In this paper, we develop a framework for discretely compounding interest rates that is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for negative interest rates and has superb calibration properties even in the presence of extremely low rates. Moreover, the measure changes along the tenor structure are significantly simplified. These properties make it an excellent base for a postcrisis multiple curve setup. Two variants for multiple curve constructions based on the multiplicative spreads are discussed. Time‐inhomogeneous Lévy processes are used as driving processes. An explicit formula for the valuation of caps is derived using Fourier transform techniques. Relying on the valuation formula, we calibrate the two model variants to market data.

中文翻译：

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多曲线Lévy远期价格模型允许负利率

在本文中，我们开发了一个基于远期价格过程方法的离散复合利率框架。这种方法具有许多优点，特别是在当前的市场环境中。与经典以及LévyLibor市场模型相比，它自然而然地允许负利率，并且即使在利率极低的情况下也具有出色的校准性能。而且，沿男高音结构的量度变化被显着简化。这些特性使其成为危机后多曲线设置的极佳基础。讨论了基于乘法点差的多曲线构造的两个变体。时间不均匀的Lévy过程用作驱动过程。使用傅里叶变换技术可以得出明确的瓶盖估价公式。