The course aims to provide a grounding in random processes leading to a solid but understandable treatment of derivative pricing and the mathematics behind it; but all done from an 'engineering' point of view. Spreadsheet and matlab software will be used for illustration and exercises. It is expected there will be guest lectures from experts. The course is in three parts. (1) Random Process background: including topics such as Markov processes, Kolmogorov forward and backward equations, Brownian motion; simulation studies will be used to assist the theoretical material. (2) Elementary Finance Background: including topics such as futures, options, swaps, futures pricing and arbitrage methods. (3) Derivative Pricing: including topics such as binomial tree-based option pricing; Ito calculus and risk neutral pricing; pricing of European and American options; and a selection from pricing of stock indices, currency exchange instruments, interest rate instruments.