Affine term structure models: A time‐change approach with perfect fit to market curves
提出一种时间变换技术，使仿射跳跃扩散模型能完美拟合收益率、提前还款或违约概率等市场曲线，解决了传统移位方法在正性约束下的局限性，并在信用违约互换、信用估值调整等应用中表现出更优的波动率与协方差效应。
Abstract We address the so‐called calibration problem , which consists of fitting in a tractable way a given model to a specified term structure such as yield, prepayment or default probability curves. Time‐homogeneous affine jump diffusions (HAJD) are tractable processes but have limited flexibility; they fail to perfectly replicate actual market curves. Applying a deterministic shift to the latter is a simple but efficient solution that is widely used by both academics and practitioners. However, the shift approach may not be appropriate when positivity is required, a common constraint when dealing with credit spreads or default intensities. In this paper, we address this problem by adopting a time‐change technique. Specific attention is paid to the Cox–Ingersoll–Ross model with compound Poisson jumps (JCIR), which remains standard for modeling intensities. Our time‐changed JCIR (TC‐JCIR) is compared to the shifted JCIR (JCIR++) in various credit applications such as credit default swap (CDS), credit default swaption, and credit valuation adjustment (CVA) under wrong‐way risk (WWR). The TC‐JCIR model is able to generate much larger implied volatilities and covariance effects than JCIR++ under positivity constraints and represents an appealing alternative to the latter.