MATH 194: INTRODUCTION TO THE MATHEMATICS OF FINANCE (WINTER 2000)
Professor: Professor R. J. Williams, Office: AP&M 6121, email: williams@math.ucsd.edu
Professor's Office Hours: Monday, Wednesday 1-2 p.m., Thursday, 5-6 p.m. (before March 16).
Final's week office hours: Monday 3-5 p.m., Tuesday 5-6 p.m, Thursday, 2.30-3.30 p.m.
Final exams and grades may be obtained in person from Professor Williams on Monday, April 3, 4-6 p.m., Tuesday, April 4, 4-6 p.m., Monday, April 10, 4-6 p.m., or by appointment. Please note that to protect the privacy of students, grades cannot be given out by email or phone, only in person.
Lecture Time: MW 2.30-3.50 p.m.
Lecture Place: AP&M 5829
Please note change of room: from Wednesday, February 2 onwards, the class lecture will meet in SSB (Social Science Building), Room 106.
Section Time: Tu 4.40-5.30 p.m. Section Place: WLH 2208
Teaching Assistant: Tucker McElroy. Office: AP&M 2325. Office Hours: MW 11:15am-12:15pm. Final's Week office hours: M, Tu 1-3 pm.

DESCRIPTION: This course is an introduction to the mathematics of financial models. The aim is to provide students with an introduction to some basic probabilistic models of finance and associated mathematical machinery. The emphasis will be on discrete time models where concepts can be developed without measure theory. (The graduate course, Math 294, which has a similar title, is at a more advanced level and has much more emphasis on continuous time models which use measure theory.)

PREREQUISITES: Math 20D, Math 20F, and Math 180A or Math 183.

TEXT: S. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell, third printing, 1999. This text will be used as a primary reference for the course. The lectures will provide a guide and expanded explanation of the relevant topics.

OTHER REFERENCES:
J. Hull, Options, Futures and other Derivative Securities, Prentice Hall, Fourth Edition, 2000.
S. Ross, An Introduction to Mathematical Finance, Options and other topics, Cambridge University Press, 1999.
P. Wilmott et al., The Mathematics of Financial Derivatives, Cambridge University Press, 1995.

OUTLINE: The course will roughly follow the topics covered in the text "Introduction to Mathematical Finance -- discrete time models" by S. Pliska. The treatment of that book will be supplemented with mathematical background and details as needed. In particular, conditional expectation, martingales, change of measure, martingale representation and optimal stopping will be discussed and relevant topics from optimization theory such as the separating hyperplane theorem and linear programming will be included. In addition, some structured computer modules to illustrate the theoretical material will accompany the course. The course will begin with the development of the basic ideas of hedging and pricing by arbitrage, and consumption and investment theory, for single period models and then multiperiod securities market models. An important example throughout will be the binomial tree model. These ideas will then be adapted and applied to price various derivative securities including European and American options, and to solve consumption investment problems. If time allows, attention will then turn to models of the interest rate market and treatment of interest rate derivatives such as caps and swaptions.

COMPUTER MODULES: These will be made available to students and will complement the theoretical material presented in the course.
A simple mathematica notebook showing how to do reduced row echelon can be obtained by clicking here.

READING: IT IS VERY IMPORTANT THAT STUDENTS READ THE ASSIGNED MATERIAL IN ADVANCE OF THE LECTURE. This will be expected and it will enable students to maximize what they get out of lectures.

HOMEWORK: For homework assignments, click here. Homework is an essential part of the course. To assimilate the theoretical material presented in lectures, it is necessary to solve problems such as those presented in the homework. IT IS OF GREAT IMPORTANCE THAT STUDENTS MAKE EVERY EFFORT TO COMPLETE EVERY HOMEWORK ASSIGNMENT, AND THAT STUDENTS SEEK HELP WITH PROBLEMS THEY HAVE NOT BEEN ABLE TO HANDLE. Homework will count for 25% of a student's grade. Homework assignments will be given out each week in class. They will be due in section on Tuesdays. Late homework will not be accepted.

EXAMINATIONS: There will be one exam in class during the quarter plus a final exam. The in class exam will count for 25% of a student's grade and the final exam for 50%. Make-up exams will not be given. For information concerning the exams, click here. In particular, the midterm and final are in different rooms from the class room.

EXAMINATION DATES:
In class exam: Wednesday, February 16, 2000. Final exam: 3--6 p.m. on Saturday, March 25, 2000, WLH 2204. The alternative final exam date is Wednesday, March 22, 1-4 p.m., Center Hall 205. Click here for more information.

FINAL COURSE GRADE: For the final grade, the homework will count 25%, the in-class exam 25%, and the final exam 50%.

OTHER COURSES: Math 168A, Introduction to Numerical Methods in Finance, will be offered in Spring 2000 by Professor Hans Sieburg. This course is designed to follow on from Math 194 and will be an excellent practical complement to the material learned in Math 194. Click here to see a description of the course and click here to see the current course home page.

LINKS TO RELATED WEB SITES (under construction):

Please direct any questions to Professor Ruth J. Williams, email: williams@math.ucsd.edu