620-302 Chance and Options Pricing

Students may only gain credit for one of 620-302, 300-316, [04]300-332.

620-301. Students with 620-201 and a strong mathematical background may be granted permission to enrol by the Head of Department.

This subject focuses on modern probability theory methods and modelling with a view to applications in science, finance and insurance. Students learn probability modelling by using the concepts of the theory of stochastic processes. They are introduced to the basic machinery of the theory, to the ideas of no-arbitrage pricing through simple binomial models, and then to stochastic calculus and to diffusion models in finance and biology. This subject demonstrates the importance of probability methods in the sciences and finance.

Topics covered include basic methods in probability and distribution theory in discrete and continuous time, the concepts of no-arbitrage asset pricing and hedging, conditional expectations, integral transforms, random walks, martingales, Brownian motion process, stochastic calculus, diffusion processes and their applications. Applications include models in finance (such as the Black-Scholes model for asset pricing and diffusion models for interest rates) and biology (such as diffusion models in genetics and population dynamics).

Up to 50 pages of written assignments due during the semester (20%); a 3-hour written examination in the examination period (80%).