MOMENT EXPLOSIONS AND LONG‐TERM BEHAVIOR OF AFFINE STOCHASTIC VOLATILITY MODELS
MOMENT EXPLOSIONS AND LONG‐TERM BEHAVIOR OF AFFINE STOCHASTIC VOLATILITY MODELS
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DOI：
10.1111/j.1467-9965.2010.00423.x
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发表时间：
2008-02
影响因子：
1.6
通讯作者：
Martin Keller-Ressel
中科院分区：
文献类型：
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作者：
Martin Keller-Ressel
考虑一类资产定价模型，其中对数价格及其随机方差的风险中性联合过程是Duffie，Filipovic和Schachermayer意义下的仿射过程。首先，我们得到了价格过程是保守的和鞅的条件。然后我们给出了模型长期行为的一些结果，包括随机方差过程的不变分布的表达式。研究了价格过程的矩爆炸，给出了给定阶矩成为无穷大的时刻的显式表达式。我们讨论了这些结果的应用，特别是隐含波动率微笑的渐近性，并得出结论与赫斯顿模型，模型的贝茨和Barndorff‐Nielsen-Shephard模型的一些计算。
We consider a class of asset pricing models, where the risk‐neutral joint process of log‐price and its stochastic variance is an affine process in the sense of Duffie, Filipovic, and Schachermayer. First we obtain conditions for the price process to be conservative and a martingale. Then we present some results on the long‐term behavior of the model, including an expression for the invariant distribution of the stochastic variance process. We study moment explosions of the price process, and provide explicit expressions for the time at which a moment of given order becomes infinite. We discuss applications of these results, in particular to the asymptotics of the implied volatility smile, and conclude with some calculations for the Heston model, a model of Bates and the Barndorff‐Nielsen–Shephard model.