Cryptocurrency Correlation Modeling with Multivariate GARCH
(2024) In Master's Thesis in Mathematical Sciences FMSM01 20241Mathematical Statistics
- Abstract
- This thesis investigates the dynamic correlation between the S&P 500 and Bitcoin returns from 2018 to 2024. To capture potential regime-specific dynamics,
a Markov Switching Model is employed to segment each return data into two
distinct states characterized by high or low volatility, using a LASSO regression
to find the appropriate explanatory variables for the returns.
Univariate GARCH(1,1) models are initially fitted to each regime’s return series. Using the parameters from the univariate models, the multivariate models
are estimated for each combination of high and low volatility regimes for both
S&P 500 and Bitcoin, for a total of four different regimes. A DCC-GARCH(1,1)
framework is used for the multivariate model. The... (More) - This thesis investigates the dynamic correlation between the S&P 500 and Bitcoin returns from 2018 to 2024. To capture potential regime-specific dynamics,
a Markov Switching Model is employed to segment each return data into two
distinct states characterized by high or low volatility, using a LASSO regression
to find the appropriate explanatory variables for the returns.
Univariate GARCH(1,1) models are initially fitted to each regime’s return series. Using the parameters from the univariate models, the multivariate models
are estimated for each combination of high and low volatility regimes for both
S&P 500 and Bitcoin, for a total of four different regimes. A DCC-GARCH(1,1)
framework is used for the multivariate model. The univariate model parameters
are fixed in the multivariate model, only estimating the remaining parameters
a and b for the correlation update equation. The parameter estimates are compared to a GARCH(1,1) and a DCC-GARCH(1,1) estimated on the complete
dataset.
This approach gives us four different parameter sets, each corresponding to a
specific volatility regime combination. The parameter sets are run on the complete dataset, giving us four different correlation and volatility estimates for
the investigated period. Finally, to get a smoother transition between regimes,
fuzzy clustering is applied to the volatility estimates.
The resulting model gives a correlation estimate that is similar to a standard
DCC-GARCH(1,1) on the dataset but is more responsive like a rolling correlation measure. We note that the correlation is at an elevated level during and
after the COVID-19 pandemic, but has dropped to pre-pandemic levels during
the end of 2023. (Less) - Popular Abstract (Swedish)
- Historiskt sett har Bitcoin ansetts vara en volatil tillgång utan koppling till traditionella investeringar som S&P 500. Därför har investerare kunnat använda Bitcoin som en "säker hamn" under nedgångar på börsen. Under COVID-19 skedde dock en oväntad förändring - korrelationen mellan Bitcoin och börsindex ökade kraftigt. I detta examensarbete undersöker vi om detta var en tillfällig svängning eller en långsiktig trend. Vår studie kan ge värdefull information till investerare om Bitcoin fortfarande kan fungera som en "säker hamn" eller om de behöver anpassa sina portföljer.
Vi använde tre olika modeller för att analysera korrelationen:
1. En enkel modell med en rullande 30/60-dagars korrelation.
2. DCC-GARCH(1,1) där parametrarna... (More) - Historiskt sett har Bitcoin ansetts vara en volatil tillgång utan koppling till traditionella investeringar som S&P 500. Därför har investerare kunnat använda Bitcoin som en "säker hamn" under nedgångar på börsen. Under COVID-19 skedde dock en oväntad förändring - korrelationen mellan Bitcoin och börsindex ökade kraftigt. I detta examensarbete undersöker vi om detta var en tillfällig svängning eller en långsiktig trend. Vår studie kan ge värdefull information till investerare om Bitcoin fortfarande kan fungera som en "säker hamn" eller om de behöver anpassa sina portföljer.
Vi använde tre olika modeller för att analysera korrelationen:
1. En enkel modell med en rullande 30/60-dagars korrelation.
2. DCC-GARCH(1,1) där parametrarna skattades för hela datamängden.
3. En viktad DCC-GARCH(1,1) modell där parametrarna skattades för olika perioder med liknande struktur. Dessa perioder identifierades med en Markov Switching Regime-modell och viktades med en Fuzzy clustering-algoritm.
Syftet med den tredje modellen är att få bättre estimeringar av parametrarna i DCC-GARCH(1,1)-modellen. Alla tre modeller visade att korrelationen var högre under och efter COVID-19. Intressant nog sjönk inte korrelationen omedelbart efter pandemin, utan behöll en förhöjd nivå under en tid. Sedan slutet av 2023 har vi dock sett en gradvis nedgång, och korrelationen ligger nu nära samma låga nivåer som före pandemin.
Vår viktade modell visade sig likna referensmodellen DCC-GARCH vad gäller strukturen på den estimerade korrelationen. Den skiljer sig dock genom att den är mer lyhörd för snabba förändringar i korrelationen. Samtidigt undviker den att överdriva volatiliteten i jämförelse med den enkla 30/60-dagars rullande korrelationen, både vid kraftiga uppgångar och nedgångar. Vi anser att detta är en viktig fördel med vår viktade modell, då den ger en mer nyanserad bild av korrelationen mellan Bitcoin och börsindex och samtidigt fångar upp förändringar i marknadsdynamiken på ett effektivt sätt. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9162285
- author
- Ottosson, Isak LU and Rauf, Nawa LU
- supervisor
- organization
- course
- FMSM01 20241
- year
- 2024
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- Bitcoin, S&P500, Markov Regime Switching, LASSO regression, DCC-GARCH, Volatility, Fuzzy Clustering
- publication/series
- Master's Thesis in Mathematical Sciences
- report number
- LUTFMS-3495-2024
- ISSN
- 1404-6342
- other publication id
- 2024:E37
- language
- English
- id
- 9162285
- date added to LUP
- 2024-06-19 10:00:26
- date last changed
- 2024-06-19 10:00:26
@misc{9162285,
abstract = {{This thesis investigates the dynamic correlation between the S&P 500 and Bitcoin returns from 2018 to 2024. To capture potential regime-specific dynamics,
a Markov Switching Model is employed to segment each return data into two
distinct states characterized by high or low volatility, using a LASSO regression
to find the appropriate explanatory variables for the returns.
Univariate GARCH(1,1) models are initially fitted to each regime’s return series. Using the parameters from the univariate models, the multivariate models
are estimated for each combination of high and low volatility regimes for both
S&P 500 and Bitcoin, for a total of four different regimes. A DCC-GARCH(1,1)
framework is used for the multivariate model. The univariate model parameters
are fixed in the multivariate model, only estimating the remaining parameters
a and b for the correlation update equation. The parameter estimates are compared to a GARCH(1,1) and a DCC-GARCH(1,1) estimated on the complete
dataset.
This approach gives us four different parameter sets, each corresponding to a
specific volatility regime combination. The parameter sets are run on the complete dataset, giving us four different correlation and volatility estimates for
the investigated period. Finally, to get a smoother transition between regimes,
fuzzy clustering is applied to the volatility estimates.
The resulting model gives a correlation estimate that is similar to a standard
DCC-GARCH(1,1) on the dataset but is more responsive like a rolling correlation measure. We note that the correlation is at an elevated level during and
after the COVID-19 pandemic, but has dropped to pre-pandemic levels during
the end of 2023.}},
author = {{Ottosson, Isak and Rauf, Nawa}},
issn = {{1404-6342}},
language = {{eng}},
note = {{Student Paper}},
series = {{Master's Thesis in Mathematical Sciences}},
title = {{Cryptocurrency Correlation Modeling with Multivariate GARCH}},
year = {{2024}},
}