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

Mbaye, Cheikh Vrins, Frédéric [UCL]

We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield, prepayment or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compound Poisson jumps, JCIR, a.k.a. SRJD), are tractable processes but have limited flexibility; they fail to replicate actual market curves. The deterministic shift extension of the latter, Hull-White or JCIR++ (a.k.a. SSRJD) is a simple but yet 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 tackle this problem by adopting a time change approach, leading to the TC-JCIR model. On the top of providing an elegant solution to the calibration problem under positivity constraint, our model features additional interesting properties in terms of variance. It is compared to the shift extension on various credit risk applications such as credit default swap, credit default swaption and credit valuation adjustment under wrong-way risk. The TC-JCIR model is able to generate much larger implied volatilities and covariance effects than JCIR++ under positivity constraint, and therefore offers an appealing alternative to the shift extension in such cases.