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摘要翻译：
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[2003]意义上的仿射过程。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。我们研究了价格过程的矩爆炸，给出了给定阶矩变为无穷大时刻的显式表达式。我们讨论了这些结果的应用，特别是对隐含波动率微笑的渐近性的应用，并给出了Heston模型、Bates模型和Barndorff-Nielsen-Shephard模型的一些计算结果。
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英文标题：
《Moment Explosions and Long-Term Behavior of Affine Stochastic Volatility
Models》
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作者：
Martin Keller-Ressel
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
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 [2003]. 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.
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PDF链接：
https://arxiv.org/pdf/0802.1823
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