We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. In particular, we introduce multi-curve models driven by a flow of tempered alpha-stable CBI processes. Such models are especially parsimonious and tractable, and can generate contagion effects among different spreads. We provide a complete analytical framework, including a detailed study of discounted exponential moments of CBI processes. The proposed approach allows for explicit valuation formulae for all linear interest rate derivatives and semi-closed formulae for non-linear derivatives via Fourier techniques and quantization. We show that a simple specification of the model can be successfully calibrated to market data.

我们开发了多条产量曲线的建模框架，这些曲线由带有迁移的连续状态分支过程（CBI过程）驱动。利用CBI跳动过程的自激行为，该方法可以重现不同银行同业拆借利率之间利差的相关经验特征。特别是，我们介绍了由缓和的α稳定CBI流程驱动的多曲线模型。这样的模型特别简单和易于处理，并且可以在不同点差之间产生传染效应。我们提供了一个完整的分析框架，包括对CBI流程折现指数矩的详细研究。所提出的方法允许通过傅立叶技术和量化为所有线性利率衍生工具提供明确的估值公式，为非线性衍生工具提供半封闭公式。