Dynamic correlation models

Abstract

Correlation is one of the most important parameters that needs to be estimated in the context of Modern Portfolio Theory. Accurate estimates of correlation are required across most applications in finance such as portfolio optimization, asset allocation, risk management, hedging and contingent claim pricing. Surprisingly, correlation estimation has not received significant attention in the finance literature compared to other estimators such as volatility. Traditionally, correlation has been modeled as a constant and unconditional variable. Over the years, practitioners have come to realize that correlation actually varies through time and several researchers have provided empirical evidence to support this view (e.g., Von Fustenberg and Jeon, 1989, Koch and Koch, 1991, Erb et al., 1994, Longin and Solnik, 1995). The recognition of the time-variability of correlation has motivated a continuously growing amount of research on a wide variety of dynamic correlation models. This research is focused on developing and investigating innovative methods for estimating and forecasting correlation between financial asset returns. Firstly, the importance of correlation estimation in financial applications is examined focusing on a risk management application. More specifically, the effect of correlation mis-estimation on Value-at-Risk calculation is investigated. Secondly, a traditional financial economics problem regarding the international financial market linkages is addressed based on a dynamic correlation structure. An application to the European bond markets volatility transmission mechanism is provided. Thirdly, an innovative methodology for forecasting correlation using the market prices of derivative instruments is developed. By applying this methodology to the Dow Jones Industrial Average index, the statistical properties and the forecasting performance of the implied correlation measure are examined. A number of important results are drawn from this research. Firstly, the accurate estimation of correlation in an important task for risk managers since errors in correlation estimation affect significantly the Value-at-Risk calculation. Secondly, by considering a dynamic correlation structure in the volatility transmission mechanism of the European bond markets, new evidence may be drawn regarding the links between these markets. Finally, correlation forecasts as implied by option prices are useful proxies of future correlation and contain additional information not included in traditional historical forecasts.