论文标题
波动必须很粗糙
Volatility has to be rough
论文作者
论文摘要
首先，我们给出了渐近的短期含义隐含波动率的渐近扩展，该扩展优化了前面的作品，并特别证明了非劳动波动率模型与波动性偏斜的权力定律不一致。其次，我们表明，鉴于波动性在期权市场中偏斜的权力定律，基础资产的持续价格动态具有非冲突波动性，可以承认套利机会。因此，波动性必须在可行的基本资产的可行市场中变得艰难，而波动性偏向于遵守权力法。
First, we give an asymptotic expansion of short-dated at-the-money implied volatility that refines the preceding works and proves in particular that non-rough volatility models are inconsistent to a power law of volatility skew. Second, we show that given a power law of volatility skew in an option market, a continuous price dynamics of the underlying asset with non-rough volatility admits an arbitrage opportunity. The volatility therefore has to be rough in a viable market of the underlying asset of which the volatility skew obeys a power law.
