Modeling and Forecasting Realized Volatility

摘要: This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting daily lower frequency volatility return distributions. Most procedures modeling financial asset volatilities, correlations, distributions rely on restrictive complicated parametric multivariate ARCH or stochastic models, which often perform poorly at frequencies. Use realized constructed from returns, in contrast, permits use traditional time series forecasting. Building theory continuous-time arbitrage-free price processes quadratic variation, we formally develop links between conditional covariance matrix concept volatility. Next, using continuously recorded observations Deutschemark / Dollar Yen spot exchange rates covering more than decade, find that forecasts simple long-memory Gaussian vector autoregression logarithmic volatilities admirably compared to popular related models. Moreover, autoregressive forecast, coupled with lognormal-normal mixture distribution implied by theoretically empirically grounded assumption normally distributed standardized gives rise well-calibrated density future correspondingly accurate quantile estimates. Our results hold promise practical large matrices relevant pricing, allocation risk management applications.