分数期限结构模型：无套利与一致性

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摘要翻译：
本文介绍了分数布朗运动驱动的Heath-Jarrow-Morton(HJM)利率模型。在Guasoni[Math.Finance 16(2006)569-582]的基础上，利用支持性论证，证明了在比例交易费用下，该模型是无套利的，这与Guasoni[Math.Finance 16(2006)569-582]是一致的。特别地，我们得到了一个性质类似于经典HJM无套利漂移限制的漂移条件。本文的第二部分讨论了与分数阶HJM动力学有关的一致性问题。利用Nagumo型条件，给出了具有分数布朗运动的HJM模型有限维不变流形的一个相当完备的刻划。作为应用，我们研究了Nelson-Siegel族与Ho-Lee模型和Hull-White模型的一致性。结果表明，类似于布朗情形，这样一个族并不符合具有确定性波动性的分数HJM动力学。事实上，不存在与Nelson-Siegel家族相一致的非平凡分数利率模型。
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英文标题：
《Fractional term structure models: No-arbitrage and consistency》
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作者：
Alberto Ohashi
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最新提交年份：
2009
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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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英文摘要：
  In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage free under proportional transaction costs in the same spirit of Guasoni [Math. Finance 16 (2006) 569-582]. In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fractional HJM dynamics. We give a fairly complete characterization of finite-dimensional invariant manifolds for HJM models with fractional Brownian motion by means of Nagumo-type conditions. As an application, we investigate consistency of Nelson-Siegel family with respect to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case such a family does not go well with the fractional HJM dynamics with deterministic volatility. In fact, there is no nontrivial fractional interest rate model consistent with the Nelson-Siegel family.
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PDF链接：
https://arxiv.org/pdf/0802.1288

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关键词：期限结构 结构模型 无套利 一致性 proportional Guasoni 2006 Math Nelson 569