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Sequential parameter and state learning in continuous time stochastic volatility models using the SMC² algorithm
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Sekventiell estimering av parametrar och tillstånd i tidskontinuerliga stokastiska volatilitetsmodeller nyttjandes SMC² algoritmen (Swedish)
Abstract [en]

In this Master’s thesis, joint sequential inference of both parameters and states of stochastic volatility models is carried out using the SMC2 algorithm found in SMC2: an efficient algorithm for sequential analysis of state-space models, Nicolas Chopin, Pierre E. Jacob, Omiros Papaspiliopoulos. The models under study are the continuous time s.v. models (i) Heston, (ii) Bates, and (iii) SVCJ, where inference is based on options prices. It is found that the SMC2 performs well for the simpler models (i) and (ii), wheras filtering in (iii) performs worse. Furthermore, it is found that the FFT option price evaluation is the most computationally demanding step, and it is suggested to explore other avenues of computation, such as GPGPU-based computing.

Abstract [sv]

I denna Masteruppsats estimeras sekventiellt parametrar och tillstånd i stokastiska volatilitetsmodeller nyttjandes SMC2 -algoritmen som återfinns i [1]. Modellerna som studeras är de kontinuerliga s.v.-modellerna (i) Heston, (ii) Bates och (iii) SVCJ, där inferens baseras på optionspriser. Vi finner att SMC2 presterar bra resultat för de enklare modellerna (i) och (ii) emedan filtrering för (iii) presterar sämre. Vi finner ytterligare att det beräkningsmässigt tyngsta steget är optionsprissättning nyttjandes FFT, därför föreslås det att undersöka andra beräkningssätt, såsom GPGPU-beräkning

Place, publisher, year, edition, pages
TRITA-MAT-E, 2015:80
Keyword [en]
SMC2, SMC, SV models
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-177104OAI: diva2:872346
Subject / course
Mathematical Statistics
Educational program
Master of Science - Applied and Computational Mathematics
Available from: 2015-11-18 Created: 2015-11-13 Last updated: 2015-11-18Bibliographically approved

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