Multi-asset modelling is of fundamental importance to financial applications such as risk management and portfolio selection. In this article, we propose a multivariate stochastic volatility modelling framework with a parsimonious and interpretable correlation structure. Building on well-established evidence of common volatility factors among individual assets, we consider a multivariate diffusion process with a common-factor structure in the volatility innovations. Upon substituting an observable market proxy for the common volatility factor, we markedly improve the estimation of several model parameters and latent volatilities. The model is applied to a portfolio of several important constituents of the S&P500 in the financial sector, with the VIX index as the common-factor proxy. We find that the prediction intervals for asset forecasts are comparable to those of more complex dependence models, but that option-pricing uncertainty can be greatly reduced by adopting a common-volatility structure. The Canadian Journal of Statistics 48: 36–61; 2020 © 2020 Statistical Society of Canada

Résumé

La modélisation multi-actifs revêt une importance fondamentale pour les applications financières telles que la gestion du risque et la gestion de portefeuille. Les auteurs proposent un cadre de modélisation multivariée de la volatilité stochastique comportant une structure de corrélation parcimonieuse et interprétable. En se fondant sur les indices bien établis de facteurs communs de volatilité entre les actifs individuels, ils considèrent un processus de diffusion multivarié avec une structure à facteurs communs pour la volatilité des innovations. Après avoir substitué le facteur commun de volatilité par un proxy observable dans les marchés, les auteurs ont considérablement amélioré l'estimation de plusieurs paramètres du modèle et des volatilités latentes. Ils appliquent également leur modèle à un portfolio composé de plusieurs titres du S&P500 dans le secteur financier, avec l'indice VIX comme facteur commun. Ils trouvent que les intervalles de prévision pour les actifs sont comparables à ceux obtenus avec des modèles de dépendance plus complexes, mais que l'incertitude dans la valorisation d'options peut être réduite substantiellement par une structure de volatilité commune. La revue canadienne de statistique 48: 36–61; 2020 © 2020 Statistical Society of Canada

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Volume48, Issue1

Special issue on Stochastic Models, Statistics and Finance

March 2020

Pages 36-61

Common-factor stochastic volatility modelling with observable proxy

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