双因子随机条件极差模型及其实证研究

Two-factor stochastic conditional range model and its empirical study

对波动率的建模和估计传统上主要基于由收盘价计算得到的收益率信息,而基于包含更多日内价格变动信息的价格极差对波动率的研究却相对较少.对经典的针对价格极差动态性建模的条件自回归极差(CARR)模型进行扩展,借鉴随机波动率(SV)模型的建模思路,同时考虑波动率的长记忆特征,引入Gamma分布刻画价格极差新息的分布,构建了双因子随机条件极差(2FSCR)模型来描述价格极差的动态性.进一步,基于连续粒子滤波算法,给出了2FSCR模型参数的极大似然估计方法,并通过蒙特卡罗模拟实验表明了该估计方法的有效性.采用上证综合指数(SSE)、深证成份指数(SZSE)、香港恒生指数(HSI)和美国标普500指数(SPX)数据进行了实证研究,结果表明:2FSCR模型相比CARR模型以及单因子的SCR模型都具有更好的数据拟合效果.进一步的模型诊断分析表明,2FSCR模型相比CARR模型和SCR模型能够更好地刻画价格极差新息的尾部分布,能够更充分地捕获波动率的动态特征(时变性、聚集性与长记忆性).采用滚动窗方法对波动率进行预测,利用价格极差与已实现波动率作为比较基准对模型的预测能力进行了比较分析,结果表明:2FSCR模型相比CARR模型和SCR模型都具有更为优越的波动率预测效果.

Studies of volatility modelling and estimation usually rely on the returns information provided by the closing prices,whereas very few studies employ price ranges,which incorporate more information on intraday price movements,to model volatility.The paper extends the classical conditional autoregressive range(CARR)model and proposes a two-factor stochastic conditional range(2FSCR)model with Gamma distribution for price ranges.The proposed model mimics the structure of the stochastic volatility(SV)model and can capture the long-range dependence(long memory property)of volatility.The maximum likelihood estimation method based on the continuous particle filters is employed to estimate the parameters of the 2FSCR model.Monte Carlo simulations show that the method performs well.The 2FSCR model is tested using data on Shanghai Stock Exchange Composite Index(SSE),Shenzhen Stock Exchange Component Index(SZSE),Hong Kong Hang Seng Index(HSI)and United States Standard&Poor*s 500 Index(SPX).The results show that the 2FSCR model fits the data better than both the CARR model and the single-factor SCR model.Model diagnostics suggest that the 2FSCR model can describe the extreme tails of the price range distribution better than the CARR and SCR models,and can capture the dynamics of the volatility(time-varying volatility,volatility clustering,and long memory property of the volatility).Using the price range and realized volatility as the benchmarks,out-of-sample predictive ability of different models,namely,the CARR,the SCR and the 2FSCR,is compared based on the rolling window scheme.The results show that the 2FSCR model does have superior predictive accuracy compared with the CARR model and the SCR model.