英文标题：
《A Consistent Stochastic Model of the Term Structure of Interest Rates
  for Multiple Tenors》
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作者：
Mesias Alfeus, Martino Grasselli and Erik Schl\\\"ogl
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最新提交年份：
2018
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英文摘要：
  Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor (\"roll-over risk\"), we construct a stochastic model framework for the term structure of interest rates in which a frequency basis (i.e. a spread applied to one leg of a swap to exchange one floating interest rate for another of a different tenor in the same currency) arises endogenously. This rollover risk consists of two components, a credit risk component due to the possibility of being downgraded and thus facing a higher credit spread when attempting to roll over short-term borrowing, and a component reflecting the (systemic) possibility of being unable to roll over short-term borrowing at the reference rate (e.g., LIBOR) due to an absence of liquidity in the market. The modelling framework is of \"reduced form\" in the sense that (similar to the credit risk literature) the source of credit risk is not modelled (nor is the source of liquidity risk). However, the framework has more structure than the literature seeking to simply model a different term structure of interest rates for each tenor frequency, since relationships between rates for all tenor frequencies are established based on the modelled roll-over risk. We proceed to consider a specific case within this framework, where the dynamics of interest rate and roll-over risk are driven by a multifactor Cox/Ingersoll/Ross-type process, show how such model can be calibrated to market data, and used for relative pricing of interest rate derivatives, including bespoke tenor frequencies not liquidly traded in the market.
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中文摘要：
明确考虑短期借款与长期借款的风险（“展期风险”），我们为利率期限结构构建了一个随机模型框架，在该框架中，频率基础（即应用于掉期的一个分支的利差，以将同一货币的一个浮动利率兑换为另一个不同期限的浮动利率）内生产生。该展期风险包括两个部分，一个是信用风险部分，因为在试图展期短期借款时，可能会被降级，从而面临更高的信用利差；另一个是反映（系统性）由于市场缺乏流动性，无法以参考利率（如LIBOR）展期短期借款的可能性。建模框架为“简化形式”，即（类似于信贷风险文献）信贷风险源未建模（流动性风险源也未建模）。然而，由于所有期限频率的利率之间的关系都是基于模型化的滚动风险建立的，因此，该框架的结构比试图为每个期限频率建立不同利率期限结构模型的文献要复杂得多。我们继续在此框架内考虑一个具体案例，其中利率和展期风险的动态由多因素Cox/Ingersoll/Ross型过程驱动，展示了如何根据市场数据校准此类模型，并将其用于利率衍生品的相对定价，包括未在市场上流动交易的定制期限频率。
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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：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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