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Correlation modelling with application to risk management
(07-2014) Markopoulou, Chrysi E.; Athens University of Economics and Business, Department of Management Science and Technology; Giannikos, Christos; Spinellis, Diomidis; Refenes, Apostolos P.
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 predict the realized hedge ratio and to explore the additive value of intraday data in a dynamic hedging context while the hedging performance is compared in terms of portfolio optimization and risk management. The thesis has reached a number of conclusions. First, correlation and correlation risk premium vary substantially over time and increase sharply during turbulent periods, while culminated during the Asian and Russian financial crisis in 1997-1998 and the subprime mortgage crisis of 2007-2009. The previously documented correlation risk premium is no longer significant during the recent 2007 – 2009 crisis, suggesting the disappearance of arbitrage opportunities. Secondly, the predictability of model-free implied correlation series suggested by statistical measures cannot be exploited in terms of economic gains, suggesting that the S&P 100 options market is efficient. Finally, forecasting the dynamics of the realized hedge ratio directly reveals predictable patterns in the evolution of the hedge ratio, resulting in improved hedging performance, in terms of both economics gains and risk measures.
Higher moments modeling and forecasting
Kostika, Eleftheria; Athens University of Economics and Business, Department of Management Science and Technology; Refenes, Apostolos P.
This thesis extends the literature on portfolio selection with higher moments by investigating how non-normality of returns and higher moments may affect hedging strategies. In order to account for time varying skewness and kurtosis in optimal hedge ratio estimation, the ARCD model proposed by Hansen (1994) is employed, in which full conditional density is modelled allowing for conditional shape parameters. In a horserace of models, the dynamic hedging effectiveness of the ARCD is compared to that obtained by OLS, error-correction, exponential moving averages, and, univariate and multivariate GARCH. Effectiveness is measured in-sample and out-of-sample using the minimum variance method. Spot and futures daily closing prices are used for stock indices from the US, UK and Germany for the period January 1999 to September 2004. The results suggest that the hedging performance using the ARCD outperforms that obtained by the competing approaches. Also, in this thesis an alternative, simplified multivariate model is proposed, the simplified Multivariate Autoregressive Conditional Density Model (S-ARCD) which is compatible with the skewness and kurtosis of the financial returns and is easy to be implemented increasing the computational efficiency. It is based also, on the Autoregressive Conditional Density Model (ARCD) proposed by Hansen (1994) and involves the estimation only of the univariate specification of the above model. The conditional variances are calculated by the simple univariate models, and the conditional covariance is then imputed from these variance estimates. The S-ARCD is illustrated to forecast the VaR of aggregate equity portfolios for the US and UK and foreign exchange portfolio for EUR and GBP against USD and is compared to the ad hoc multivariate version of GARCH (Wang, Yao, 2005) and BEKK models. The results, using both statistical and economic criteria, suggest that the simplified multivariate version of ARCD performs at least well as the other two models indicating the higher moments’ importance in volatility forecasting and VaR calculation. Finally, the thesis examines the Autoregressive Conditional Density (ARCD) application in combination with the framework of Hasbrouck (1995) in order to investigate empirically the predictive ability of error-correction models based on the cointegration relationship between option and spot prices. Although the cointegration relationship between spot and option prices has been studied in the literature, the implications in terms of error-correction modelling have not yet been empirically examined. Using daily index and option closing prices from the US, France and Germany we identify significant cointegration relationships in each market and estimate nonlinear error-correction models. Also, the role of higher moments in the cointegration relationship is not important. The error-correction model results suggest that both option and spot prices contain information about option price returns.