英文标题：
《Coherent Chaos Interest Rate Models》
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作者：
Dorje C. Brody and Stala Hadjipetri
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最新提交年份：
2014
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英文摘要：
  The Wiener chaos approach to interest rate modelling arises from the observation that the pricing kernel admits a representation in terms of the conditional variance of a square-integrable random variable, which in turn admits a chaos expansion. When the expansion coefficients factorise into multiple copies of a single function, then the resulting interest rate model is called coherent, whereas a generic interest rate model will necessarily be incoherent. Coherent representations are nevertheless of fundamental importance because incoherent ones can always be expressed as a linear superposition of coherent elements. This property is exploited to derive general expressions for the pricing kernel and the associated bond price and short rate processes in the case of an n-th order chaos model for each $n$. The pricing formulae for bond options and swaptions are obtained in closed forms for a number of examples. An explicit representation for the pricing kernel of a generic---incoherent---model is then obtained by use of the underlying coherent elements. Finally, finite-dimensional realisations of the coherent chaos models are investigated in detail. In particular, it is shown that a class of highly tractable models can be constructed having the characteristic feature that the discount bond price is given by a piecewise flat (simple) process.
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中文摘要：
利率建模的维纳混沌方法源于这样一个观察：定价核允许以平方可积随机变量的条件方差表示，而这反过来又允许混沌展开。当展开系数分解为单个函数的多个副本时，所得的利率模型称为一致的，而一般的利率模型必然是不一致的。然而，相干表示具有根本重要性，因为非相干表示总是可以表示为相干元素的线性叠加。利用这一性质，在每n$为一个n阶混沌模型的情况下，导出了定价核和相关债券价格及短期利率过程的一般表达式。债券期权和互换期权的定价公式是以封闭形式给出的。然后，通过使用基本的相干元素，得到了一般的非相干模型的定价核的显式表示。最后，详细研究了相干混沌模型的有限维实现。特别地，证明了可以构造一类高度可处理的模型，其特征是贴现债券价格由分段平坦（简单）过程给出。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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