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A Brief Study of the Multifractal Model of Asset Returns.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2012 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Understanding the processes that determine price variations is important in evaluating risks in the financial system. Many of the conventional models used to describe price variations are based on the model of Brownian motion. This model fails to take into account large price deviations, dependence and clustering that are present in financial markets. This thesis attempts to explain an alternative method, the Multifractal Model of Asset Returns (MMAR), based mainly on the three papers published by Mandelbrot, Fisher and Calvet in 1997. MMAR allows for large price deviations, clustering and dependence of price variation. In this thesis, the theoretical framework of MMAR is covered and some empirical tests are then carried out on the JPY/USD and SEK/USD exchange rate to show the faults of the conventional model and to examine the validity of the MMAR. The Hurst exponents of the exchange rates are estimated and the results seem to indicate there are some signs of multifractality for the JPY/USD rate. It is however difficult to measure the value of the MMAR in relationship to the complexity it brings.

Abstract [sv]

För att kunna bedöma finansiella risker, är det viktigt att förstå hur priser varierar. Konventionella modeler som har använts för att modellera prisvariationer bygger på Brownsk rörelse. Brownsk rörelse, tar dock ej hänsyn till stora prisförändringar, klusterfenomen och eventuellt beroende mellan prisförändringar. Syftet med denna uppsats är att presentera en alternativ modell, Multifractal Modelf of Asset Returns, (MMAR), som huvudsakligen bygger på tre artiklar publicerade av Mandelbrot, Fisher och Calvet år 1997. MMAR tillåter stora prisförändringar, klusterfenomen och beroende mellan prisförändringar. I denna uppsats framställs den teoretiska bakgrunden och sedan utförs ett antal empiriska tester av MMAR på valutakurserna JPY/USD och SEK/USD. Detta utmynnar i en uppskattning av Hurst-exponenten och resultaten tycks indikera att det finns multifraktalitet i JPY/USD-kursen. Det är dock svårt att uppskatta värdet hos MMAR i förhållande till den komplexitet som tillförs.

Place, publisher, year, edition, pages
2012. , 25 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-103870OAI: oai:DiVA.org:kth-103870DiVA: diva2:562079
Uppsok
Technology
Supervisors
Available from: 2013-01-15 Created: 2012-10-23 Last updated: 2013-02-11Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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