摘要翻译：
本文提出了一种计算分段常数参数超指数可加模型中障碍期权价格和希腊值的算法。我们得到了第一次通过概率的显式半解析表达式。该解基于随机化和显式矩阵Wiener-Hopf分解。利用这一结果，我们导出了障碍期权的价格和希腊的拉普拉斯-傅立叶变换的显式表达式。作为一个数值例子，用一组参数计算了下入式数字看涨期权和下入式看涨期权的价格和希腊值，这些参数是通过同时校准Stoxx50E看涨期权跨罢工和四个不同到期日得到的。通过与Monte-Carlo模拟结果的比较，表明该方法快速、准确、稳定。
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英文标题：
《Pricing and hedging barrier options in a hyper-exponential additive
  model》
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作者：
Marc Jeannin and Martijn Pistorius
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最新提交年份：
2009
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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：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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英文摘要：
  In this paper we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage probability. The solution rests on a randomization and an explicit matrix Wiener-Hopf factorization. Employing this result we derive explicit expressions for the Laplace-Fourier transforms of the prices and Greeks of barrier options. As a numerical illustration, the prices and Greeks of down-and-in digital and down-and-in call options are calculated for a set of parameters obtained by a simultaneous calibration to Stoxx50E call options across strikes and four different maturities. By comparing the results with Monte-Carlo simulations, we show that the method is fast, accurate, and stable.
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PDF链接：
https://arxiv.org/pdf/0812.3117