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Mathematics of Finance Math 423 Section 001, T TH 11:40am - 1:00pm, 1060 East Hall Dr. Ahmet Duran 3826 East Hall, (734) 763-1184 durana @umich.edu, www.umich.edu/~durana Office Hours T TH 1:10-2:30pm Description Introduction to the mathematical models used in finance and economics, risk-free assets, risky assets, dynamics of stock prices, binomial and trinomial tree models, discrete time market models, continuous-time stochastic processes, Brownian motion, investment strategies, martingale property, fundamental theorem of asset pricing, portfolio management, capital asset pricing model, forward and futures contracts, general properties of options, option pricing, Cox-Ross-Rubinstein formula, early exercise feature (American options), Itô’s lemma, Black-Scholes formula, Black-Scholes differential equation, financial engineering, hedging option positions, hedging business risk, variable interest rates, and stochastic interest rates. Prerequisites Linear algebra (Math 217), basic probability (Math 425) and a course in programming (EECS 183) Text Mathematics for Finance: An introduction to financial engineering, Capinski and Zastawniak, Published by Springer, ISBN: 1-85233-330-8 Additional References • Bodie, Kane and Marcus: Investments • Cornuejols and Tutuncu: Optimization Methods in Finance: Mathematics, Finance and Risk • Hull: Options, Futures and Other Derivatives • Roman: Introduction to the Mathematics of Finance • Shreve: Stochastic Calculus for Finance Vol. I & II • Wilmott, Howison and Dewynne: The Mathematics of Financial Derivatives Course Website You can visit the course website via www.umich.edu/~durana and https://ctools.umich.edu. I will post announcements, homework assignments, messages, and other course resources on the course webpage regularly. You may access to answer files for homework, quiz and exam via only https://ctools.umich.edu.Grading Policy and Important Dates _ • You will be expected to read each section before it is discussed in class. • I will assign homework problems in class (and on the course webpage) regularly; I will collect homework at the beginning of class meeting. No late homework will be accepted. • I will collect two computer assignments. • We will have five quizzes. I do not give make up quizzes, but I will drop your lowest quiz grade. • We will have one midterm exam on Tuesday, 2/19/08. I do not give makeup exams. • Our final exam is cumulative. • All exams are closed-book, proctored tests. • You will be allowed one 3x5” index card with hand-written formulas for the midterm exam and two for the final exam. • Your final grade will be determined according to the following weights: Quiz + Homework + Computer Assignment 30% Midterm Exam 30% Final Exam 40% Syllabus I plan to cover Chapters 1-10 of the text; if time permits, we may also cover Chapter 11 or other additional topics. A tentative course schedule appears below. If you miss a lecture, you should be sure to get the notes from a classmate. Tentative Schedule for Math 423-001 T TH 1/3/08Ch. 1 1/8/08Ch. 2. 1/10/08Ch. 3 1/15/08Ch. 3 Quiz 1 1/17/08Ch. 3 1/22/08Ch. 4 HW 1 1/24/08Ch. 4 1/29/08Ch. 4 Quiz 2 1/31/08Ch. 5 2/5/08Ch. 5 HW 2 2/7/08Ch. 52/12/08Ch. 6 2/14/08Review, Q&A 2/19/08EXAM 1 2/21/08Ch. 7 2/26/08Winter recess 2/28/08Winter recess 3/4/08Ch. 7 3/6/08Ch. 7 Computer Assignment 1 3/11/08Ch. 8 Quiz 3 3/13/08Ch. 8 3/18/08Ch. 8 HW 3 3/20/08Ch. 9 3/25/08Ch. 9 Quiz 4 3/27/08Ch. 9 4/1/08Ch. 10 Computer Assignment 2 4/3/08Ch. 10 4/8/08Ch. 10 Quiz 5 4/10/08Ch. 11 4/15/08Review, Q&A FINAL EXAM: Thursday, April 17, 10:30 am - 12:30


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