波动率预测：隐含波动率的预测能力分析-摘要

摘要

波动率一般指资产收益率的标准差或方差。波动率在风险管理、资产定价等领域扮演着重要的角色，因而对波动率预测的研究吸引了学术界和业界的极大关注。大致上可以将预测未来波动率的方法分为三种类别：历史波动率预测，时间序列模型预测，以及隐含波动率预测。由期权价格反向推导出来的隐含波动率被认为是未来波动率的市场预期，理论上隐含波动率应该能更好地预测未来波动率。

前人对隐含波动率的预测能力做了不少研究，但得出的结论并不一致且研究本身存在不少缺陷。为了对隐含波动率的预测能力做一个完整全面可靠的研究，本文避免了早期文献中普遍存在的“到期时间不对称”和“数据重叠”问题，且首次将SABR 模型应用于波动率预测领域，在此基础上比较了历史波动率、GARCH 时间序列模型以及4 种不同的隐含波动率模型在7 天、14 天以及30 天等三个不同预测期的预测效果，并分析了各个波动率之间的相对信息含量关系。

本文实证结果表明，不管预测期长短，所有类型的波动率对未来波动率都有一定的预测能力，但是不同波动率适用的预测期不同。对于7 天和30 天预测，我们发现隐含波动率效果较好，而对于14 天预测，GARCH 时间序列模型则表现更优。就隐含波动率本身而言，整体上SABR 模型隐含波动率预测效果要优于其它隐含波动率，这说明把SABR 模型应用于波动率预测领域是可行且有效的。

关键词：波动率预测；隐含波动率；SABR 模型

Abstract

Volatility usually means the standard deviation or the variance of an asset’s return, which plays an important role in risk management a nd asset pricing. That’s why volatility forecasting greatly arouses the attention of academics and financial industries. Generally we can classify the volatility forecasting methods into three categories, namely, historical volatility forecast, time series model forecast, and implied volatility forecast. The implied volatility derived backward from option prices is considered as the market's expectation of future volatility, and theoretically it should be able to predict the future volatility better.

Previous studies have done researches on the forecasting ability of implied volatilities. However, their results are mixed and most studies have some deficiencies. To provide a complete and reliable study on the forecasting performance of implied volatilities, this paper avoids the maturity mismatch and data overlapping problems commonly found in previous studies, and applies the SABR model in the volatility forecasting field for the first time. We compare the forecasting performance of implied volatilities derived from 4 different models with historical volatility and GARCH time series model, for different periods of time, i.e., 7 days, 14 days and 30 days ahead, and analyses their relative information content.

Our empirical result shows that, despite the periods of time, each kind of volatility has some forecasting ability on future volatility, but different volatilities suit for different time periods. Implied volatilities are better in 7-day and 30-day forecasts, while GARCH time series model forecasts future volatility well in 14-day forecast. As far as implied volatilities are concerned, the SABR model implied volatility dominates other implied volatilities, which implies that the application of SABR model in volatility forecasting field is useful and feasible.

Key words: volatility forecasting; implied volatilities; the SABR model.