Correlation modelling with application to risk management

Abstract

Accurate estimation and prediction of correlation is of paramount importance in asset allocation, risk management and hedging applications, particularly in light of recent studies that provide evidence of increased correlation during periods of high volatility, leading to diminishing diversification benefits in states of nature that are most needed. The time-variability of the correlation process has fuelled extensive literature on dynamic correlation modelling. In an attempt to depart from correlation estimation based on projections from historical data, two alternative measures of correlation, namely the implied and the realized correlation, have been proposed in the recent literature. Remarkably, in contrast to volatility estimates, existing studies on the informational efficiency and forecasting performance of respective correlation measures are rather limited.This thesis focuses on exploring the dynamics that govern the evolution of correlation risk premium and its components, namely implied and realized correlation, and assessing the impact of predictability to portfolio allocation, hedging and trading decisions. First, the time-variation and certain distribution characteristics of the correlation risk premium, defined as the difference of realized and implied correlation, are examined. The information content of market –specific and macroeconomic variables, which have been previously reported as proxies of the business cycles, in predicting future premium is also evaluated. Secondly, a model-free measure of implied correlation is proposed and the question of predictable dynamics in the evolution of the series is investigated both in statistical and economic terms. A trading strategy designed to exploit daily changes of the series sets the foundation for addressing the efficient market hypothesis. Finally, based on the distributional properties of realized volatility, correlation and hedge ratio, an alternative forecasting methodology is applied to predictthe realized hedge ratio and to explore the additive value of intraday data in a dynamichedging context while the hedging performance is compared in terms of portfoliooptimization and risk management.The thesis has reached a number of conclusions. First, correlation and correlationrisk premium vary substantially over time and increase sharply during turbulent periods,while culminated during the Asian and Russian financial crisis in 1997-1998 and thesubprime mortgage crisis of 2007-2009. The previously documented correlation riskpremium is no longer significant during the recent 2007 – 2009 crisis, suggesting thedisappearance of arbitrage opportunities. Secondly, the predictability of model-freeimplied correlation series suggested by statistical measures cannot be exploited in termsof economic gains, suggesting that the S&P 100 options market is efficient. Finally,forecasting the dynamics of the realized hedge ratio directly reveals predictable patternsin the evolution of the hedge ratio, resulting in improved hedging performance, in termsof both economics gains and risk measures.