Modeling and Forecasting Realized Volatility
Modeling and Forecasting Realized Volatility
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DOI：
10.2139/ssrn.267792
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发表时间：
2001-01
期刊：
影响因子：
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通讯作者：
T. Andersen;T. Bollerslev;F. Diebold;Paul Labys
中科院分区：
文献类型：
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作者：
T. Andersen;T. Bollerslev;F. Diebold;Paul Labys
本文提供了一个将高频日内数据整合到日常和低频波动率和收益分布的测量、建模和预测中的一般框架。大多数建模和预测金融资产回报波动性、相关性和分布的程序依赖于限制性和复杂的参数多元ARCH或随机波动性模型，这些模型在日内频率下通常表现不佳。相比之下，利用高频日内回报构建的已实现波动率，允许使用传统的时间序列程序进行建模和预测。在连续时间无套利价格过程理论和二次变分理论的基础上，我们正式建立了条件协方差矩阵与实现波动率概念之间的联系。接下来，使用超过十年的德国马克/美元和日元/美元即期汇率的连续记录观察，我们发现，与流行的每日ARCH和相关模型相比，简单的长记忆高斯向量自回归对对数日已实现波动率的预测表现令人钦佩。此外，向量自回归波动率预测，加上正态分布标准化收益的理论和经验假设所隐含的参数对数正态-正态混合分布，产生了对未来收益的校准良好的密度预测，以及相应的准确的分位数估计。我们的研究结果为在资产定价、资产配置和金融风险管理应用中相关的大协方差矩阵的实际建模和预测提供了希望。
This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark / Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quantile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.