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. / 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

Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.