Realized Volatility: Macroeconomic determinants, Forecasting and Option trading

The estimation and modeling of financial volatility asset has been one of the most active research areas because of its crucial importance in asset pricing, risk management and portfolio allocation. However, the main problem is that volatility is not directly observable. Common approaches to deal with the latency of the volatility are the parametric (Generalized) Autoregressive Conditional Heteroskedasticity ((G)ARCH) family of models introduced by Engle (1982) and Bollerslev (1986) or the stochastic volatility (SV) models (see, for example, Taylor, 1986). With the growing availability of high frequency price data and based on the theory of quadratic variation, the estimation of volatility has moved from latent volatility model to non-parametric realized measures. Andersen et al. (2001) and Barndorff-Nielsen and Shephard (2002) introduced the Realized Variance as the sum of squared returns over non-overlapping intervals within a sampling period. In theory, the realized variance is an unbiased and highly efficient estimator that converges to the integrated variance when the length of the intra-day intervals goes to zero. In addition, Christensen and Podolskij (2007) and Martens and van Dijk (2007) proposed the Realized Range-based Variance. This estimator is defined as the sum of the squared ranges (i.e. the difference between the maximum and minimum prices observed during a period) over non-overlapping intervals. It is a consistent and highly efficient estimator of the integrated volatility and it is about five times more efficient than realized variance. Then, volatility becomes observable and it is possible to model it in order to obtain forecasts that are needed in many financial applications. In practice, the implementation of realized estimation measures in the reality of high frequency data faces various difficulties. These estimators are based on the assumptions that the prices follow a continuous sample path and they are sensitive to microstructure noise, which can cause severe problems for the estimator’s consistency. This PhD thesis aims at modeling and forecasting volatility, and contributes to the financial econometrics literature in three different directions. The first chapter, a joint work with Professor Massimiliano Caporin, considers the modeling and forecasting of volatility based on the realized range estimator and explores the performance of alternative specifications that take into account the distinct behavior and stylized facts of financial volatility time series. The second chapter focuses on the economic determinants of financial volatility and analyzes the predictive ability that macroeconomic and financial variables have when forecasting volatility. Finally, the third chapter deals with the evaluation of alternative estimators and forecasting models of volatility from an economic point of view. More in detail, in the first chapter , we concentrate on the estimation of volatility through the realized range-based for 16 stocks traded at the New York Stock Exchange (NYSE) and we consider the impact of the microstructure noise in high frequency data and correct our estimations following the procedure of Martens and van Dijk (2007). In addition, we model the volatility series accounting for the asymmetric effect on volatility caused by lagged returns and the long-range dependence, the volatility clustering in the volatility and non-Gaussianity of the innovations of the model. In particular, we specify an Heterogenuos Autoregressive (HAR) model introduced by Corsi (2009), leverage effects with respect to the return and the volatility, GARCH and GJR-GARCH variance and the Normal Inverse Gaussian (NIG) distribution. The empirical analysis of the forecast performance in 16 stocks suggests that the introduction of asymmetric effects with respect to the returns and the volatility in the HAR model results in significant improvement in the point forecasting accuracy. In the second chapter, we investigate the role that macroeconomic and financial variables play when modeling and forecasting daily stocks volatility. We depart from the estimated series in Chapter 1 and we extend the model including economic and financial variables that capture the present and the future state of the economy. We perform an in-sample and out-of-sample empirical analysis in 16 series of stock volatility. We find that macroeconomic and financial variables, in particular proxies for market risk expectation and credit risk, are significantly correlated with the first principal component of the volatility series and they have a highly in-sample explanatory power. Then, we consider an out-of-sample forecasting exercise to analyze the improvement that results from the introduction of the macroeconomic variables that better perform in our in-sample analysis. Variables such as the VIX and the credit default swap index for the US bank sector produce significant improvements in the forecasting accuracy. Last, exploring the impact during the 2008-2009 financial crisis, we observe a higher correlation between the credit default swap index and the volatility reflecting an increase in the perceived credit risk, while there is no significant improvement in the out-of-sample predictions. In the last chapter, we examine and compare the performance of alternative realized estimators of volatility and of different time series forecasting models from an economic point of view. We consider an investor that speculates on the future level of the volatility and invests in a buy-and-hold option strategy depending on his expected level of volatility, that is obtained from different estimators and forecasting models. We implement the trading strategy with weekly S&P 500 Index options and compute volatility from a high frequency series for S&P 500 Futures. The volatility estimators are based on the realized volatility and the realized range and they are robust to microstructure noise and jumps while out-of-sample forecast are obtained with Autoregressive fractional integrated moving average (ARFIMA) models. Additionally, to account for the possibility of confusing long memory with process with short memory and structural change in levels we take into consideration the ARFIMA model with random level shift component recently introduced by Varneskov and Perron (2011) and Grassi and Santucci de Magistris (2011). The main results show that realized range based estimator corrected for the presence of microstructure noise and discontinuities in the price process produces the highest returns. Moreover, the choice of the realized estimator for the volatility seems to be more important than the forecasting models. Finally, positive annualized profits of up to more than 60% are obtained for the trading period before the financial 2008-2009 crisis.