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Particle-based Stochastic Volatility in Mean model
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Partikel-baserad stokastisk volatilitet medelvärdes model (Swedish)
Abstract [en]

This thesis present a Stochastic Volatility in Mean (SVM) model which is estimated using sequential Monte Carlo methods. The SVM model was first introduced by Koopman and provides an opportunity to study the intertemporal relationship between stock returns and their volatility through inclusion of volatility itself as an explanatory variable in the mean-equation. Using sequential Monte Carlo methods allows us to consider a non-linear estimation procedure at cost of introducing extra computational complexity. The recently developed PaRIS-algorithm, introduced by Olsson and Westerborn, drastically decrease the computational complexity of smoothing relative to previous algorithms and allows for efficient estimation of parameters. The main purpose of this thesis is to investigate the volatility feedback effect, i.e. the relation between expected return and unexpected volatility in an empirical study. The results shows that unanticipated shocks to the return process do not explain expected returns.

Abstract [sv]

Detta examensarbete presenterar en stokastisk volatilitets medelvärdes (SVM) modell som estimeras genom sekventiella Monte Carlo metoder. SVM-modellen introducerades av Koopman och ger en möjlighet att studera den samtida relationen mellan aktiers avkastning och deras volatilitet genom att inkludera volatilitet som en förklarande variabel i medelvärdes-ekvationen. Sekventiella Monte Carlo metoder tillåter oss att använda icke-linjära estimerings procedurer till en kostnad av extra beräkningskomplexitet. Den nyligen utvecklad PaRIS-algoritmen, introducerad av Olsson och Westerborn, minskar drastiskt beräkningskomplexiteten jämfört med tidigare algoritmer och tillåter en effektiv uppskattning av parametrar. Huvudsyftet med detta arbete är att undersöka volatilitets-återkopplings-teorin d.v.s. relationen mellan förväntad avkastning och oväntad volatilitet i en empirisk studie. Resultatet visar på att oväntade chockar i avkastningsprocessen inte har förklarande förmåga över förväntad avkastning.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:317
Keywords [en]
Stochastic volatility model, Volatility feedback theory, hidden Markov model, particle filter, Expectation-Maximization algorithm, PaRIS-algorithm
Keywords [sv]
Stokastisk volatilitets modell, dold Markov modell, partikel-filter, Förväntan-Maximering algorithm, PaRIS-algoritm, volatilitets-återkopplings-teori
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-257505OAI: oai:DiVA.org:kth-257505DiVA, id: diva2:1347997
External cooperation
CIMalgo
Subject / course
Financial Mathematics
Educational program
Master of Science - Industrial Engineering and Management
Supervisors
Examiners
Available from: 2019-09-06 Created: 2019-09-03 Last updated: 2019-09-06Bibliographically approved

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