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We address the so-called calibration problem which consists of fitting in atractable way a given model to a specified term structure like, e.g., yield ordefault probability curves. Time-homogeneous jump-diffusions like Vasicek orCox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), aretractable processes but have limited flexibility; they fail to replicate actualmarket curves. The deterministic shift extension of the latter (Hull-White orJCIR++) is a simple but yet efficient solution that is widely used by bothacademics and practitioners. However, the shift approach is often notappropriate when positivity is required, which is a common constraint whendealing with credit spreads or default intensities. In this paper, we tacklethis problem by adopting a time change approach. On the top of providing anelegant solution to the calibration problem under positivity constraint, ourmodel features additional interesting properties in terms of impliedvolatilities. It is compared to the shift extension on various credit riskapplications such as credit default swap, credit default swaption and creditvaluation adjustment under wrong-way risk. The time change approach is able togenerate much larger volatility and covariance effects under the positivityconstraint. Our model offers an appealing alternative to the shift in suchcases.

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