actuarial preparation at Stony Brook see  Actuarial Program

The course satisfies the WRTD requirement of the Stony Brook Curriculum.  Extensive writing required in the homework.

1. Accumulation functions (simple, compounded, general) - 5 hours
2. Yield rates, Approximate yield rates - 4 hours
3. Annuities (simple, geometric, arithmetic) 5 - hours
4. Loan repayment - 5 hours
5. Bonds - 3 hours
6. Term structure of interest rates / Spot rates / Forward rates - 3 hours
7. Options (Call, Put, Put-Call parity) - 4 hours
8. Duration/Convexity - 3 hours
9. Problems from the Financial Mathematics portion of the actuary exams - 5  hours
10. Examinations and Review - 5 hours

Learning Outcomes for AMS 318, Financial Mathematics

1.) The overriding learning goal of this course is to prepare students to pass the Financial Mathematics exam of the Society of Actuaries.

2.) Understand, and solve, problems involving, the theory of interest.
* simple interest:
* compound interest;
* discounting future interest;
* nominal rates of interest.

3.) Understand, and solve, problems involving the mathematics of annuities.
* annuities immediate, due and deferred;
* different payment rates;
* yield rates for annuities;
* level annuities with different payment periods;
* continuously paying annuities.

4.) Understand, and solve, problems involving yield rates and loans.
* value of investments with a single deposit;
* value of investments with multiple deposits;
* dollar-weighted yield rates;
* amortization schedules;
* sinking fund method;
* loans with other repayment patterns.

5.) Understand the fundamentals of bond, stock, commodity futures, and associated derivatives as well as arbitrages involving these investments.
* price formulas for bonds;
* bond amortization schedules;
* callable and floating-rate bonds;
* common and preferred stocks;
* going long and short in stocks;
* arbitrage;
* forward contracts and commodities futures;
* options and ways to price them;
*swaps. 