Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
The GARCH-copula model for gaugeing time conditional dependence in the risk management of electricity derivatives
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
GARCH-copula modellen för att uppskatta tidsbetingat beroende vid riskhanteringen av eletricitetsderivat (Swedish)
Abstract [en]

In the risk management of electricity derivatives, time to delivery can be divided into a time grid, with the assumption that within each cell of the grid, volatility is more or less constant. This setup however does not take in to account dependence between the different cells in the time grid.

This thesis tries to develop a way to gauge the dependence between electricity derivatives at the different places in the time grid and different delivery periods. More specifically, the aim is to estimate the size of the ratio of the quantile of the sum of price changes against the sum of the marginal quantiles of the price changes.

The approach used is a combination of Generalised Autoregressive Conditional Heteroscedasticity (GARCH) processes and copulas. The GARCH process is used to filter out heteroscedasticity in the price data. Copulas are fitted to the filtered data using pseudo maximum likelihood and the fitted copulas are evaluated using a goodness of fit test.

GARCH processes alone are found to be insufficient to capture the dynamics of the price data. It is found that combining GARCH with Autoregressive Moving Average processes provides better fit to the data. The resulting dependence is the found to be best captured by elliptical copulas. The estimated ratio is found to be quite small in the cases studied. The use of the ARMA-GARCH filtering gives in general a better fit for copulas when applied to financial data. A time dependency in the dependence can also be observed.

Abstract [sv]

GARCH-copula modellen för att uppskatta tidsbetingat beroende vid riskhanteringen av eletricitetsderivat Vid riskhantering av elektrictitetsderivat kan, tid till leverans delas upp I ett rutnät med antagandet att volatiliteten kan anses konstant för varje ruta i nätet. Detta upplägg tar emellertid inte hänsyn till beroende mellan de olika rutorna i rutnätet.

Detta examensarbeta försöker att utveckla en metod för att uppskatta detta beroende för eletricitetsderivat som befinner sig i på olika platser i rutnätet och som har olika leveransperioder. Mer specifikt är målet att uppskatta kvoten mellan kvantilen av summerade prisförändringar mot summan av de marginella kvantilerna hos prisförändringar.

Angreppsättet är en kombination av så kallade Generelised Autoregressive Conditional Heteroscedasticity (GARCH) och så kallade copulas. GARCH processen används för att filtrera ut heteroskedicitet i prisdatan. Copulas passas till den filtrerade via pseduo maximum likelihood och ett test av anpassningens kvalitet tillämpas.

GARCH processer allena visar sig vara otillräckliga för att fånga dynamiken i prisdatan. Det visar sig att en kombination av GARCH och autoregressive moving avergae (ARMA) processer ger en bättre anpassning till data. Det resulterande beroendet visar sig fångas bäst av elliptiska copulas. Den skattade kvoten visar sig vara rätt liten i de studerade fallen. Användingen av ARMA-GARCH visar sig också ge en bättre anpassning till copulas när de används till finansiell data. En tidsbetingning i beroendet kan också observeras.

Place, publisher, year, edition, pages
2017.
Series
TRITA-MAT-E, 2017:49
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-209966OAI: oai:DiVA.org:kth-209966DiVA: diva2:1119548
External cooperation
Nasdaq Clearing AB
Subject / course
Mathematical Statistics
Educational program
Master of Science in Engineering -Engineering Physics
Supervisors
Examiners
Available from: 2017-07-04 Created: 2017-07-04 Last updated: 2017-07-04Bibliographically approved

Open Access in DiVA

fulltext(2227 kB)17 downloads
File information
File name FULLTEXT01.pdfFile size 2227 kBChecksum SHA-512
0186922c9f86d1d2dc72d622d0ee25ddfa3025590f90ca91fb8a8349da02f81ac3b5a4090ba19bf60ba3f287dc14db62cfa93af4ee53d41bed0ce31813237d18
Type fulltextMimetype application/pdf

By organisation
Mathematical Statistics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 17 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 68 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf