In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability density. The method involves preintegration with respect to one well chosen integration variable to obtain a smooth function of the remaining variables, followed by the application of a tailored lattice Quasi-Monte Carlo rule to integrate over the remaining variables.

翻译：本文提出并分析了一种估计亚式期权三种相关量的方法：公平价格、累积分布函数以及概率密度函数。该方法首先针对一个精心选取的积分变量进行预积分，从而获得关于剩余变量的光滑函数；随后应用定制的格点准蒙特卡洛规则对剩余变量进行积分。