发帖
雷达卡
英文标题：
《Short-time at-the-money skew and rough fractional volatility》
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作者：
Masaaki Fukasawa
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最新提交年份：
2015
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英文摘要：
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time-to-maturity tends to zero. For this purpose we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.
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中文摘要：
众所周知，SPX期权的Black-Scholes隐含波动率偏斜在到期时间上遵循幂律。我们构建了一个动态符合幂律的标的资产价格过程模型。该模型的波动过程由分数布朗运动驱动，Hurst参数小于一半。分数布朗运动与驱动资产价格过程的布朗运动相关。我们推导了当到期时间趋于零时隐含波动率的渐近展开式。为此，我们引入了一种新的方法来验证这种扩展，这使我们能够处理比文献中更一般的模型。为了证明这样一个标准模型不能动态地与幂律相一致，在一个本质上最小的正则性条件下也处理了局部随机波动率模型。
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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