Financial cross-ownership as a structural explanation for rising stock correlations in crisis times

Bertschinger, Nils; Araneda, Axel A.


Systemic risk has been studied extensively since the latest financial crisis. On the one hand, empirical measures of systemic risk have been proposed and applied to market data. A common idea underlying these measures states that asset prices tend to fall collectively during crisis times. Correspondingly, the correlation, in a dynamical and conditional framework, between different assets as well as between single assets and the overall market has been proposed by several scholars as a measure of contagion in turbulent periods. Nowadays, it is an established “stylized fact” that asset correlations rise during crisis times. On the other hand, network models have made important contributions towards understanding systemic risk from a theoretical perspective. Especially the seminal work of Eisenberg & Noe is well-known in this respect, forming the basis for numer- ous studies of financial contagion arising from cross-ownership of debt. Suzuki, an extension of this basic model allowing for cross-ownership of debt as well as equity, provides an interesting, alternative viewpoint connecting the valuation of interbank contracts with derivative pricing. The famous Merton model, which relates the debt and equity of a firm with European put and call options respectively, provides an established framework for pricing credit risk of single firms. Yet, in case of cross-ownership, firms cannot be considered individually and risk management has to take into account the potential for financial contagion. Indeed, all firms have to be valued collectively and self-consistently when taking into account cross-ownership. Here we show that network valuation models can readily explain the stylized fact concerning the rise of correlations during crisis times. For instance, the bivariate Suzuki model, with cross-ownership of debt only and one external business asset per company, shows that rising correlation emerges as a direct consequence from financial cross-holdings when considered from an ex-ante perspective. In particular, using a combination of analytic results and numerical simulations, we prove that the risk-neutral values of both firms are strongly correlated when these are insolvent – even with uncorrelated business assets. Thereby providing a structural explanation for rising correlations as firm values remain uncorrelated as long as both are solvent.

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Fecha de publicación: 2019
Año de Inicio/Término: September 9–11, 2019