Estimating the Wishart Affine Stochastic Correlation Model Using the Empirical Characteristic Function

47 Pages Posted: 6 Dec 2007 Last revised: 24 Jan 2017

See all articles by José Da Fonseca

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Florian Ielpo

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES); Unigestion

Date Written: August 13, 2012

Abstract

In this paper, we present and discuss the estimation of the Wishart Affine Stochastic Correlation (WASC) model introduced in Da Fonseca et al. (2006) under the historical measure. We review the main estimation possibilities for this continuous time process and provide elements to show that the utilization of empirical characteristic function-based estimates is advisable as this function is exponential affine in the WASC case. We thus propose to use the estimation strategy presented in Carrasco et al. (2003), using a continuum of moment conditions based on the characteristic function. We investigate the behavior of the estimates through Monte Carlo simulations. Then, we present the estimation results obtained using a dataset of equity indexes: SP500, FTSE, DAX and CAC. On the basis of these results, we show that the WASC captures many of the known stylized facts associated with financial markets, including the negative correlation between stock returns and volatility. It also helps reveal interesting patterns in the studied indexes'covariances and their correlation dynamics.

Keywords: Wishart Process, Empirical Characteristic Function, Stochastic Correlation

JEL Classification: C32, C51, G12, G15

Suggested Citation

Da Fonseca, José and Grasselli, Martino and Ielpo, Florian, Estimating the Wishart Affine Stochastic Correlation Model Using the Empirical Characteristic Function (August 13, 2012). Available at SSRN: https://ssrn.com/abstract=1054721 or http://dx.doi.org/10.2139/ssrn.1054721

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

Martino Grasselli

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

Florian Ielpo (Contact Author)

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES) ( email )

106-112 Boulevard de l'hopital
106-112 Boulevard de l'Hôpital
Paris Cedex 13, 75647
France

Unigestion ( email )

8c, avenue de Champel CP 387
CP 387
Genève 12, CH 1211
Switzerland

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