# Financial Mathematics

University of Queensland

## Course Description

• ### Course Name

Financial Mathematics

• ### Host University

University of Queensland

• ### Location

Brisbane, Australia

• ### Area of Study

Finance, Mathematics

• ### Language Level

Taught In English

• ### Prerequisites

MATH1051 + MATH1052 + (STAT2003 or STAT2004)

Recommended Prerequisite

STAT2003 + COSC2500

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Host University Units

2
• Recommended U.S. Semester Credits
4
• Recommended U.S. Quarter Units
6
• ### Overview

Course Description
Introduction to financial mathematics and its applications. Mathematical models of annuities, equity and fixed-income products, futures and forward contracts, the term structure of interest rates and investment returns.

Course Introduction
This course is an introduction to financial and actuarial mathematics. It introduces basic concepts and principles in finance and basic mathematical and statistical tools used by financial mathematicians and actuaries. Topics covered will include a selection from the following: compound interest and annuities, discounted cashflow valuation, risk and return, fixed interest securities, valuation by arbitrage and replication, derivative securities including futures, swaps and options, the term structure of interest rates, stochastic models for investment returns, modern portfolio and financial theory, risk management.

Learning Objectives
After successfully completing this course you should be able to:

1. INTEREST RATES AND ANNUITIES
• 1.1 Understand the function of the financial system and the role played by financial mathematicians and actuaries
• 1.2 Model the cash flows of a range of financial contracts in discrete and continuous time
• 1.3 Understand and derive the relationships between interest rates across different time periods
• 1.4 Define, derive and use the compound interest and annuity functions of relevance to financial mathematicians and actuaries

2. STOCHASTIC AND FINANCIAL MODELING
• 2.1 Define and use an equation of value when cash flows are uncertain
• 2.2 Show how both discrete- and continuous-time discounted cash flow techniques can be used to appraise investments
• 2.3 Mathematically describe the investment characteristics of fixed income assets (debt), equity (shares) and financial derivatives
• 2.4 Understand arbitrage pricing and use arbitrage pricing for futures/forwards, swap contracts, and foreign exchange markets
• 2.5 Understand and perform basic calculations relating to the term structure of interest rates (yield curve)
• 2.6 Understand and derive simple stochastic interest rate models

3. PORTFOLIO CONSTRUCTION AND ANALYSIS
• 3.1 Derive and understand simple stochastic models for equity (shares)
• 3.2 Derive and understand the main results of modern portfolio theory
• 3.3 Define and identify a coherent risk measure
• 3.4 Define and understand the role of risk measures in the management of risky assets

4. OPTIONS AND THE BLACK-SCHOLES MODEL
• 4.1 Understand the defining characteristics of options and options markets
• 4.2 Understand the notion of risk-neutral pricing and the fundamental theorems of asset pricing in a simple one-period setting
• 4.3 Have a basic appreciation and understanding of the derivation of the Black-Scholes model by the heat equation
• 4.4 Understand how the notions of arbitrage and replication are used in the derivation of the Black-Scholes model

Class Contact
3 Lecture hours, 1 Tutorial hour

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.