Modelling the existence of joint large movements of asset prices in financial theory may potentially lead to significant improvements in specific areas of finance, such as asset pricing, optimal portfolio choice, derivatives valuation and hedging, and management and measurement of financial risks. However, the construction and estimation of models taking into account large movements of asset prices is a non-trivial task. Large movements may be directly modelled but more often their characteristics are implicitly assumed by adopting a general probability distribution used to model the asset prices.
There is no economic or statistical theory supporting any specific probability distribution for joint large asset returns. Hence, a model has to be assumed which may or may not be based on data analysis. For decades the standard probability distribution selected for asset prices was the multivariate normal. Still today, financial regulators base their directives largely on models with an underlying normal distribution.
Assuming a multivariate normal distribution for asset price returns implies that, asymptotically, large joint price movements occur independently. Yet, financial market crashes, for instance those occurred in 1929 or in 1987, had effects across several markets and financial institutions. Hence the multivariate normal distribution may underestimate the probability of joint large financial events. The need for alternative models has been recognised by practitioners and academics.
Attempts to depart from normality have been made specifically in terms of modelling large events. Examples of studies focussed on the univariate behavior of large movements in financial markets are Cotter (2006), Danielsson and de Vries (2000), Jansen and de Vries (1991), Longin (1996), Longin (2005) and McNeil and Frey (2000). There is not much literature on the more difficult case of modelling multivariate large movements: Longin and Solnik (2001) study the extreme correlation between international markets by modelling the dependence of bivariate extreme events with the logistic function proposed by Gumbel (1961). Poon et al. (2004) emphasize the importance of distinguishing between dependent and independent extreme events and use the logistic function to model the case of dependence.
In these studies, the dependence structure between the extreme events in different markets is estimated through a parametric model from extreme value theory assumed a priori. The natural scarcity of observed extreme events does not facilitate model specification tests. A related reference on the pitfalls and opportunities in the use of extreme value theory in finance is Diebold et al. (1998). Further, when the number of risk factors increases the appropriateness of a parametric model becomes dubious, its estimation more difficult and the results less reliable.
Download
Semi-parametric estimation of joint large movements of risky assets
