Here and throughout, we use the generic term "volatilities" in reference both to variances (or st... more Here and throughout, we use the generic term "volatilities" in reference both to variances (or standard deviations) and covariances (or correlations). When important, the precise meaning will be clear from context. 2 Earlier empirical work exploiting related univariate approaches from a heuristic perspective includes French, Schwert and Stambaugh (1987) and Schwert (1989), who rely on daily returns to estimate models for monthly realized U.S. equity volatility, and Hsieh (1991), who fits an AR(5) model to a time series of daily realized logarithmic volatilities constructed from 15-minute S&P500 returns.-2-simple exponential smoothing methods for construction of volatility forecasts, coupled with an assumption of conditionally normally distributed returns. This approach is exemplified by J.P. Morgan's highly influential RiskMetrics, see J.P. Morgan (1997). Although such methods exploit outright counterfactual assumptions and almost certainly are suboptimal, such defects must be weighed against considerations of feasibility, simplicity and speed of implementation in high-dimensional environments. Set against this background, we seek improvement along two important dimensions. First, we propose a new rigorous procedure for volatility forecasting and return fractile, value-at-risk (VaR), calculation that efficiently exploits the information in intraday return observations. In the process, we document significant improvements in predictive performance relative to the standard procedures that rely on daily data alone. Second, our methods achieve a simplicity and ease of implementation that allows for ready accommodation of higher-dimensional return systems. We achieve these dual objectives by focusing on an empirical measure of daily return variability termed realized volatility, which is easily computed from high-frequency intra-period returns. The theory of quadratic variation reveals that, under suitable conditions, realized volatility is not only an unbiased ex-post estimator of daily return volatility, but also asymptotically free of measurement error, as discussed in Andersen, Bollerslev, Diebold and Labys (2001a) (henceforth ABDL) as well as concurrent work by Barndorff-Nielsen and Shephard (2000, 2001). Building on the notion of continuous-time arbitrage-free price processes, we progress in several directions, including more rigorous theoretical foundations, multivariate emphasis, and links to modern risk management. Empirically, by treating the volatility as observed rather than latent, our approach greatly facilitates modeling and forecasting using simple methods based directly on observable variables. 2 Although the basic ideas apply quite generally, we focus on the highly liquid U.S. dollar ($), Deutschemark (DM), and Japanese yen (¥) spot exchange rate markets in order to illustrate and evaluate our methods succinctly under conditions that allow for construction of good realized volatility measures. Our full sample consists of nearly thirteen years of continuously recorded spot quotations from 1986 through 1999. During this period, the dollar, Deutschemark and yen constituted the main axes of the international financial system, and thus spanned the majority of the systematic currency risk faced by most large institutional investors and international corporations.
Here and throughout, we use the generic term "volatilities" in reference both to variances (or st... more Here and throughout, we use the generic term "volatilities" in reference both to variances (or standard deviations) and covariances (or correlations). When important, the precise meaning will be clear from context. 2 Earlier empirical work exploiting related univariate approaches from a heuristic perspective includes French, Schwert and Stambaugh (1987) and Schwert (1989), who rely on daily returns to estimate models for monthly realized U.S. equity volatility, and Hsieh (1991), who fits an AR(5) model to a time series of daily realized logarithmic volatilities constructed from 15-minute S&P500 returns.-2-simple exponential smoothing methods for construction of volatility forecasts, coupled with an assumption of conditionally normally distributed returns. This approach is exemplified by J.P. Morgan's highly influential RiskMetrics, see J.P. Morgan (1997). Although such methods exploit outright counterfactual assumptions and almost certainly are suboptimal, such defects must be weighed against considerations of feasibility, simplicity and speed of implementation in high-dimensional environments. Set against this background, we seek improvement along two important dimensions. First, we propose a new rigorous procedure for volatility forecasting and return fractile, value-at-risk (VaR), calculation that efficiently exploits the information in intraday return observations. In the process, we document significant improvements in predictive performance relative to the standard procedures that rely on daily data alone. Second, our methods achieve a simplicity and ease of implementation that allows for ready accommodation of higher-dimensional return systems. We achieve these dual objectives by focusing on an empirical measure of daily return variability termed realized volatility, which is easily computed from high-frequency intra-period returns. The theory of quadratic variation reveals that, under suitable conditions, realized volatility is not only an unbiased ex-post estimator of daily return volatility, but also asymptotically free of measurement error, as discussed in Andersen, Bollerslev, Diebold and Labys (2001a) (henceforth ABDL) as well as concurrent work by Barndorff-Nielsen and Shephard (2000, 2001). Building on the notion of continuous-time arbitrage-free price processes, we progress in several directions, including more rigorous theoretical foundations, multivariate emphasis, and links to modern risk management. Empirically, by treating the volatility as observed rather than latent, our approach greatly facilitates modeling and forecasting using simple methods based directly on observable variables. 2 Although the basic ideas apply quite generally, we focus on the highly liquid U.S. dollar ($), Deutschemark (DM), and Japanese yen (¥) spot exchange rate markets in order to illustrate and evaluate our methods succinctly under conditions that allow for construction of good realized volatility measures. Our full sample consists of nearly thirteen years of continuously recorded spot quotations from 1986 through 1999. During this period, the dollar, Deutschemark and yen constituted the main axes of the international financial system, and thus spanned the majority of the systematic currency risk faced by most large institutional investors and international corporations.
Uploads
Papers by Abdul Raziq