A stochastic volatility model with flexible extremal dependence structure
A stochastic volatility model with flexible extremal dependence structure
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DOI：
10.3150/15-bej699
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发表时间：
2016-08-01
期刊：
影响因子：
1.5
通讯作者：
Drees, Holger
中科院分区：
文献类型：
--
作者：
Janssen, Anja;Drees, Holger
具有重尾创新的随机波动过程是一个众所周知的金融时间序列模型。在这些模型中，对数回报的极值主要由i.i.d创新序列的极值驱动，这导致了一种非常强的渐近独立形式，即对于所有正滞后，尾部依赖系数等于1/2。我们提出了另一类具有重尾波动率的随机波动率模型，并检验了它们的极值行为。特别是，研究表明，虽然滞后极值观测值通常是渐近独立的，但它们的尾部依赖系数可以取1/2（对应于精确独立性）和1（与渐近依赖性相关）之间的任何值。因此，与经典SV模型相比，该类允许在连续观察之间具有更灵活的极端依赖关系，因此可以更实际地描述观察到的金融回报聚类。在圆锥（0,∞）的正则变化框架下，分析了滞后观测值的极值依赖结构(d)。作为两个辅助结果，我们得到了关于随机矩阵与正则随机向量乘积在（0,∞）(d)上的正则变分的一个新的breiman型定理，以及关于正则随机变量乘积的联合极值行为的一个陈述。
Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads to a very strong form of asymptotic independence, that is, the coefficient of tail dependence is equal to 1/2 for all positive lags. We propose an alternative class of stochastic volatility models with heavy-tailed volatilities and examine their extreme value behavior. In particular, it is shown that, while lagged extreme observations are typically asymptotically independent, their coefficient of tail dependence can take on any value between 1/2 (corresponding to exact independence) and 1 (related to asymptotic dependence). Hence, this class allows for a much more flexible extremal dependence between consecutive observations than classical SV models and can thus describe the observed clustering of financial returns more realistically.The extremal dependence structure of lagged observations is analyzed in the framework of regular variation on the cone (0, infinity)(d). As two auxiliary results which are of interest on their own we derive a new Breiman-type theorem about regular variation on (0, infinity)(d) for products of a random matrix and a regularly varying random vector and a statement about the joint extremal behavior of products of i.i.d. regularly varying random variables.