论文标题
关于在随机波动模型下亚洲选项的隐含波动性
On the implied volatility of Asian options under stochastic volatility models
论文作者
论文摘要
在本文中，我们研究了以固定的罢工价格的算术亚洲选项的含义含义波动的短期行为。假定资产价格遵循具有一般随机波动过程的黑色choles模型。使用Malliavin微积分的技术，例如预期的ITO公式，我们首先计算成熟度收敛到零时，选项的隐含波动率的水平。然后，我们发现依赖于波动率模型的粗糙度的隐含波动率的偏斜偏差和短期成熟渐近公式。我们将一般结果应用于SABR模型和粗糙的Bergomi模型，并提供了一些数值模拟，以确认偏斜的渐近公式的准确性。
In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility process. Using techniques of the Malliavin calculus such as the anticipating Ito's formula we first compute the level of the implied volatility of the option when the maturity converges to zero. Then, we find and short maturity asymptotic formula for the skew of the implied volatility that depends on the roughness of the volatility model. We apply our general results to the SABR model and the rough Bergomi model, and provide some numerical simulations that confirm the accurateness of the asymptotic formula for the skew.
