At the end of this course, the student will learn:

• the basics of fixed income securities and portfolio optimisation under discrete time models
• European and American type option pricing via Binomial (Lattice or Tree) method
• how to derive and solve the famous Black-Scholes differential equation for options
• Monte Carlo methods and variance reduction techniques in option pricing
• to generate pseudo-random numbers from a given distribution, in particular, normal distribution
• the basics of numerical solutions of stochastic differential equations, Euler-Maruyama scheme
• finite-difference methods to solve partial differential equations (PDEs) and apply the techniques in valuation of options
• the basic principles of pricing American options using PDEs and hence free boundary problems
• basic principles of control problems