About the course

Mathematical finance

Prerequisites:
Mathematics prerequisites: MATH 20 and MATH 40, or MATH 60; MATH 23; and COSC 1; or Equivalent coursework in other majors. If in doubt, please see the instructor.
Project and/or homework will have computational component to it. Therefore programming knowledge is useful. In particular you will learn Excel (the bread and butter of the financial industry), if you do not already know it.

Financial Derivatives rely on mathematical models for their priciing and analysis. This is a fairly new application area of mathematics, having come into full force in the industry in the 1980s after Black, Scholes and Merton created a precise formulation for prices of Stock Options. In Math 86 you will be introduced to basics of financial derivatives; in particular pricing of options and hedging using mathematical methods. The topics covered in this course are roughly as listed below. This may be modified as we move along in the semester. The topics while not covered in any one text will closely follow Chapters 1 - 6 of text by Steven E. Shreve, for the mathematical content. I will supplement this material with additional information in Finance and the practical aspects of it, where needed.

1. Risk, the important assets, arbitrage, hedging, using options in hedging

2. Pricing of European options using Binomial Asset pricing model, risk neutral probabilities

3. Random Variables, Distributions, Expectations, Conditional expectations

4. Martingales and Markov processes

5. Pricing of American options and stopping times

6. Pricing of Options using Black-Scholes Merton formula

7. Fixed Income Derivatives

Classes

Room: Haldeman 028
Lectures: "11" slot : MWF 11:30am - 12:35pm.
X-hour: Tuesdays (same room) 12:15 pm - 1:05 pm. Will be used for group work and for lecture when announced.

Staff

Instructor: Seema Nanda Office Hours: M 1:00 - 2:15; W 1:00 - 2:15. or by apointment

Textbook

The following three books complement each other and are good resources for a basic knowledge of mathematical finance

1. Stochastic Calculus for Finance I: The Binomial Asset Pricing Model By Steven S. Shreve (Springer 2004)- largely a mathematical book with little insight into finance. We will closely follow Chapters 1 - 6 of text.

2. Options, Futures and other Derivatives by John C Hull (any edition) - An excellent book to understand the nitty gritty of the workings of financial instruments and trading.

3. The Concepts and Practice of Mathematical Finance by Mark S. Joshi (Cambridge University Press) - A book that spans an intuitive approach and mathematical content of the subject, and is written in a mathematical framework.

Grading

Your grade will be determined (tentatively) as follows: Homework 55%, Quiz (unannounced) 10%, Group Project 35%.
Grading scheme will be finalized after a discussion in class.

Homework

Homework will be assigned regularly and will usually be due in about one week from date of assignment. Expect to see 6 to 8 homework assignments during the quarter.

Group Project

Guidelines: You may choose the topic of your group project and the members of your group subject to some guidelines and approval of instructor. The project must have a mathematical component to it, as well as a computational component.

Honor Code

Students are encouraged to work collaboratively on homework problems. However the written solutions turned in must be based on what a student has understood herself/himself. Students must acknowledge names of those whose help they have received, collaborated with, and sources of information. Students must not write solutions that may be found on the web, without referencing the source. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Honor Code.

If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me for clarifications.

Disabilities

Students with disabilities, including "invisible" disabilities such as chronic diseases and learning disabilities are requested to discuss with me by close of second week of the quarter, so that appropriate help as needed can be obtained. These conversations are kept confidential, although the Academic Skills Center may be consulted to verify the documentation of the disability and advise on an appropriate response to the need. Dartmouth College has an active program to help students with disabilities.