Black-Scholes模型中亚式期权波动率的次领头阶修正
数理金融
2024-12-17 v3 概率论
摘要
Black-Scholes模型中亚式期权隐含波动率的短到期极限由几何布朗运动时间平均的大偏差性质决定。在本文中,我们利用Hartman-Watson分布的渐近展开,推导出该隐含波动率的次领头阶修正。该结果用于计算小到期展开中亚式期权价格的次领头阶修正,从而锐化了使用大偏差理论得到的领头阶结果。我们展示了与Black-Scholes模型中亚式期权定价的精确基准的良好数值一致性。
引用
@article{arxiv.2407.05142,
title = {Subleading correction to the Asian options volatility in the Black-Scholes model},
author = {Dan Pirjol},
journal= {arXiv preprint arXiv:2407.05142},
year = {2024}
}
备注
17 pages, 5 figures. Expanded version of the published paper, including also the convexity of the subleading Asian volatility. v2: fixed a typo in the convexity result. v3: fixed typos in several equations and corrected one numerical value in Table 1