利率混沌模型的标定

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摘要翻译：
本文利用混沌系数的多项式-指数参数化方法，将利率混沌模型与市场数据进行标定。我们确定了一类单变量模型，它允许我们以受控的方式从高阶混沌中引入复杂性，同时保持相当的分析可处理性。特别地，我们根据正态密度和累积分布函数的初等组合，导出了一变量三级混沌模型中债券和期权价格的显式表达式。然后，我们将混沌模型的校准性能与已知的基准模型进行了比较。对于期限结构的校正，我们发现混沌模型可以与Svensson模型相媲美，其优点是保证正性，并与利率的动态随机演化相一致。对于期权数据的校准，混沌模型优于Hull和White以及rational对数正态模型，并与LIBOR市场模型相当。
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英文标题：
《Calibration of Chaotic Models for Interest Rates》
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作者：
Matheus R Grasselli and Tsunehiro Tsujimoto
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最新提交年份：
2011
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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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英文摘要：
  In this paper we calibrate chaotic models for interest rates to market data using a polynomial-exponential parametrization for the chaos coefficients. We identify a subclass of one-variable models that allow us to introduce complexity from higher order chaos in a controlled way while retaining considerable analytic tractability. In particular we derive explicit expressions for bond and option prices in a one-variable third chaos model in terms of elementary combinations of normal density and cumulative distribution functions. We then compare the calibration performance of chaos models with that of well-known benchmark models. For term structure calibration we find that chaos models are comparable to the Svensson model, with the advantage of guaranteed positivity and consistency with a dynamic stochastic evolution of interest rates. For calibration to option data, chaos models outperform the Hull and White and rational lognormal models and are comparable to LIBOR market models.
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PDF链接：
https://arxiv.org/pdf/1106.2478

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关键词：distribution Combinations Quantitative coefficients calibration 分析 model 期权 系数 market