A Nested Factor Model for Non-Linear Dependences in Stock Returns

23 Pages Posted: 14 Sep 2013

Date Written: September 12, 2013

Abstract

The aim of our work is to propose a natural framework to account for all the empirically known properties of the multivariate distribution of stock returns. We define and study a "nested factor model", where the linear factors part is standard, but where the log-volatility of the linear factors and of the residuals are themselves endowed with a factor structure and residuals. We propose a calibration procedure to estimate these log-vol factors and the residuals. We find that whereas the number of relevant linear factors is relatively large (10 or more), only two or three log-vol factors emerge in our analysis of the data. In fact, a minimal model where only one log-vol factor is considered is already very satisfactory, as it accurately reproduces the properties of bivariate copulas, in particular the dependence of the medial-point on the linear correlation coefficient, as reported in Chicheportiche and Bouchaud (2012). We have tested the ability of the model to predict Out-of-Sample the risk of non-linear portfolios, and found that it performs significantly better than other schemes.

Suggested Citation

Chicheportiche, Rémy and Bouchaud, Jean-Philippe, A Nested Factor Model for Non-Linear Dependences in Stock Returns (September 12, 2013). Available at SSRN: https://ssrn.com/abstract=2324754 or http://dx.doi.org/10.2139/ssrn.2324754

Rémy Chicheportiche (Contact Author)

Ecole Centrale Paris ( email )

Paris
France

Jean-Philippe Bouchaud

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France
+33 1 49 49 59 20 (Phone)

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