Fischer Black

MTH210, Fall 2009

Introduction to Financial Mathematics

Solutions to the Midterm Homework Sets Blackboard Web Links Handouts

Myron Scholes
  • Prerequisites
  • Course Description
  • Textbook
  • Office Hours
  • Homework
  • Midterm Exam
  • Final Exam
  • Extra Credit
  • Grading Policy
  • Course Schedule

    •   Robert Merton
    Robert Merton

    Prerequisites The courses which are prerequisites for MTH210 are MTH201 or ECO230.

    Course Description There are two sections of MTH210 for Fall 2009.

    MTH210 is an undergraduate course on some mathematical aspects of finance; namely, the theory of pricing derivatives of financial instruments. A financial derivative is any financial instrument derived from a more basic one such as a stock, bond or commodity. Most of the course will be dedicated to exploring the implications of binomial models involving financial derivatives (such as futures and forward contracts, in addition to put and call options), which illustrate the central idea of arbitrage pricing. We will employ the binomial model and, more generally, the tree model to understand several topics (such as the Cox-Ross-Rubinstein formula, incomplete markets, European and American options, interest-rate derivatives, and bond pricing). The question we will investigate is how one should invest, under certain assumptions on volatility and rates of return. Along the way we will consider the Capital Asset Pricing Model (for which Markowitz, Miller, and Sharpe were awarded the Nobel Prize in Economics in 1990). Other topics of interest are random walks, Brownian motion, stochastic differential equations, Itô processes and Itô’s lemma, and the Optional Sampling Theorem and its implications for market timing. Toward the end of the semester we will heuristically pass to a continuum limit and obtain the celebrated Black-Scholes-Mertons formula for options pricing. (Mertons and Scholes received the Nobel Prize in Economics for this work in 1997. Black would also have received a portion of the award except for the fact of his untimely death, since the award cannot be made posthumously.) Another important topic is the efficient market theory, which underlies the random walk/Brownian motion model for stock prices. For this topic, we mainly refer to Malkiel’s revised and updated paperback. This is one of the books you can read and write a report on for extra credit.

    Textbook We will use the following two textbooks:

    Office Hours We encourage you to contact your instructor by email.

    Homework There will be approximately 13 homework sets. Each homework set will count for 30 points. We will count the highest 10 homework sets for a total of 300 points toward your semester grade. Homework sets will be assigned each Monday in class and are due each Monday, exactly one week after being assigned. There will be a mailbox labeled MTH210 in the mailroom in Hylan Building 913. Please put your homework writeup in the mailbox by 1700 each Monday. Once your homework has been graded, it will be returned to you in class. Please note that no late homework assignments will be accepted. If you foresee a problem doing the work, please tell us at least one week before the due date.

    Midterm Exam We will have a common exam for both sections of MTH210 outside the regular class times. The tentative date for the midterm exam is Tuesday, November 3, from 08:00 to 09:15 in Hoyt Hall. The midterm exam will be worth a total of 300 points. For the midterm exam, you may bring one sheet of handwritten notes (single-sided only) and a calculator.

    Final Exam The scheduled final exam date for both sections of MTH210 is Tuesday, December 15, from 0830 to 1130. The final exam will be worth a total of 400 points. For the final exam, you may bring one sheet of handwritten notes (double-sided) and a calculator.

    Extra Credit There will be an opportunity for extra credits in the form of an essay, at least five pages in length (single-spaced). It will be worth a total of 30 points (or three percent of the semester grade) and must be submitted before the last day of classes, Friday, December 11. In order to do the extra credit assignment, please tell your instructor by November 1. You should read Burton Malkiel’s Random Walk Down Wall Street, or consult with your instructor if there is a book not on the list you want to read. The book should be on financial mathematics and address issues from the class.

    Grading Policy Your semester grade will be derived from the following four components:

    The cut-offs for letter grades will be determined on the basis of the total numerical score achieved on the homework, exams, and class participation. You will be able to access your accumulated scores and view your current grade at any time. The grading program we will use is called BlackBoard.