英文标题：
《Kriging of financial term-structures》
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作者：
Areski Cousin (SAF), Hassan Maatouk (GdR MASCOT-NUM, LIMOS,
DEMO-ENSMSE), Didier Rulli\\`ere (SAF)
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最新提交年份：
2016
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英文摘要：
Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The proposed method is based on a generalization of kriging models with linear equality constraints (market-fit conditions) and shape-preserving conditions such as monotonicity or positivity (no-arbitrage conditions). We define the most likely curve and show how to build confidence bands. The Gaussian process covariance hyper-parameters under the construction constraints are estimated using cross-validation techniques. Based on observed market quotes at different dates, we demonstrate the efficiency of the method by building curves together with confidence intervals for term-structures of OIS discount rates, of zero-coupon swaps rates and of CDS implied default probabilities. We also show how to construct interest-rate surfaces or default probability surfaces by considering time (quotation dates) as an additional dimension.
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中文摘要：
由于缺乏可靠的市场信息，建立财务期限结构可能会带来很大程度的不确定性。在本文中，我们提出了一种新的术语结构插值方法，该方法扩展了经典的样条函数技术，增加了不确定性的量化。该方法基于克里格模型的推广，该模型具有线性等式约束（市场拟合条件）和形状保持条件，如单调性或正性（无套利条件）。我们定义了最可能的曲线，并展示了如何建立置信区间。利用交叉验证技术估计构造约束下的高斯过程协方差超参数。基于观察到的不同日期的市场报价，我们通过构建OIS贴现率、零息掉期利率和CDS隐含违约概率的期限结构曲线和置信区间，证明了该方法的有效性。我们还展示了如何通过将时间（报价日期）作为一个额外维度来构造利率曲面或违约概率曲面。
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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：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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