摘要翻译：
本文以Heston模型为例，在随机波动性框架下研究了波动性对股票价格的依赖性。更具体地说，我们考虑固定股价回报下的方差（波动率平方）的条件期望是回报和时间的函数。该函数的行为取决于初始股价收益分布密度。特别地，我们证明了条件方差期望图在股票价格收益均值附近是向下凸的。对于高斯分布，这种影响很强，但随着分布在无穷远处的衰减减慢，这种影响减弱并变得可以忽略不计。
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英文标题：
《A certain estimate of volatility through return for stochastic
  volatility models》
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作者：
Mikhail Martynov, Olga Rozanova
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最新提交年份：
2011
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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 study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed stock price return as a function of the return and time. The behavior of this function depends on the initial stock price return distribution density. In particular, we show that the graph of the conditional expectation of variance is convex downwards near the mean value of the stock price return. For the Gaussian distribution this effect is strong, but it weakens and becomes negligible as the decay of distribution at infinity slows down.
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PDF链接：
https://arxiv.org/pdf/1009.5129