filtrations and martingales

n completion of this module the student should be able to:
1. use filtrations and martingales to model market developments;
2. develop appropriate stochastic methods to evaluate return rates on risky assets and their derivatives;
3. derive and apply the Black-Scholes formula to price an option on a stock modelled by a random walk;
4. independently choose, apply and manipulate professional tools to model markets and value assets;
5. develop an understanding of current research methods in finance and summarise current research in this area.
Indicative Content
1. Review of probability: discrete and continuous random variables, properties, normal distribution, convergence of random variables, limit theorems
2. Review of statistics: sampling and estimation, parameter estimation, regression techniques, tests for normality, Bayesian techniques
3. Discrete time stochastic processes and their application in financial analysis
Conditional expectation, Markov chains, filtrations, martingales
4. Continuous time stochastic processes and their application in financial analysis
Brownian motion, stochastic integrals, Ito calculu

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