Chaos and coherence: a new framework for interest–rate modelling
Chaos and coherence: a new framework for interest–rate modelling
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混沌与连贯性：利率建模的新框架
DOI：
10.1098/rspa.2003.1236
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
L. Hughston
中科院分区：
文献类型：
--
作者：
D. Brody;L. Hughston
提出了一套随机金融的基本公理，其中状态价格密度起着重要的作用，而状态价格密度又决定了利率期限结构的随机动态。状态价格密度是势的事实意味着存在一个渐近随机变量X∞，其条件方差是状态价格密度。然后，维纳混沌展开技术可以应用于X∞，从而使我们能够根据混沌展开的确定性系数来‘参数化’贴现债券系统的动力学。利用这种方法，我们发现存在一个从所有允许项结构轨迹空间到与基础概率空间上的平方可积随机变量空间自然相关的对称Fock空间F的自然映射。F的一个元素是相干的或非相干的，一个随机债券价格系统必然由F的一个非相干元素来表示。利用F的线性，我们得到了债券价格系统、波动率结构、短期利率以及与任意可接受的期限结构模型相关的风险溢价的简单解析公式。还开发了对外汇市场和一般资产系统的扩展。
A set of elementary axioms for stochastic finance is presented wherein a prominent role is played by the state–price density, which in turn determines the stochastic dynamics of the interest–rate term structure. The fact that the state–price density is a potential implies the existence of an asymptotic random variable X∞ with the property that its conditional variance is the state–price density. The Wiener chaos expansion technique can then be applied to X∞, thus enabling us to ‘parametrize’ the dynamics of the discount–bond system in terms of the deterministic coefficients of the chaos expansion. Using this method, we find that there is a natural map from the space of all admissible term–structure trajectories to the symmetric Fock space F naturally associated with the space of square-integrable random variables on the underlying probability space. An element of F is either coherent or incoherent, and a stochastic bond–price system is necessarily represented by an incoherent element of F. Making use of the linearity of F we derive simple analytic formulae for the bond–price system, the volatility structure, the short rate, and the risk premium associated with an arbitrary admissible term–structure model. Extensions to foreign–exchange markets and general asset systems are also developed.
影响因子：
4
作者：
D. Nualart
通讯作者：
D. Nualart