units

MTH3251

Faculty of Science print version

This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

# MTH3251 - Financial mathematics

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Offered

Clayton

• First semester 2016 (Day)

### Synopsis

Random variables, application to models of random payoffs. Conditional expectation. Normal distribution and multivariate normal distribution. Best predictors. Stochastic (random) processes. Random walk. Limit theorems. Brownian motion. Ito integral and Ito's formula. Black-Scholes, Ornstein-Uhlenbeck process and Vasicek's stochastic differential equations. Martingales. Gambler's ruin. Fundamental theorems of Mathematical Finance. Binomial and Black-Scholes models. Models for Interest Rates. Risk models in insurance. Ruin probability bound. Principles of simulation. Use of Excel package.

### Outcomes

On completion of this unit students will be able to:

1. Appreciate the modern approach to evaluation of uncertain future payoffs;

1. Describe the concepts of arbitrage and fair games and their relevance to finance and insurance;

1. Understand conditional expectation, martingales, and stopping times, as well as the Optional Stopping Theorem;

1. Interpret models of random processes such as random walk, Brownian motion and diffusion, and stochastic differential equations;

1. Use Ito's formula and basic stochastic calculus to solve some stochastic differential equations;

1. Apply the Fundamental theorems of asset pricing to the Binomial and Black-Scholes models, as well as models for bonds and options on bonds;

1. Formulate discrete time Risk Model in Insurance and use the Optional Stopping Theorem to control probabilities of ruin;

1. Simulate stochastic processes and solutions of stochastic differential equations, and obtain prices by simulations.

### Assessment

Assignments: 20%
Weekly exercises: 10%
Final examination (three hours): 70%

Three 1-hour lectures and one 1-hour support class per week 