Sequential Monte Carlo Methods in Practice

Abstract

With the continuous increase in computational power, sequential Monte Carlo methods have emerged as an efficient technique for estimating unknown data in a world consisting of nonlinearity and non-Gaussianity. In this thesis, we are building a theoretical foundation by the help of Bayesian statistics, that can be applied to numerous real-world problems. We are interested in solving the prob- lem of estimating an unknown signal process given certain observations, where both processes are modelled as Markovian, nonlinear, non-Gaussian state-space models. In particular, we will try to estimate the unobserved volatility dynamics for the S&P 500 index using observed returns and a slight modification of Hes- ton’s stochastic volatility model. This will be done by the sequential importance resampling filter, which we will also combine with Markov chain Monte Carlo for parameter estimation. Our overall goal is to propose another alternative to Heston’s model, by investigating how well the model responds to measuring volatility when including data from the financial crisis of 2007-2008.

Keywords: Bayesian inference; sequential Monte Carlo; volatility filtering; fi- nancial econometrics; particle Markov chain Monte Carlo