Radial Basis Function generated Finite Differences for option pricing problems
Radial Basis Function generated Finite Differences for option pricing problems
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DOI：
10.1016/j.camwa.2017.11.015
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发表时间：
2017-12
期刊：
影响因子：
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通讯作者：
S. Milovanovic;L. Sydow
中科院分区：
文献类型：
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作者：
S. Milovanovic;L. Sydow
本文提出了一种基于径向基函数有限差分（RBF-FD）和二阶后向微分公式（BDF-2）的期权定价方法。我们使用依赖于形状参数ε的高斯RBF。该参数的选择对于该方法的性能至关重要。我们选择ε作为常数h− 1，并推导出1D和2D中不同模板尺寸的常数的合适值。这个常数独立于问题参数，如标的资产的波动率和市场利率。在RBF-FD期权定价的文献中，形状参数使用了一个常数。我们表明，这总是导致病态减少h，而我们提出的方法避免了这种病态。我们提出的数值计算结果的问题，在1D，2D和3D展示我们的方法，如离散稀疏性，节点放置的灵活性，和容易的尺寸可扩展性，这提供了高的计算效率和精度的有用功能。
In this paper we present a numerical method to price options based on Radial Basis Function generated Finite Differences (RBF-FD) in space and the Backward Differentiation Formula of order 2 (BDF-2) in time. We use Gaussian RBFs that depend on a shape parameter ε. The choice of this parameter is crucial for the performance of the method. We chose ε as const⋅ h− 1 and we derive suitable values of the constant for different stencil sizes in 1D and 2D. This constant is independent of the problem parameters such as the volatilities of the underlying assets and the interest rate in the market. In the literature on option pricing with RBF-FD, a constant value of the shape parameter is used. We show that this always leads to ill-conditioning for decreasing h, whereas our proposed method avoids such ill-conditioning. We present numerical results for problems in 1D, 2D, and 3D demonstrating the useful features of our method such as discretization sparsity, flexibility in node placement, and easy dimensional extendability, which provide high computational efficiency and accuracy.