620-302 Chance and Options Pricing

Note

Credit Points

HECS Band

Coordinator

Prerequisites

620-301. Students with 620-201 or 620-203 and a strong mathematical background may be granted permission to enrol by the head of department.

Semester

Contact

Subject Description

This subject focuses on modern probability methods and modelling with the view of the application to science, finance and insurance. Students learn probability modelling by using the concepts of stochastic processes. They learn basic models based on Brownian motion and apply these to continuous-time models of asset prices. Students are introduced to stochastic calculus and to diffusion models in finance and biology as well as Monte Carlo simulations for these models. This subject demonstrates the importance of probability methods in finance and the sciences.

Topics covered include basic methods in probability and distribution theory in discrete and continuous time, transforms, conditioning, random walk, martingales, Brownian motion, Ito's formula, Brownian motion calculus, stochastic differential equations and diffusions; levy processes and their applications; applications include models in finance (such as the Black-Scholes model, multidimensional asset model and the Vasicek model for interest rates), and in biology (such as diffusion models in genetics and population dynamics); and Monte Carlo simulations of price processes of stocks and options.

Assessment

Up to 50 pages of written assignments; a 3-hour end-of-semester written examination; and class tests totalling not more than 1.5 hours.