英文标题：
《New analytic approach to address Put - Call parity violation due to
discrete dividends》
---
作者：
Alexander Buryak and Ivan Guo
---
最新提交年份：
2014
---
英文摘要：
The issue of developing simple Black-Scholes type approximations for pricing European options with large discrete dividends was popular since early 2000\'s with a few different approaches reported during the last 10 years. Moreover, it has been claimed that at least some of the resulting expressions represent high-quality approximations which closely match results obtained by the use of numerics. In this paper we review, on the one hand, these previously suggested Black-Scholes type approximations and, on the other hand, different versions of the corresponding Crank-Nicolson numerical schemes with a primary focus on their boundary condition variations. Unexpectedly we often observe substantial deviations between the analytical and numerical results which may be especially pronounced for European Puts. Moreover, our analysis demonstrates that any Black-Scholes type approximation which adjusts Put parameters identically to Call parameters has an inherent problem of failing to detect a little known Put-Call Parity violation phenomenon. To address this issue we derive a new analytic approximation which is in a better agreement with the corresponding numerical results in comparison with any of the previously known analytic approaches for European Calls and Puts with large discrete dividends.
---
中文摘要：
开发简单的Black-Scholes型近似值来为具有大量离散股息的欧洲期权定价的问题自2000年初以来就很流行，在过去10年中报告了几种不同的方法。此外，有人声称，至少一些结果表达式表示高质量的近似值，这些近似值与通过使用数值计算得到的结果非常匹配。在本文中，我们一方面回顾了以前提出的Black-Scholes型近似，另一方面回顾了相应的Crank-Nicolson数值格式的不同版本，主要关注其边界条件的变化。出人意料的是，我们经常观察到分析结果和数值结果之间存在重大偏差，这对于欧洲看跌期权来说可能尤其明显。此外，我们的分析表明，任何Black-Scholes型近似，如果将Put参数调整为与调用参数相同的参数，都存在无法检测到鲜为人知的Put调用奇偶校验违反现象的固有问题。为了解决这个问题，我们推导了一种新的解析近似方法，与之前已知的具有大离散红利的欧式看涨期权和看跌期权的解析方法相比，它与相应的数值结果更为一致。
---
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
--

---
PDF下载：
-->