#### Description

Introduction to the basic concepts in mathematical finance for undergraduate students with a strong mathematical background particularly in probability theory. The focus is on mathematical methods in pricing of derivative securities, portfolio management, and on related questions of mathematical finance. Some emphasis is placed on the Black-Scholes formula and its applications to the pricing of options.

#### Prerequisites

Minimum grade of C- in MATH141; and 1 course with a minimum grade of C- from (STAT400, STAT410); and permission of CMNS-Mathematics department.

Recommended MATH246, MATH240, MATH241, MATH340, or MATH341.

Level of Rigor

Standard

Sample Textbooks

An Elementary Intro. to Math. Finance: Options & Other Topics, by Sheldon Ross

Applications

Finance

If you like this course, you might also consider the following courses

STAT470, AMSC420/MATH420

Additional Notes

Duplicate credit with BMGT444.

#### Topics

From a recent course outline:

A Random Walk Down the Wall Street

Financial Markets and Instruments

Interest Rates and Present Value Analysis

Normal Distribution of Stock Returns

Introduction to Option Pricing

Capital Asset Pricing Model and Arbitrage Pricing Theory

The Multi-period Binomial Model

The Black-Scholes Option Pricing Formula and its Proof

Applications of the Black-Scholes Formula

Trading and Hedging of Options

Utility Functions and Portfolio Theory

Bond Mathematics

Interest Rate Derivatives and Related Models

Risk Measurement and Risk Management

NOTE: The course BMGT 343 is an introduction to investments, covering the many investment instruments in use today. This course is not necessary for the mathematics of MATH 424, but BMGT 343 provides real-world context and motivation for MATH 424, and is a valuable course in its own right. BMGT 343 is available to non-BMGT majors only on a space available basis: in the summer, and in the academic year from hold files (after BMGT majors are served). BMGT 220-221-340 are prerequisites for BMGT 343, but students may take BMGT 343 (given space available as above) on a caveat-emptor basis without the prerequisites. Part of the reason for these three prerequisites to BMGT 343 is the need in BMGT to manage course sequencing for their majors; our experience is that a good student in math or the sciences can do well in BMGT 343 without the prerequisites.