These units aim to integrate a basic understanding of how financial markets work with the analytic tools for modelling their time dependent structures. Since these structures are based on random ("stochastic") processes, stochastic models underpin the methods. Where feasible, analytic methods are developed. The aim is to present as much financial theory about securities markets as possible without requiring the advanced mathematics that is associated with continuous time models. Topics include single period securities markets, valuation of contingent claims, portfolio management, stochastic volatility, the binomial model, value at risk, credit modelling applications.