Modeliranje tržnega tveganja v kontekstu nelinearnih in večdimenzionalnih odvisnosti z modelom GMMN-GARCH : magistrsko delo

Pozne, Jaša (author), Košir, Tomaž (mentor)

S spremembami finančne regulative se je povečala potreba po naprednih metodah ocenjevanja tveganj. V delu je predstavljen model GMMN-GARCH, ki združuje GARCH za modeliranje volatilnosti časovnih vrst ter GMMN za zajemanje kompleksnih odvisnosti med spremenljivkami. Za zmanjšanje dimenzionalnosti podatkov in izboljšanje računske učinkovitosti je bila uporabljena metoda glavnih komponent (PCA). Model se je izkazal za robustnega in fleksibilnega, saj natančno zajema porazdelitev logaritmiranih donosov in omogoča prilagajanje trenutnim tržnim razmeram. Rezultat je učinkovit in zanesljiv pristop za ocenjevanje tveganj, primeren za uporabo v sodobnih finančnih okoljih.

• Language: Slovenian
• Keywords: GARCH, metoda glavnih komponent (PCA), generativna omrežja za ujemanje momentov (GMMN), maksimalno neskladje med prvimi momenti (MMD), tržno tveganje, nelinearne večdimenzionalne odvisnosti.
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2025
• PID: 20.500.12556/RUL-176656
• COBISS.SI-ID: 260124419
• Publication date in RUL: 07.12.2025

Secondary language

• Language: English
• Title: Modelling market risk in the context of nonlinear and multidimensional dependencies using the GMMN-GARCH model

Abstract

Evolving financial regulations have increased the demand for advanced risk assessment methods. This study presents a GMMN-GARCH model, combining GARCH for volatility modelling in time series with GMMN to capture complex interdependencies among variables. Principal component analysis (PCA) was used to reduce data dimensionality and improve computational efficiency. The model demonstrated robustness and flexibility, accurately reflecting the distribution of log-returns while adapting to current market conditions. Overall, it provides an effective and reliable approach for risk assessment in contemporary financial environments.

• Keywords: GARCH, principal component analysis (PCA), generative moment matching networks (GMMN), maximum mean discrepancy (MMD), market risk, nonlinear multivariate dependencies.