The aim of the course is to explain in very simple - namely discrete
time - settings the fundamental ideas of modelling of financial markets
and pricing of derivative securities using the principle of no
arbitrage. Even the simplest of all models with only one time step
allows several important notions to be illustrated. The module
progresses with more complex models - with many time steps and several
stocks - which are developed along with the corresponding theory of
pricing and hedging derivative securities such as options or forwards.
Relatively simple mathematical considerations lead to powerful notions
and techniques underlying the theory - such as viability, completeness,
self-financing and replicating strategies, arbitrage and equivalent
martingale measures. These are directly applicable in practice,
particularly in the continuous time limiting theory developed in a
subsequent module. The general methods are applied in detail in
particular to pricing and hedging European and American options within
the Cox-Ross-Rubinstein (CRR) binomial tree model. The Black-Scholes
model as the limit of CRR models is discussed to pave the way for the
continuous time theory.

- Teacher: Dr. Javed Hussain