Estimation of Yu and Meyer bivariate stochastic volatility model by iterated filtering

Abstract

In financial applications, understanding the asset correlation structure is crucial to tasks such as asset pricing, portfolio optimisation, risk management, and asset allocation. Thus, modelling the volatilities and correlations of multivariate stock market returns is of great importance. This paper proposes the iterated filtering algorithm for estimating the bivariate stochastic volatility model of Yu and Meyer. The iterated filtering method is a frequentist-based approach that utilises particle filters and can be applied to estimating the parameters of non-linear or non-Gaussian state-space models. The paper presents an empirical example that demonstrates the way in which the proposed estimation method might be used to estimate the correlation between the returns of two assets: Standard and Poor’s 500 index and the price of gold in US dollars. This is accompanied by a simulation study that proves the validity of the approach.

Estimation of the Cholesky Multivariate Stochastic Volatility Model Using Iterated Filtering

“…Iterated filtering has demonstrated successful applications to various State Space Models, predominantly within the context of epidemiology (Bhadra et al, 2011;He et al, 2009;King et al, 2008;Stocks et al, 2020;You et al, 2020). Additionally, it has been employed in economic modelling, particularly for univariate (Bretó, 2014;Szczepocki, 2020) and bivariate (Szczepocki, 2022) stochastic volatility models.…”