Instructor: Professor Gábor Francsics

Introduction to Financial Mathematics

MTH 457--001 Spring 2013

Introduction: The goal of the course is to introduce the students to the modern mathematical concepts, techniques and methods used in finance. The course is intended for juniors and seniors interested in financial applications of mathematics. Financial mathematics is a practical subject. Therefore the course will concentrate not only on the theory but also on numerical computation. The course is also one of the recommended course of the Actuarial Science Specialization program of the mathematics department. The course also helps to prepare for the actuarial FM exam and for the financial economics segment (FME) of the actuarial exam M.

Class Meetings: MWF 12:40AM-13:30PM, Room A332, Wells Hall.

Office Hours: Monday, Wednesday 11:00AM-12:00 noon, or by appointments, D310 Wells Hall.

Textbook: The required textbook is [1] Wilmott, Howison, Dewynne: The Mathematics of Financial Derivatives: a Student Introduction, Cambridge University Press, 1995.
Recommended Textbook:
Two textbooks are recommended: [2] R.L. McDonald, Derivatives Markets, Addison Wesley, 3/e edition, 2013.
[3] S.M. Ross, A first course in probability, Prentice Hall, 8/e edition, 2010.
Other very good books related to the course: [4] J.C. Hull, Options, Futures and Other Derivatives, Prentice Hall, 7th edition, 2008.
[5] N. Taleb, Dynamic Hedging, Wiley, 1996.
[6] D.J. Higham, An Introduction to financial option valuation, Cambridge Univ. Press, 2004.

Exams: There will be two midterm exams and a comprehensive third exam. The tentative dates for the midterm exams are Exam 1: Wednesday, February 20,
Exam 2: Wednesday, April 3.
There will be a comprehensive ”take home third exam” distributed on Wednesday, April 24. The deadline of the comprehensive third exam will be 4:00PM, Friday, April 26. No make-up exams will be given.

Grading policy: Your final grade for the course will be based upon the homework assignments, projects, quizzes, and classroom participation (30%), the mid-term exams (20% each) and the comprehensive third exam (30%). The total worth of the homework assignments, projects, quizzes, and classroom participation will be 75 points. Each midterm exam will be worth of 50 points. The comprehensive third exam will be worth of 75 points. If the final total of your points is in the range below then you are guaranteed the corresponding grade:

Material:
Preview of financial mathematics, basic and derivative financial instruments, arbitrage, hedging, random walk model of stock prices. Pricing of futures and forward contracts. European and American options, Black-Scholes model, derivation of the Black-Scholes equation, explicit solution. Partial differential equations, diffusion equation, initial and boundary conditions. American options, the free boundary conditions. Numerical methods, the binomial model, etc.

Recommended Homework Problems from the Textbook:
Chapter 1: 1, 2, 3, 4.
Chapter 2: 1, 2, 3, 4*, 5*.
Chapter 3: 1, 2, 3, 4, 5, 6, 7, 8, 9.
Chapter 4: 1*, 2, 3.
Chapter 5:
Chapter 6:
Chapter 7:
Chapter 10: