Financial contagion and asset pricing

Abstract

Asset market interconnectedness can give rise to significant contagion risks during periods of financial crises that extend beyond the risks associated with changes in volatilities and correlations. These channels include the transmission of shocks operating through changes in the higher order comoments of asset returns, including changes in coskewness arising from changes in the interaction between volatility and average returns across asset markets. These additional contagion channels have nontrivial implications for the pricing of options through changes in the payoff probability structure and more generally, in the management of financial risks. The effects of incorrectly pricing risk has proved to be significant during many financial crises, including the subprime crisis from mid 2007 to mid 2008, the Great Recession beginning 2008 and the European debt crisis from 2010. Using an exchange options model, the effects of changes in the comoments of asset returns across asset markets are investigated with special emphasis given to understanding the effects on hedging risk during financial crises. The results reveal that by not correctly pricing the risks arising from higher order moments during financial crises, there is significant mispricing of options, while hedged portfolios during noncrisis periods become exposed to price movements in times of crises.

Introduction

The subprime financial crisis of 2007–2008, immediately followed by the Great Recession in mid 2008, and more recently the European debt crisis beginning 2010, reveal significant risks that arise from the interconnectedness of asset markets in the global financial landscape. The magnitude of shock transmissions from one market to others often far exceed expectations based on normal market linkages and dependence structures between assets (Dungey et al., 2010). Not only do the codependence structures across financial markets change dramatically during periods of financial turbulence, these changes often extend beyond the usual changes in market correlation, and include additional crisis transmission channels operating through higher order comoments of asset returns (Fry et al., 2010).

The effect of changes in the comoments of asset returns on recent financial crises are highlighted in Table 1, Table 2. Table 1 provides the descriptive statistics on the first three moments of equity returns for five European countries and the US over four periods: a noncrisis period (January 3, 2006–July 25, 2007), and three crisis periods consisting of the subprime crisis (July 26, 2007–September 14, 2008), the Great Recession (September 15, 2008–December 31, 2012) and the European debt crisis (January 1, 2010–August 30, 2012) compared to the noncrisis period. All six countries are characterized by falls in average returns and increases in volatility during each crisis. Skewness also increases during the crisis periods, changing from negative skewness in the noncrisis period for equity returns of all six countries to either positive skewness or smaller negative skewness. Table 2 shows that similar results occur for coskewness between pairs of equity returns of countries, with coskewness changing from being negative in the noncrisis period to being either positive or a smaller negative coskewness in the crisis periods. The only exception is in Table 2 where coskewness between the US and Greece (last block of the table) becomes more negative during the Great Recession, changing from $-0.181$ to $-0.238$.

As the statistics in Table 1, Table 2 allude, asset mispricing can be particularly significant during periods of financial crisis and contagion and that this has important implications for market participants engaged in the hedging of financial risks and for financial regulators seeking to manage risks across the financial institutions. This is particularly the case for exchange option contracts written on two or more assets where changes in the dependence structure of the underlying assets have a direct impact on the price of the option. Significant risk exposures to changes in higher order moments remain if hedging strategies are formulated using the standard Black–Scholes model that invokes multivariate normality.

To investigate the effects of contagion during financial crises on alternative hedging strategies, an exchange options model is developed following Fry et al. (2010) which extends the usual Black–Scholes assumption of lognormal prices of the underlying assets that an option is written on, to a more general distribution that allows for the effects of higher order moments as well as comoments arising from coskewness (see also Flynn et al., 2005, Lim et al., 1998, Martin et al., 2005, Lim et al., 2005, Lim et al., 2006 in the case of non-exotic options). Special attention is given to identifying the size of mispricing from higher order comoments of asset returns during the crisis periods and how it impacts upon hedging strategies. The key results of the analysis reveal significant mispricing of options during financial crises from not pricing the risks associated with higher order moments. The analysis also shows that portfolios that are hedged against price movements during noncrisis periods become exposed to unfavorable price movements during periods of crises.

The adoption of a generalized normal distribution to capture higher order codependence in asset returns represents a natural choice as Fry et al. (2010) show that Lagrange multiplier tests of contagion can be derived which relate to existing tests of comoments such as coskewness. An alternative approach to capture higher order dependence is based on using copulas (Patton, 2006, Rodriguez, 2007, Harvey, 2010, Busetti and Harvey, 2011). This approach is also adopted by Martin and Wang (2013) who propose a nonparametric test of contagion. Earlier approaches, especially in the context of modeling options in the presence of nonnormal asset returns, consist of the lognormal mixture model of Melick and Thomas (1997); the Edgeworth expansion of Jarrow and Rudd, 1982, Corrado and Su, 1997; the Hermite polynomial approximation of Ane (1999); the nonparametric density estimator of Aït-Sahalia et al. (2001); and the neural network approach of Garcia and Gencay (2000).

In addition to the above, there are a range of methods focussing on the importance of transmission channels of contagion operating in higher order moments or crisis measurement through extreme value methods. Usually these are in applications which are not focussed on options, however are worth mentioning here. Most of these methods use the information in the extreme (crisis) periods in subtly different ways to understand crises and contagion. Dungey et al. (2010) provide a summary of the key methods. For example, Favero and Giavazzi, 2002, Pesaran and Pick, 2007 test for contagion in the outliers of asset returns; Bae et al. (2003) propose a coexceedance test based on a multinomial logit model; whereas Aït-Sahalia et al. (2010) allow for mutual jumps using a Hawkes process. Others use extreme value measures either to forecast crisis events such as in the early warning system literature of Frankel and Rose, 1996, Kaminsky and Reinhart, 1999 and more recently by Lo Duca and Peltonen (2013), or to detect a state of crisis such as the exchange market pressure index of Eichengreen et al., 1995, Eichengreen et al., 1996 and extensions thereof. Related literature is by Diebold and Yilmaz (2009) who identify changes in the connectedness of asset markets during financial crises.

The rest of the paper proceeds as follows. Section 2 sets out an exchange option contract where the bivariate generalized normal distribution is specified to allow for contagious channels operating through higher order moments and comoments during periods of financial crises. To investigate the effects of these additional channels of contagion on exchange options, a bivariate generalized lognormal distribution is introduced to model the joint stochastic behavior of the underlying asset prices at the time the option contract matures. The results show that changes in coskewness can change the mass of the joint probability distribution of prices, resulting in changes in the probabilities of the payoffs and, in turn, the price of the options. The analysis is extended in Section 3 where the effects on hedging strategies are discussed in the presence of contagion during financial crises. Concluding comments and implications for portfolio management during financial crises are provided in Section 4.