Course Syllabus for

Financial Statistics Finansiell statistik

FMSN60F, 7.5 credits

Valid from: Autumn 2020
Decided by: Professor Thomas Johansson
Date of establishment: 2020-05-19

General Information

Division: Mathematical Statistics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMSN60
Teaching language: English

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.

Goals

Knowledge and Understanding

For a passing grade the doctoral 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: ItÃ´'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.

Competences and Skills

For a passing grade the doctoral 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.

Course 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.

Course Literature

Henrik Madsen, E. & Nielsen, J.: Statistics for Finance. Chapman and Hall/CRC, 2015.

Instruction Details

Types of instruction: Lectures, laboratory exercises, exercises, project

Examination Details

Examination formats: Written report, seminars given by participants