英文标题：
《Approaches to Asian Option Pricing with Discrete Dividends》
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作者：
Jacob Lundgren, Yuri Shpolyanskiy
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最新提交年份：
2021
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英文摘要：
The method and characteristics of several approaches to the pricing of discretely monitored arithmetic Asian options on stocks with discrete, absolute dividends are described. The contrast between method behaviors for options with an Asian tail and those with monitoring throughout their lifespan is emphasized. Rates of convergence are confirmed, but greater focus is put on actual performance in regions of accuracy which are realistic for use by practitioners. A hybrid approach combining Curran\'s analytical approximation with a two-dimensional finite difference method is examined with respect to the errors caused by the approximating assumptions. For Asian tails of equidistant monitoring dates, this method performs very well, but as the scenario deviates from the method\'s ideal conditions, the errors in the approximation grow unfeasible. For general monitoring straightforward solution of the full three-dimensional partial differential equation by finite differences is highly accurate but suffers from rapid degradation in performance as the monitoring interval increases. For options with long monitoring intervals a randomized quasi-Monte Carlo method with control variate variance reduction stands out as a powerful alternative.
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中文摘要：
描述了在具有离散绝对股息的股票上进行离散监控算术亚式期权定价的几种方法及其特点。强调了具有亚洲尾的选项的方法行为与在其整个生命周期内进行监控的选项的方法行为之间的对比。收敛速度已得到确认，但更关注的是准确度区域的实际性能，这对于实践者来说是现实的。结合Curran的分析近似和二维有限差分法，研究了近似假设引起的误差。对于等距监测日期的亚洲尾部，该方法表现得非常好，但随着情景偏离该方法的理想条件，近似误差变得不可行。对于一般监测，通过有限差分直接求解全三维偏微分方程具有很高的精度，但随着监测间隔的增加，性能会迅速下降。对于具有长监测间隔的选项，带有控制变量方差减少的随机拟蒙特卡罗方法是一种强有力的替代方法。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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