Affine term structure models: A time-change approach with perfect fit to market curves

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.