英文标题：
《Affine term structure models : a time-changed approach with perfect fit
to market curves》
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作者：
Cheikh Mbaye and Fr\\\'ed\\\'eric Vrins
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最新提交年份：
2020
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英文摘要：
We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), are tractable processes but have limited flexibility; they fail to replicate actual market curves. The deterministic shift extension of the latter (Hull-White or JCIR++) is a simple but yet efficient solution that is widely used by both academics and practitioners. However, the shift approach is often not appropriate when positivity is required, which is a common constraint when dealing with credit spreads or default intensities. In this paper, we tackle this problem by adopting a time change approach. On the top of providing an elegant solution to the calibration problem under positivity constraint, our model features additional interesting properties in terms of implied volatilities. It is compared to the shift extension on various credit risk applications such as credit default swap, credit default swaption and credit valuation adjustment under wrong-way risk. The time change approach is able to generate much larger volatility and covariance effects under the positivity constraint. Our model offers an appealing alternative to the shift in such cases.
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中文摘要：
我们解决所谓的校准问题，该问题包括以可处理的方式将给定模型拟合到指定的期限结构，如收益率或违约概率曲线。时间均匀跳跃扩散，如Vasicek或Cox-Ingersoll-Ross（可能与复合泊松跳跃，JCIR耦合），是可处理的过程，但灵活性有限；它们无法复制实际的市场曲线。后者的确定性移位扩展（Hull-White或JCIR++）是一种简单但有效的解决方案，被学者和实践者广泛使用。然而，当需要积极性时，转移方法通常不合适，这是处理信用利差或违约强度时的常见约束。在本文中，我们通过采用时间变化方法来解决这个问题。除了为正性约束下的校准问题提供一个优雅的解决方案外，我们的模型还具有隐含波动率方面的其他有趣特性。将其与各种信用风险应用（如信用违约掉期、信用违约掉期期权和错误方式风险下的信用估值调整）的转移扩展进行了比较。在正性约束下，时变方法能够产生更大的波动性和协方差效应。在这种情况下，我们的模型为这种转变提供了一种有吸引力的替代方案。
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分类信息：

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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