We consider the class of affine LIBOR models with multiple curves, which is an analytically tractable class of discrete tenor models that easily accommodates positive or negative interest rates and positive spreads. By introducing an interpolating function, we extend the affine LIBOR models to a continuous tenor and derive expressions for the instantaneous forward rate and the short rate. We show that the continuous tenor model is arbitrage-free, that the analytical tractability is retained under the spot martingale measure, and that under mild conditions an interpolating function can be found such that the extended model fits any initial forward curve. This allows us to compute value adjustments (i.e. XVAs) consistently, by solving the corresponding ‘pre-default’ BSDE. As an application, we compute the price and value adjustments for a basis swap, and study the model risk associated to different interpolating functions.

中文翻译：

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具有多个曲线的仿射LIBOR模型的连续男高扩展及其在XVA中的应用

我们考虑具有多条曲线的仿射LIBOR模型的类别，这是离散的期限模型的分析性易于处理的类别，可轻松适应正或负利率和正利差。通过引入插值函数，我们将仿射LIBOR模型扩展到连续的期限，并导出瞬时正向利率和短期利率的表达式。我们表明，连续的男高音模型是无套利的，在点mar测度下保留了分析的可延展性，并且在温和的条件下可以发现内插函数，以使扩展模型适合任何初始正向曲线。通过解决相应的“默认前” BSDE，这使我们能够一致地计算值调整（即XVA）。作为应用程序，我们计算基础互换的价格和价值调整，