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Copula Based VaR Estimation for Portfolio Using Hierarchical Clustering

Triantafillidis, Hektor LU and Woxström, Alexander LU (2024) In Master’s Theses in Mathematical Sciences 2024 FMSM01 20241
Mathematical Statistics
Abstract
This paper focuses on constructing models that predict a Value at Risk (VaR) estimation for financial portfolios using hierarchical clustering and copulas. Traditional VaR models often assume linear dependencies and normal distributions, which can be poor assumptions for financial data - especially during extreme market events. This paper introduces a non-linear modeling approach using copulas to capture the complex dependencies and tail risks among portfolio components. More precisely, the paper applies hierarchical clustering to group stocks from the OMXS30GI index, then models these sub-portfolios with various copula families, including t-Copula, Gumbel, Clayton, and Frank copula.

The approach is performed in four main steps: first... (More)
This paper focuses on constructing models that predict a Value at Risk (VaR) estimation for financial portfolios using hierarchical clustering and copulas. Traditional VaR models often assume linear dependencies and normal distributions, which can be poor assumptions for financial data - especially during extreme market events. This paper introduces a non-linear modeling approach using copulas to capture the complex dependencies and tail risks among portfolio components. More precisely, the paper applies hierarchical clustering to group stocks from the OMXS30GI index, then models these sub-portfolios with various copula families, including t-Copula, Gumbel, Clayton, and Frank copula.

The approach is performed in four main steps: first clustering the stocks based on different metrics, modeling stock returns with ARMA-GARCH models, applying copula models to sub-portfolios, and lastly backtesting the VaR predictions. The backtesting was performed over a period from January 2020 to March 2024, using daily data to retrain the copula models and a fixed clusters.

Results show that copula-based models outperform traditional methods in predicting
VaR. Among the tested models, the Gumbel and t-Copula showed the best performance
in terms of exceedances and statistical tests, confirming their ability to capture
tail dependencies. This paper contributes to the field of financial risk management
by providing a method for VaR estimation for larger portfolios that accounts for
non-linear dependencies and extreme events. (Less)
Popular Abstract
An important driver of long term portfolio performance is risk management. Value at-Risk (VaR) is a popular method used in finance to estimate the maximum loss of a portfolio over a given period. To do this, traditional VaR methods make assumptions that generally do not align with the nature of real financial data. Using advanced statistical tools called clustering and copulas, a new model with less strict assumptions could be developed - more accurately predicting VaR than the traditional models.
Please use this url to cite or link to this publication:
author
Triantafillidis, Hektor LU and Woxström, Alexander LU
supervisor
organization
course
FMSM01 20241
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master’s Theses in Mathematical Sciences 2024
report number
LUTFMS-3494-2024
ISSN
1404-6342
other publication id
2024:E25
language
English
id
9164040
date added to LUP
2024-06-19 10:10:19
date last changed
2024-06-19 10:10:19
@misc{9164040,
  abstract     = {{This paper focuses on constructing models that predict a Value at Risk (VaR) estimation for financial portfolios using hierarchical clustering and copulas. Traditional VaR models often assume linear dependencies and normal distributions, which can be poor assumptions for financial data - especially during extreme market events. This paper introduces a non-linear modeling approach using copulas to capture the complex dependencies and tail risks among portfolio components. More precisely, the paper applies hierarchical clustering to group stocks from the OMXS30GI index, then models these sub-portfolios with various copula families, including t-Copula, Gumbel, Clayton, and Frank copula.

The approach is performed in four main steps: first clustering the stocks based on different metrics, modeling stock returns with ARMA-GARCH models, applying copula models to sub-portfolios, and lastly backtesting the VaR predictions. The backtesting was performed over a period from January 2020 to March 2024, using daily data to retrain the copula models and a fixed clusters.

Results show that copula-based models outperform traditional methods in predicting
VaR. Among the tested models, the Gumbel and t-Copula showed the best performance
in terms of exceedances and statistical tests, confirming their ability to capture
tail dependencies. This paper contributes to the field of financial risk management
by providing a method for VaR estimation for larger portfolios that accounts for
non-linear dependencies and extreme events.}},
  author       = {{Triantafillidis, Hektor and Woxström, Alexander}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master’s Theses in Mathematical Sciences 2024}},
  title        = {{Copula Based VaR Estimation for Portfolio Using Hierarchical Clustering}},
  year         = {{2024}},
}