仿射LIBOR模型
The affine LIBOR models
摘要：
我们提供了一个通用的和灵活的方法来LIBOR建模类仿射因子过程的基础上。我们的方法尊重LIBOR利率非负的基本经济要求，以及金融数学的基本要求，即LIBOR利率是关于其自身远期测度的可分析的鞅。此外，最重要的是，我们的方法还导致分析易处理的表达式的多LIBOR的回报。因此，这种方法结合了著名的远期价格模型与经典LIBOR利率模型的优点。添加了几个例子，并显示了典型的波动率微笑。我们相信，基于CIR过程的LIBOR模型可能是特别感兴趣的应用程序，因为封闭式的上限和互换的估值公式推导。
英文摘要：
We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are non-negative, and the basic requirement from mathematical finance that LIBOR rates are analytically tractable martingales with respect to their own forward measure. Additionally, and most importantly, our approach also leads to analytically tractable expressions of multi-LIBOR payoffs. This approach unifies therefore the advantages of well-known forward price models with those of classical LIBOR rate models. Several examples are added and prototypical volatility smiles are shown. We believe that the CIR-process based LIBOR model might be of particular interest for applications, since closed form valuation formulas for caps and swaptions are derived.
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