6 points, SCA Band 2, 0.125 EFTSL
Undergraduate - Unit
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
School of Mathematical Sciences
- First semester 2017 (Day)
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.
On completion of this unit students will be able to:
- Appreciate the modern approach to evaluation of uncertain future payoffs;
- Describe the concepts of arbitrage and fair games and their relevance to finance and insurance;
- Understand conditional expectation, martingales, and stopping times, as well as the Optional Stopping Theorem;
- Interpret models of random processes such as random walk, Brownian motion and diffusion, and stochastic differential equations;
- Use Ito's formula and basic stochastic calculus to solve some stochastic differential equations;
- Apply the Fundamental theorems of asset pricing to the Binomial and Black-Scholes models, as well as models for bonds and options on bonds;
- Formulate discrete time Risk Model in Insurance and use the Optional Stopping Theorem to control probabilities of ruin;
- Simulate stochastic processes and solutions of stochastic differential equations, and obtain prices by simulations.
Weekly exercises: 10%
Examination (3 hours): 70%
Three 1-hour lectures and one 2-hour support class per week
See also Unit timetable information
This unit applies to the following area(s) of study
Students must be enrolled in the Master of Financial Mathematics or have passed: one of MTH1030, MTH1035, ENG1005, ETC2440 and one of MTH2010, MTH2015, MTH2032, MTH2040, MTH2222, ENG2005, ETC2520.