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Modelling of Stochastic Volatility using Partially Observed Markov Models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Modellering av Stokastisk Volatilitet genom Partiellt Observerbara Markovmodeller (Swedish)
Abstract [en]

In this thesis, calibration of stochastic volatility models that allow correlation between the volatility and the returns has been considered. To achieve this, the dynamics has been modelled as an extension of hidden Markov models, and a special case of partially observed Markov models. This thesis shows that such models can be calibrated using sequential Monte Carlo methods, and that a model with correlation provide a better fit to the observed data. However, the results are not conclusive and more research is needed in order to confirm this for other data sets and models.

Abstract [sv]

Detta examensarbete behandlar kalibrering av stokastiska volatilitetsmodeller som tillåter korrelation mellan volatiliteten och avkastningen. För att uppnå detta beteende har dynamiken modellerats som ett specialfall av partiellt observerbara Markovmodeller som är en utvidgning av dolda Markovmodeller (HMMer). I denna masteruppsats visas att dessa typer av modeller kan kalibreras med sekventiella Monte Carlo-metoder och att dessa modeller ger en bättre anpassning till observerad data. Resultaten är emellertid inte entydiga och det är nödvändigt utreda frågan vidare för andra modelltyper och andra datamängder.

Place, publisher, year, edition, pages
TRITA-MAT-E, 2016:62
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-192878OAI: diva2:974083
External cooperation
Subject / course
Mathematical Statistics
Educational program
Master of Science - Applied and Computational Mathematics
Available from: 2016-09-23 Created: 2016-09-21 Last updated: 2016-09-23Bibliographically approved

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