英文标题：
《Black-Scholes in a CEV random environment》
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作者：
Antoine Jacquier and Patrick Roome
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最新提交年份：
2017
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英文摘要：
Classical (It\\^o diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential L\\\'evy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \\cite{Tank} for an overview), and more recently rough volatility models \\cite{AlosLeon, Fukasawa}. We suggest here a different route, randomising the Black-Scholes variance by a CEV-generated distribution, which allows us to modulate the rate of explosion (through the CEV exponent) of the implied volatility for small maturities. The range of rates includes behaviours similar to exponential L\\\'evy models and fractional stochastic volatility models.
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中文摘要：
经典（It）随机波动率模型无法捕捉到小到期隐含波动率的陡度。跳跃，尤其是指数Lāevy和仿射模型，它们表现出小的成熟度爆炸式微笑，历史上曾被提出来纠正这一点（参见{Tank}的概述），最近的粗糙波动率模型{AlosLeon，Fukasawa}。我们在这里提出了一种不同的方法，通过CEV生成的分布将Black-Scholes方差随机化，这使我们能够调节小到期日隐含波动率的爆炸率（通过CEV指数）。利率的范围包括类似于指数列维模型和分数随机波动率模型的行为。
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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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