多重收益率曲线建模的通用HJM框架
A general HJM framework for multiple yield curve modeling
摘要：
我们提出了一个通用的框架，为建模的多重收益率曲线后出现的最后金融危机。在一般的半鞅环境下，我们提供了一个HJM方法来模拟FRA利率和简单的复合OIS无风险远期利率之间的乘法利差的期限结构。我们推导出一个HJM漂移和一致性条件，确保没有套利，此外，我们展示了如何构建模型，使乘法价差大于1，并下令相对于男高音的长度。当驱动半鞅被指定为仿射过程时，我们得到了一个灵活的马尔可夫结构。最后，我们表明，建议的框架允许统一和扩展最近的几种方法，多个收益率曲线建模。
英文摘要：
We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.
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