Fall 2001

MATH 478.01 (3 credit), Tu_Th, 2:30PM-3:45PM, Wickersham 124

**Corequisites:**MATH 335

*Mathematical Statistics I***Instructor:**Dr. Buchanan

Office: Wickersham 112, Phone: 872-3659, FAX: 871-2320

Office Hours: 1:30PM-2:20PM (M-F), or by appointment

Email:`Robert.Buchanan@millersville.edu`

URL:`http://banach.millersville.edu/~bob`**Textbook:**Sheldon M. Ross,

*An Introduction to Mathematical Finance: Options and Other Topics*, Cambridge University Press, Cambridge, 1999.**Objectives:**The objectives of this course include introducing the students to the mathematical treatment of risk-neutral valuation, arbitrage, options, futures, and derivatives. One of the main mathematical results to be covered is the derivation, understanding, and use of the Black-Scholes formula for pricing options. A comparison of the assumptions underlying this pricing model and actual financial markets will be made to understand the utility and limitations of the Black-Scholes formula.

**Course Contents:**- The semester activities may include exposure to and exploration of
the following topics.
Partial Topic List:

- Review of elementary probability: probabilities and events, conditional probability, random variables, expected values, covariance, and correlation.
- Normal random variables: continuous random variables, properties of normal random variables, the Central Limit Theorem.
- Brownian motion: geometric Brownian motion and its development as a limit of simpler models.
- Review of interest rates and present value analysis: rates of return and continuously varying interest rates.
- Fixed-income securities: value formulas, bond details, yield, duration.
- Term structure of interest rates: yield curve, forward rates, floating rate bonds.
- Capital asset pricing model: market equilibrium, capital market line, security market line, investment implications.
- Examples pricing contracts via arbitrage.
- General principles: utility functions, risk aversion, linear pricing, portfolio choice, finite models, risk-neutral pricing.
- The Arbitrage Theorem: the Fundamental Theorem of Financial Mathematics and multiperiod binomial models.
- The Black-Scholes formula: properties of Black-Scholes option cost, estimating the volatility parameter, and pricing Put Options.
- Valuing by expected utility: limitations of arbitrage pricing, portfolio selections, estimating covariances, mean variance analysis of risk-neutral-priced Call Options, and single period rates of return.
- Interest rate derivatives: examples, theory, and pricing applications,

**Attendance:**Students are expected to attend all class meetings. If you must be absent from class on the day an assignment is due, you must complete and hand in the assignment prior to the absence. If you know you will be absent on the day of a test, you must notify me before the time the test is scheduled in order to schedule a make-up test. Students who miss a test should provide a valid excuse, otherwise you will not be allowed to make up the test. Tests should be made up within one week of their scheduled date. No final exam exemptions.

**Homework:**Students are expected to do their homework and participate in class. Students should expect to spend a minimum of three hours outside of class on homework and review for every hour spent in class. Occasionally specific homework problems will be assigned for collection and grading. Students should submit all homework by the date due. Late homework will not be accepted without valid excuse. Discussion between students on homework assignments is encouraged, but homework submitted for grading should be written up separately.

**Tests:**There will be a midterm test (Friday, October 5, 2001) and a comprehensive final examination (Friday, December 14, 2001, 12:30PM-2:30PM). I will not ``curve'' midterm or exam grades.

**Grades:**Course grade will be calculated as follows.

Midterm test 20% Final exam 20% Homework/Projects 60% Course grades will be based on the student's participation in the seminar and their graded written homework. I keep a record of students' homework scores. Students should also keep an individual record of graded assignments. I will not ``curve'' course grades. The course letter grades will be calculated as follows.

90-92 A 93-100 A 80-82 B 83-86 B 87-89 B 70-72 C 73-76 C 77-79 C 60-62 D 63-66 D 67-69 D 0-59 F **Final Word:**Math is not a spectator sport. What you learn from this course and your final grade depend mainly on the amount of work you put forth. Daily contact with the material through homework assignments and review of notes taken during lectures is extremely important.

Robert.Buchanan@millersville.edu

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