标题： 利用马里亚文微积分的看涨障碍期权短期行为分析 显示英文标题

标题： On the short-time behaviour of up-and-in barrier options using Malliavin calculus

摘要： 在本文中，我们研究了在广泛一类随机波动率模型下，向上敲入障碍期权的短期到期渐近行为。我们的方法使用了通常用于线性随机偏微分方程的马尔可夫微分技巧，来分析对数价格过程的最大值的分布。我们推导了一个集中不等式，并以到期时间表示最大值密度的显式边界。这些结果给出了当到期时间消失时，向上敲入障碍期权价格的渐近衰减率的上界。我们进一步展示了我们框架在粗糙伯格米模型中的适用性，并通过数值实验验证了理论结果。 显示英文摘要

摘要： In this paper we study the short-maturity asymptotics of up-and-in barrier options under a broad class of stochastic volatility models. Our approach uses Malliavin calculus techniques, typically used for linear stochastic partial differential equations, to analyse the law of the supremum of the log-price process. We derive a concentration inequality and explicit bounds on the density of the supremum in terms of the time to maturity. These results yield an upper bound on the asymptotic decay rate of up-and-in barrier option prices as maturity vanishes. We further demonstrate the applicability of our framework to the rough Bergomi model and validate the theoretical results with numerical experiments.