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摘要翻译：
本文讨论了障碍期权定价的一种高阶精确隐式有限差分方法。通过这种方式，各种类型的障碍期权被定价，包括支付回扣的障碍期权和支付股息的股票期权。此外，可以连续或离散地监测屏障。除了高阶精度和坐标变换的伸展效应外，该方法的主要特点在于基于概率的最优边界条件确定。与类似的定价方法相比，这导致了更快和更准确的结果。本方案的优点特别体现在离散监测障碍期权的估值上，它产生的价值最接近于从唯一可用的半分析估值方法得到的价值。
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英文标题：
《High-order accurate implicit methods for the pricing of barrier options》
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作者：
J.C. Ndogmo and D. B. Ntwiga
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最新提交年份：
2007
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on dividend-paying-stocks. Moreover, the barriers may be monitored either continuously or discretely. In addition to the high-order accuracy of the scheme, and the stretching effect of the coordinate transformation, the main feature of this approach lies on a probability-based optimal determination of boundary conditions. This leads to much faster and accurate results when compared with similar pricing approaches. The strength of the present scheme is particularly demonstrated in the valuation of discretely monitored barrier options where it yields values closest to those obtained from the only semi-analytical valuation method available.
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PDF链接：
https://arxiv.org/pdf/0710.0069
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