英文标题：
《Pricing foreign exchange options under stochastic volatility and
interest rates using an RBF--FD method》
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作者：
Fazlollah Soleymani and Andrey Itkin
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最新提交年份：
2019
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英文摘要：
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented by an It\\^{o}\'s diffusion with time--dependent drift, and with a full matrix of correlations. It is known that prices of FX options in this model can be found by solving an associated backward partial differential equation (PDE). However, it contains non--affine terms, which makes its difficult to solve it analytically. Also, a standard approach of solving it numerically by using traditional finite--difference (FD) or finite elements (FE) methods suffers from the high computational burden. Therefore, in this paper a flavor of a localized radial basis functions (RBFs) method, RBF--FD, is developed which allows for a good accuracy at a relatively low computational cost. Results of numerical simulations are presented which demonstrate efficiency of such an approach in terms of both performance and accuracy for pricing FX options and computation of the associated Greeks.
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中文摘要：
本文提出了一种在考虑随机利率和外汇汇率随机波动的模型中对外汇期权进行定价的数值方法。该模型考虑了四个随机驱动因素，每个驱动因素都由一个随时间变化的漂移It ^{o}扩散和一个完整的相关矩阵表示。众所周知，该模型中外汇期权的价格可以通过求解相关的后向偏微分方程（PDE）来确定。然而，它包含非仿射项，这使得它很难解析求解。此外，使用传统的有限差分（FD）或有限元（FE）方法对其进行数值求解的标准方法存在计算量大的问题。因此，本文提出了一种局部径向基函数（RBF）方法，即RBF—FD，它以相对较低的计算成本获得了较好的精度。数值模拟结果表明，该方法在外汇期权定价和相关希腊货币计算的性能和准确性方面都是有效的。
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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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一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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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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