英文标题：
《Compact Finite Difference Scheme with Hermite Interpolation for Pricing
American Put Options Based on Regime Switching Model》
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作者：
Chinonso Nwankwo, Weizhong Dai, Ruihua Liu
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最新提交年份：
2020
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英文摘要：
We consider a system of coupled free boundary problems for pricing American put options with regime-switching. To solve this system, we first employ the logarithmic transformation to map the free boundary for each regime to multi-fixed intervals and then eliminate the first-order derivative in the transformed model by taking derivatives to obtain a system of partial differential equations which we call the asset-delta-gamma-speed equations. As such, the fourth-order compact finite difference scheme can be used for solving this system. The influence of other asset, delta, gamma, and speed options in the present regime is estimated based on Hermite interpolations. Finally, the numerical method is tested with several examples. Our results show that the scheme provides an accurate solution that is fast in computation as compared with other existing numerical methods.
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中文摘要：
我们考虑了一个具有制度转换的美式看跌期权定价的耦合自由边界问题系统。为了解决这个系统，我们首先使用对数变换将每个区域的自由边界映射到多个固定区间，然后通过求导数消除变换模型中的一阶导数，得到一个偏微分方程系统，我们称之为asset delta gamma速度方程。因此，四阶紧致有限差分格式可用于求解该系统。根据Hermite插值估计当前体制中其他资产、delta、gamma和速度选项的影响。最后，通过几个算例对数值方法进行了验证。我们的结果表明，与现有的其他数值方法相比，该格式提供了计算速度快的精确解。
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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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