英文标题：
《A computational spectral approach to interest rate models》
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作者：
Luca Di Persio and Michele Bonollo and Gregorio Pellegrini
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最新提交年份：
2015
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英文摘要：
  The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\\xi}, hence acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigorous Uncertainty Quantification (UQ) method which aims at providing reliable numerical estimates for some uncertain physical quantities defining the dynamic of certain engineering models and their related simulations. In the present paper we exploit the PCE approach to analyze some equity and interest rate models considering, without loss of generality, the one dimensional case. In particular we will take into account those models which are based on the Geometric Brownian Motion (gBm), e.g. the Vasicek model, the CIR model, etc. We also provide several numerical applications and results which are discussed for a set of volatility values. The latter allows us to test the PCE technique on a quite large set of different scenarios, hence providing a rather complete and detailed investigation on PCE-approximation\'s features and properties, such as the convergence of statistics, distribution and quantiles. Moreover we give results concerning both an efficiency and an accuracy study of our approach by comparing our outputs with the ones obtained adopting the Monte Carlo approach in its standard form as well as in its enhanced version.
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中文摘要：
多项式混沌展开（PCE）技术利用正交多项式的适当线性组合来恢复有限的二阶随机变量，这些正交多项式是给定随机量{\\xi}的函数，因此充当一种随机基。PCE方法是一种数学上严格的不确定性量化（UQ）方法，其目的是为定义某些工程模型及其相关模拟动态的一些不确定物理量提供可靠的数值估计。在本文中，我们利用PCE方法来分析一些考虑了一维情况的权益和利率模型，但没有失去一般性。特别是，我们将考虑那些基于几何布朗运动（gBm）的模型，例如Vasicek模型、CIR模型等。我们还提供了一些数值应用和结果，讨论了一组波动率值。后者使我们能够在大量不同的场景中测试PCE技术，从而对PCE近似的特征和属性，如统计、分布和分位数的收敛性，提供了一个相当完整和详细的研究。此外，我们还通过将我们的结果与采用蒙特卡罗方法的标准形式和增强形式得到的结果进行比较，给出了我们的方法的效率和准确性研究的结果。
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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：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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