Math 449: Fixed Income Mathematics
This course is an introduction to the most fundamental topic in Financial
Mathematics: interest rates and fixed income instruments. Fixed income instruments
include bonds, loans, mortgages and even instruments, such as swaps, whose cash flows
are not fixed. The main idea of the course was best summed up by a mentor of mine on
Wall Street who said “Money now is better than money later and everything else is
details.” Well, we’ll dwell thoroughly on the details without losing sight of the main idea.
The material will serve as a foundation to the more advanced topics in Financial
Mathematics such as derivatives, credit default swaps, disaster insurance and longevity
trading. Fixed income instruments, whose cash flows are largely predictable, can be
priced to more objectively than other financial securities such as stocks and stock options
which allows for analysis with fewer assumptions and is therefore a good place to start
the journey in Financial Mathematics.
The course will emphasize implementation in Excel.
Goals of the Course
My main goals are to make sure that you…
1. understand the mechanics of the fixed income securities
2. have command of the mathematical techniques used to evaluate the price and
price sensitivity to market moves
3. know and understand the industry conventions
4. are able to implement all concepts as useful applications in Excel
Lecturer: Pavel Grinfeld
Office: Korman 291
Phone:215-219-3548 (but don’t call unless in emergency)
Office Hours Tue-Thu 2:3.30pm and by appointment
Lecture Schedule: Curtis 455 T/TR 3:30-5pm
Textbook (Optional): Fixed Income Mathematics by Frank Fabozzi
1. Review of relevant mathematics. Limits, geometric series, Taylor series, linear
systems, null spaces.
2. Introduction to Excel and VBA programming
3. Loans. Interest Rates. Compounding terms. The continuous compounding limit.
4. Mortgages. Mortgage calculator in Excel.
5. Bonds. Compounding conventions. Term structure of interest rates.
6. Yield curve arbitrage. Yield curve stripping..
7. Duration, convexity, portfolio immunization
8. Introduction to forwards. Futures price of a security.
9. Forward curve, forward rates.
11. Bond trading strategies.
1. Frequent homework assignments (10%)
2. Midterm (30%/30%)
3. Final project(30%)