Abstract
In this paper we consider a portfolio selection problem defined for irregularly spaced observations. We use the Independent Component Analysis for the identification of the dependence structure and continuous-time GARCH models for the marginals. We discuss both estimation and simulation of market prices in a context where the time grid of price quotations differs across assets. We present an empirical analysis of the proposed approach using two high-frequency datasets that provides better out-of-sample results than competing portfolio strategies except for the case of severe market conditions with frequent rebalancements.
Highlights
Conditional heteroskedasticity is a well-known stylized fact observed in financial time series
We use continuous-time models for the dynamics of the independent components extracted from real market time series
The independence of the components and the estimation algorithm for COGARCH( p, q) models proposed in Iacus et al (2018) constitutes the main ingredients of a portfolio optimization problem where the objective function is expressed as a linear combination of expected portfolio wealth and a homogeneous risk measure
Summary
Conditional heteroskedasticity is a well-known stylized fact observed in financial time series. The objective function in the portfolio selection problem is a combination of the expected terminal wealth and a specific risk measure2 Another possible way to address this modeling issue would be to use multivariate COGARCH processes as defined in Stelzer (2010) but with additional numerical estimation burden in a multivariate context where the fitting is based on a quasi-maximum likelihood procedure. The discrete process in (5) has been used in Iacus et al (2018) for the construction of a pseudo-maximum likelihood estimation procedure for a COGARCH( p, q) model based on the assumption of normality for i,n. This procedure generalizes the approach proposed in Maller et al (2008) for a COGARCH(1, 1) model.
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