We place a very strong emphasis on implementation. When you take our Financial Mathematics courses be prepared to spend time learning new tools and developing real life financial applications. Excel is often the best tool as it provides a very nice GUI and a diverse suite of mathemtatical functions. When heavier computations are necessary, we recommend Matlab. Finally, one of the best ways to deploy your applications is via an internet browser. We can teach you how to develop web applications with GWT (although I am still learning GWT myself) or as a sever-side application (I prefer Java Server Pages). Also, you are always welcome to use your favorite tool whether it's Java, C++, Scheme or any other enviroment. Remember - we are just as happy to learn as we are to teach!
The reason for the emphasis on implementation is twofold. First, being able to build your own implementations of your ideas is a great skill. First of all, it will distinguish you from your colleagues (unless they also took our courses) and will make you more marketable. Not having to wait for someone to program you ideas and to be able to actively interact with your tools is just a superior proffesional experience. Second, learning by programming is very effective. It requires that you understand the main idea and that you work out all the details. Overlooking a detail, no matter how small, will precude your program from running correctly. By the time you have built a working program - you have understood the material thoroughly!
Math 449 - Fixed Income Mathematics is an introduction to interest rates. It is important because interest rates are a critical element of every financial product. The Mathematics of fixed income securities is very simple - it is merely a repeated application of geometric series. The challenging part of the course is learning to distinguish between mathematical facts, conventions and terms of contracts. (For example, semiannual compounding - is it a quoting convention or a material part of a contract that affects the cash flows? The answer is it depends.) The course covers compounding, yield curves, yield curve arbitrage and yield curve stripping. The discussed financial intruments include loans, bonds, mortgages and mortgage-back securities, and swaps.
Math 498 - Introduction to Derivative Securities. Derivative products have become ubiquotous in today's financial markets. If you are reading this and you don't know what financial derivatives are you can read this Wikipedia entry. Financial derivativs allowed Financial Mathematics to become the exciting and advnaced subject that it is today. This course provides an overview of financial derivatives with an emphasis on the mathematical aspects of the subject. The course will cover futures and forwards, European options, binary options, currency and quanto options and we will also discuss some of the implications of American features. The course with introduce the arbitrage theory which is the most important assumption on which most of the basic pricing models are based. In this course, we will not derive the celebrated Black-Scholes formulas but we will make active use of them.
Math 498 - Derivative Securities Pricing. This course is about the best part in Financial Mathematics! It may also be the most Mathematically challenging course in the sequence. In this course, we will show how the assumption of lognormal behavior of underlying securities, such as stocks, combined with the no-arbitrage assumption leads to the celebrated Black-Scholes formulas. In the process, we will develop the important elements of stochastic calculus and Ito's formula.