Aim
The course should be regarded as the statistical part of a course package also including TEK180 Financial Valuation and Risk Management and FMS170 Valuation of Derivative Assets. Its purpose is to give the student tools for constructing models for risk valuation and pricing, based on data.

Knowledge and understanding
For a passing grade the student must

• handle variance models such as the GARCH family, stochastic volatility, and models used for high-frequency data,

• use basic tools from stochastic calculus: Itô's formula, Girsanov transformation, martingales, Markov processes, filtering,

• use tools for filtering of latent processes, such as Kalman filters and particle filters,

• statistically validate models from some of the above model families.

Skills and abilities
For a passing grade the student must

• be able to find suitable stochastic models for financial data,

• work with stochastic calculus for pricing of financial contracts and for transforming models so that data becomes suitable for stochastic modelling,

• understand when and how filtering methods should be applied,

• validate a chosen model in relative and absolute terms,

• solve all parts of a modelling problem using financial and statistical theory (from this course and from other courses) where the solution includes model specification, inference, and model choice,

• present the solution in a written technical report, as well as orally,

• utilise scientific articles within the field and related fields.

Contents
The course deals with model building and estimation in non-linear dynamic stochastic models for financial systems. The models can have continuous or discrete time and the model building concerns determining the model structure as well as estimating possible parameters. Common model classes are, e.g., GARCH models with discrete time or models based on stochastic differential equations in continuous time. The course participants will also meet statistical methods, such as Maximum-likelihood and (generalised) moment methods for parameter estimation, kernel estimation techniques, non-linear filters for filtering and prediction, and particle filter methods.

The course also discusses prediction, optimization, and risk evaluation for systems based on such descriptions.

Literature
Madsen, H, Nielsen, J N, Lindström, E, Baadsgaard, M & Holst, J: Statistics in Finance. IMM, DTU, Lyngby and KFSigma, Lund 2006.