Clifford Paul et al. Numerical Methods in Finance. Part A

Unpublished, 2010. — 144 p.The aim of this module is to learn to think about modeling in finance. To practice thinking about what is driving cause and effect in some simple models. To analyze the models numerically.
In order to do this we shall have the following objectives. We shall learn
how to use MatLAB to explore with models
Basics of numerical linear algebra, ill-posed systems, numerical iteration schemes;
The simplest Markov chain models in finance
The law of large numbers, central limit theorem, large deviations theory and risk, Markowitz portfolio theory
Discrete stochastic volatility models and distributions with ’fat tails’.
CRR and Black-Scholes models: theory and numerics
General properties of systems of ODE’s and stochastic ODE’s, the simplest numerical schemes for solving (S)DE’s, stochastic volatility in continuous time.