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 calculus

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