# MATH 5760/6890, FALL 2011 Introduction to Mathematical Finance I

## Programming:

Computer implementation is an essential component of this subject, and you will be required to do some of your coursework
with computer programs. Either Matlab or Excel will be acceptable, but we strongly encourage you to start with some basic
Matlab programming if you have no prior experience with any computer programming.

## Outline:

This is the first part of a two-semester sequence course on mathematical finance. In the Fall semester, we will examine the
fundamental principles of financial derivatives from both financial and mathematical perspectives, and demonstrate how the
mathematical tools from stochastic calculus, differential equations and numerical methods join forces to form an essential
part in modern finance. The emphasis of the course is a mathematical understanding of the intrinsic relationships among
various financial instruments, which serves as a basis for investment decisions and trading strategies. The central theme of
the Fall semester is the classic Black-Scholes-Merton model, and we plan to give a thorough treatment of the original model,
with extensive discussions on the practical extensions in response to various disadvantages of the original model. One of
the most intuitive and transparent approaches to illustrate that is also extensively used in practice is the binomial tree model.
It contains most of the essential idea of the Black-Scholes-Merton methodology, and it can be naturally extended to build
more general continuous-time models. Time permitting, we will include as much real life examples as possible to make this
a rewarding experience for those who plan to pursue a career in this direction, as well as those who are just intrigued by the
subject and its impact on our society.

## Topics to be Covered:

• Introduction to investment securities and financial derivatives
• Random walk and Brownian motion
• Interest rates and present value analysis
• Concept of arbitrage and pricing based on no-arbitrage principle
• Binomial models (one-period and multi-period)
• Black-Scholes formula
• Practical issues in option pricing: dividend, American put, adding jumps, and volatility estimates
• Incomplete market and utility valuation
• Optimization models
• Stochastic dynamic programming
• Exotic options
• Autoregressive models and return analysis

• Homework Assignments (60%): taken from the textbook;
• Midterm Project (10%): a project that will require handling practical data;
• Take-Home Final (30%): a comprehensive exam that covers all the materials and it will be made available at
the beginning of the last week of class.

## Math 6890:

For Students Registered for Math 6890: If you are a PhD student in a non-mathematics program, you may register at the
6000 level. However, you will be required to do extra work for the course which may include: more theoretical exercises
in homework assignments and exams, and research oriented projects. Grading curve for Math 6890 is separated from the
rest of the class.