Does the Hurst index matter for option prices under fractional volatility?
Does the Hurst index matter for option prices under fractional volatility?
复制标题
赫斯特指数对于分数波动率下的期权价格重要吗？
DOI：
10.1007/s10436-016-0289-1
复制
发表时间：
2017
影响因子：
1
通讯作者：
M.
中科院分区：
文献类型：
--
作者：
Funahashi;H. and Kijima;M.
本研究探讨了分数波动率对期权价格的影响。为此，我们开发了一种当波动率遵循分数布朗运动时欧式或有债权定价的近似方法。通过大量的数值实验，我们证实分数波动率下微笑幅度的下降比标准随机波动率模型下的下降要慢得多。我们还表明，当期限较短且均值回归速度较慢时，分数波动率下的 Hurst 指数对期权价格具有至关重要的影响。相反，赫斯特指数对长期期权价格的影响减小。
This study examines the effect of fractional volatility on option prices. To this end, we develop an approximation method for the pricing of European-style contingent claims when volatility follows a fractional Brownian motion. Through extensive numerical experiments, we confirm that the decrease in the smile amplitude under fractional volatility is much slower than that under the standard stochastic volatility model. We also show that the Hurst index under fractional volatility has a crucial impact on option prices when the maturity is short and speed of mean reversion is slow. On the contrary, the impact of the Hurst index on option prices reduces for long-dated options.