英文标题：
《A First Option Calibration of the GARCH Diffusion Model by a PDE Method》
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作者：
Yiannis A. Papadopoulos and Alan L. Lewis
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最新提交年份：
2018
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英文摘要：
Time-series calibrations often suggest that the GARCH diffusion model could also be a suitable candidate for option (risk-neutral) calibration. But unlike the popular Heston model, it lacks a fast, semi-analytic solution for the pricing of vanilla options, perhaps the main reason why it is not used in this way. In this paper we show how an efficient finite difference-based PDE solver can effectively replace analytical solutions, enabling accurate option calibrations in less than a minute. The proposed pricing engine is shown to be robust under a wide range of model parameters and combines smoothly with black-box optimizers. We use this approach to produce a first PDE calibration of the GARCH diffusion model to SPX options and present some benchmark results for future reference.
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中文摘要：
时间序列校准通常表明，GARCH扩散模型也可以是期权（风险中性）校准的合适候选者。但与流行的赫斯顿模型不同，它缺乏一个快速、半解析的解决方案来为普通期权定价，这可能是它没有以这种方式使用的主要原因。在本文中，我们展示了一个高效的基于有限差分的PDE解算器如何有效地替代解析解，从而在不到一分钟的时间内实现精确的选项校准。所提出的定价引擎在广泛的模型参数下表现出鲁棒性，并与黑盒优化器平滑结合。我们使用这种方法首次对SPX期权的GARCH扩散模型进行PDE校准，并给出一些基准结果，以供将来参考。
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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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