英文标题：
《Exact simulation pricing with Gamma processes and their extensions》
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作者：
Lancelot F. James, Dohyun Kim and Zhiyuan Zhang
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最新提交年份：
2013
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英文摘要：
  Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic volatility (SV) models makes exact simulation difficult. In this paper, we present a nontrivial SV model that parallels the notable Heston SV model in the sense of admitting exact path simulation as studied by Broadie and Kaya. The instantaneous volatility process of the proposed model is driven by a Gamma process. Extensions to the model including superposition of independent instantaneous volatility processes are studied. Numerical results show that the proposed model outperforms the Heston model and two other L\\\'evy driven SV models in terms of model fit to the real option data. The ability to exactly simulate some of the path-dependent derivative prices is emphasized. Moreover, this is the first instance where an infinite-activity volatility process can be applied exactly in such pricing contexts.
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中文摘要：
当金融衍生产品的定价公式没有解析解时，对潜在状态变量的精确路径模拟在模拟金融衍生产品的价格或其敏感性方面具有重要的实际意义。然而，一般来说，大多数非平凡随机波动率（SV）模型固有的复杂依赖结构使得精确模拟变得困难。在本文中，我们提出了一个非平凡的SV模型，该模型与著名的Heston SV模型在允许精确路径模拟的意义上相似，正如Broadie和Kaya所研究的那样。该模型的瞬时波动过程由伽马过程驱动。研究了该模型的扩展，包括独立瞬时波动过程的叠加。数值结果表明，所提出的模型在模型拟合实物期权数据方面优于赫斯顿模型和另外两个勒夫驱动的SV模型。强调了精确模拟某些路径相关衍生产品价格的能力。此外，这是第一个可以在这种定价环境下精确应用无限活动波动过程的实例。
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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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