摘要翻译：
本文旨在研究具有随机波动性的广义Fong-Vasicek双因素利率模型。在该模型中，随机短期利率的离散度（波动率的平方）也是随机的，它遵循一个非负过程，波动率与离散度的平方根成正比。假设离散随机过程的漂移是一个相当一般的形式，特别是包括一个根的线性函数（产生原始的Fong-Vasicek模型）或一个三个根的类三次函数（产生用于描述波动性聚类的广义Fong-Vasicek模型）。我们考虑了关于随机离散度的极限分布的平均债券价格。债券的平均价格取决于时间和当前的短期利率水平，就像许多流行的单因素利率模型一样，特别是Vasicek和Cox-Ingersoll-Ross模型。然而，作为本文的一个主要结果，我们表明不存在这样的单因素模型产生与上述平均值相同的债券价格。
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英文标题：
《On non-existence of a one factor interest rate model for volatility
  averaged generalized Fong-Vasicek term structures》
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作者：
B. Stehlikova, D. Sevcovic
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最新提交年份：
2008
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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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：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  The purpose of this paper is to study the generalized Fong--Vasicek two-factor interest rate model with stochastic volatility. In this model the dispersion of the stochastic short rate (square of volatility) is assumed to be stochastic as well and it follows a non-negative process with volatility proportional to the square root of dispersion. The drift of the stochastic process for the dispersion is assumed to be in a rather general form including, in particular, linear function having one root (yielding the original Fong--Vasicek model or a cubic like function having three roots (yielding a generalized Fong--Vasicek model for description of the volatility clustering). We consider averaged bond prices with respect to the limiting distribution of stochastic dispersion. The averaged bond prices depend on time and current level of the short rate like it is the case in many popular one-factor interest rate model including in particular the Vasicek and Cox--Ingersoll-Ross model. However, as a main result of this paper we show that there is no such one-factor model yielding the same bond prices as the averaged values described above.
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PDF链接：
https://arxiv.org/pdf/0811.0473