620-302 Chance and Options Pricing

Credit cannot be gained for both 620-302 and 300-332.

620-301. Students with 620-201 or [01]620-203 and a strong mathematical background may be granted permission to enrol by the Head of Department.

This subject focuses on modern probability methods and modelling with a view to applications in 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 the sciences and finance.

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; and 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).

This subject contributes to developing students' generic skills as well. These include the ability to adopt new ideas, from participation in the lecture program, and to develop creative ways of solving unfamiliar problems, especially through practice classes.

Up to 50 pages of written assignments (20%) and a 3-hour end-of-semester written examination (80%).