Correlation Structure of International Equity Markets During Extremely Volatile Periods

Correlation in international equity returns is unstable over time. It has been suggested that the international correlation of large stock returns, especially negative ones, differs from that of usual returns. It is in periods of extreme negative returns that the benefits of international risk diversification are most desired and that the question of international correlation is most relevant to risk-averse agents. If return distributions are not multivariate normal, the usual standard deviation and correlation of returns do not provide sufficient information. Additional information can be gained by focusing directly on the properties of extreme returns. While the interest in stock market crashes and booms is large, no study has specifically focused on the correlation between large price movements. A major econometric issue is to specify the multivariate distribution of extreme returns implied by a given distribution of returns. In this paper, we work directly on large returns and study the dependence structure of international equity markets during extremely volatile periods. We use the results of extreme value theory to model the multivariate distribution of large returns, using monthly data from January 1959 to December 1996 for the five largest stock markets. We find that the correlation of large positive returns are not inconsistent with the assumption of multivariate normality. However, the correlation of large negative returns is much greater than expected, suggesting that the benefits of international risk reduction in extremely volatile periods have been overstated.international equity market; volatility; correlation; extreme value theory

Extreme correlation of international equity markets

Testing the hypothesis that international equity market correlation increases in volatile times is a difficult exercise and misleading results have often been reported in the past because of a spurious relationship between correlation and volatility. This paper focuses on extreme correlation, that is to say the correlation between returns in either the negative or positive tail of the multivariate distribution. Using "extreme value theory" to model the multivariate distribution tails, we derive the distribution of extreme correlation for a wide class of return distributions. Using monthly data on the five largest stock markets from 1958 to 1996, we reject the null hypothesis of multivariate normality for the negative tail, but not for the positive tail. We also find that correlation is not related to market volatility per se but to the market trend. Correlation increases in bear markets, but not in bull markets.International equity markets; volatility; correlation and extreme value theory

A backward dual representation for the quantile hedging of Bermudan options

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of the pricing function. This algorithm is similar to the usual American backward induction, except that it requires two additional Fenchel transformations at each exercise date. We provide numerical illustrations

Numerical investigation of acoustic solitons

Acoustic solitons can be obtained by considering the propagation of large amplitude sound waves across a set of Helmholtz resonators. The model proposed by Sugimoto and his coauthors has been validated experimentally in previous works. Here we examine some of its theoretical properties: low-frequency regime, balance of energy, stability. We propose also numerical experiments illustrating typical features of solitary waves

Anisotropic behaviour law for sheets used in stamping: A comparative study of steel and aluminium

For a car manufacturer, reducing the weight of vehicles is an obvious aim. Replacing steel by aluminium moves towards that goal. Unfortunately, aluminium's stamping numerical simulation results are not yet as reliable as those of steel. Punch-strength and spring-back phenomena are not correctly described. This study on aluminium validates the behaviour law Hill 48 quadratic yield criterion with both isotropic and kinematic hardening. It is based on the yield surface and on associated experimental tests (uniaxial test, plane tensile test, plane compression and tensile shearing)