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摘要翻译：
本文提出了一种计算由Levy过程驱动的障碍期权的价格和希腊值的变换方法。本文给出了具有超指数跳跃的指数Levy模型中单障碍期权的价格和灵敏度随时间变化的Laplace变换的解析表达式。反演这些单一的拉普拉斯变换产生快速，准确的结果。这些结果被用来构造指数广义超指数(GHE)Levy模型中障碍期权的价格和敏感性的近似。后一类包括许多在定量金融中使用的利维模型，如方差伽玛(VG)、KoBoL、广义双曲和正态逆高斯(NIG)模型。证明了近似价格和灵敏度的收敛性。为了提供一个数值例子，在驱动过程为VG和NIG Levy过程的情况下，将这种变换方法与蒙特卡罗模拟进行了比较。参数校准为Stoxx50E看涨期权。
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英文标题：
《A transform approach to compute prices and greeks of barrier options
driven by a class of Levy processes》
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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 propose a transform method to compute the prices and greeks of barrier options driven by a class of Levy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Levy model with hyper-exponential jumps. Inversion of these single Laplace transform yields rapid, accurate results. These results are employed to construct an approximation of the prices and sensitivities of barrier options in exponential generalised hyper-exponential (GHE) Levy models. The latter class includes many of the Levy models employed in quantitative finance such as the variance gamma (VG), KoBoL, generalised hyperbolic, and the normal inverse Gaussian (NIG) models. Convergence of the approximating prices and sensitivities is proved. To provide a numerical illustration, this transform approach is compared with Monte Carlo simulation in the cases that the driving process is a VG and a NIG Levy process. Parameters are calibrated to Stoxx50E call options.
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PDF链接：
https://arxiv.org/pdf/0812.3128
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