Math 497F Homepage

Mathematics 497F, Spring 2013

The Final is Thursday, May 2nd from 4:40 to 6:30 in 273 Willard. It is comprehensive, but it will concentrate on the second half of the course.

Midterm on Thursday, March 28th covering up to March 1st, 6:30-7:45 in 110 Osmond.

The new problems will be posted on Angel, where you will also find a DropBox to upload your solutions.

Office Hours: Tue 1:30-3:30 and F 2:20--3:20 (or by appt.)
My office is in McAllister, room 235 ( Contact )

Syllabus: MATH 497F Introduction to Financial Mathematics

Introduction: some examples of financial instruments, the idea of "no-arbitrage" pricing, the language of probability.
The binomial no-arbitrage pricing model (Fundamental theorem of asset pricing in one period economy, chapter 1).
More probability concepts with financial applications (conditional expectations, martingales, Radon-Nikodym derivatives, Markov processes, chapters 2 and 3).
American derivative securities (chapter 4).
Random walks (chapter 5).
Introduction to interest rate models (chapter 6).
Introduction to continuous time models (the Black-Scholes formula and its properties).

This course is an introduction to no-arbitrage pricing for financial instruments (options) in discrete time. I plan to cover as much as possible from the required textbook and to concentrate on the mathematical aspects of the theory that are usually not covered in the related Finance courses. We will also discuss the Black-Scholes formula and its properties.

Prerequisites: Math 140 and 141. Some knowledge of probability theory and more advanced calculus courses will be very useful.

Required Textbook: Steve Shreve, Stochastic calculus for finance I. The binomial asset pricing model. Springer Verlag, 2004. xvi+187 pp. ISBN: 0-387-40100-8.

Optional Textbook: Victor Goodman and Joseph Stampfli, The mathematics of finance: modeling and hedging. AMS 2001.

Optional Textbook: John Hull, Options, Futures, and other derivatives. Course work. Read the weekly material from the file lectures.pdf, which you can find on Angel. The file shows you what you need to read for each week. Listen to the presentations files for each week, which can be found in the corresponding folder week(nr). The homework for that week will be found in the same folder, as well as a few other useful materials, such as practice homeworks or additional examples. In the folder week(nr) you will find also a dropbox for your homeworks, which can be submitted also directly to me (put it under my door, not in the mailbox). There are five such videos for the first week, and they can be found in the folder week1.

Grade: 30% homeworks (weekly, due one week after assignement), 20% quizes (one every two-three weeks), 20% midterm (first half of material), 30% final (comprehensive, but concentrating on the second half of the class). As usual, 90% will earn you an A, 80% will earn you a B, 70% will earn you a C. These cutoffs may be lowered (but not increased). You need 50% to pass the course. No late homework will be accepted unless prior permission is granted. No make-up exams are available except by prior arrangements and only under extenuating circumstances.

All Penn State Policies regarding ethics and honorable behavior apply to this course.

Old Homeworks: