Financial Statistics
Finansiell statistik

FMSN60F, 7.5 högskolepoäng

Gäller från och med: Autumn 2020
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2020-05-19

Allmänna uppgifter

Avdelning: Mathematical Statistics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMSN60
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

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.

Kurslitteratur

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

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, laborationer, övningar, projekt

Kursens examination

Examinationsformer: Skriftlig rapport, seminarieföredrag av deltagarna
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förkunskapskrav: FMSF10 Stationary Stochastic Processes
Förutsatta förkunskaper: EXTF45 Financial Management and preferrably also one or several of FMSN45 Time series analysis, TEK180/EXTQ35 Financial Valuation and Risk Management, and FMSN25 Valuation of Derivative Assets.

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: www.maths.lth.se/matstat/kurser/fmsn60/