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摘要翻译：
本文采用高阶弱逼近格式，对利率理论中的一般HJM方程提出了有效的数值方法。由于相对低维的集成空间，这些方案允许QMC实现。只要保证QMC-收敛的最优阶，所得到的算法的复杂度远低于多级MC算法的复杂度。为了使这些方法适用于现实世界的问题，我们引入并使用了加权函数空间的设置，使得所讨论的方程的无界收益和无界特征仍然是允许的。我们还提供了一个实现，在这里我们有效地校准HJM方程到caplet数据。
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英文标题：
《Efficient simulation and calibration of general HJM models by splitting
schemes》
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作者：
Philipp Doersek and Josef Teichmann
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最新提交年份：
2011
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Functional Analysis 功能分析
分类描述：Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间，函数空间，实函数，积分变换，分布理论，测度理论
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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：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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英文摘要：
We introduce efficient numerical methods for generic HJM equations of interest rate theory by means of high-order weak approximation schemes. These schemes allow for QMC implementations due to the relatively low dimensional integration space. The complexity of the resulting algorithm is considerably lower than the complexity of multi-level MC algorithms as long as the optimal order of QMC-convergence is guaranteed. In order to make the methods applicable to real world problems, we introduce and use the setting of weighted function spaces, such that unbounded payoffs and unbounded characteristics of the equations in question are still allowed. We also provide an implementation, where we efficiently calibrate an HJM equation to caplet data.
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PDF链接：
https://arxiv.org/pdf/1112.5330
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