Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

55 Pages Posted: 22 Apr 2019

See all articles by Cheikh Mbaye

Cheikh Mbaye

Catholic University of Louvain (UCL) - Louvain Finance (LFIN)

Frédéric D. Vrins

Louvain Finance Center (LFIN), UC Louvain; Center for Operations Research and Econometrics (CORE), UC Louvain

Date Written: March 28, 2019

Abstract

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), 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++) is a simple but yet efficient solution that is widely used by both academics and practitioners. However, the shift approach is often not appropriate when positivity is required, which is a common constraint when dealing with credit spreads or default intensities. In this paper, we tackle this problem by adopting a time change approach. On the top of providing an elegant solution to the calibration problem under positivity constraint, our model features additional interesting properties in terms of implied volatilities. 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 time change approach is able to generate much larger volatility and covariance effects under the positivity constraint. Our model offers an appealing alternative to the shift in such cases.

Keywords: credit risk, model calibration, default model, stochastic intensity, affine process, time change

Suggested Citation

Mbaye, Cheikh and Vrins, Frederic Daniel, Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves (March 28, 2019). Available at SSRN: https://ssrn.com/abstract=3366800 or http://dx.doi.org/10.2139/ssrn.3366800

Cheikh Mbaye

Catholic University of Louvain (UCL) - Louvain Finance (LFIN)

34 Voie du Roman Pays - L1.03.01
Louvain-la-Neuve, 1348
Belgium

Frederic Daniel Vrins (Contact Author)

Louvain Finance Center (LFIN), UC Louvain ( email )

Voie du Roman Pays 34
Louvain-la-Neuve, 1348
Belgium

HOME PAGE: http://www.uclouvain.be/frederic.vrins

Center for Operations Research and Econometrics (CORE), UC Louvain ( email )

Voie du Roman Pays 34
Louvain-la-Neuve,, B-1348
Belgium

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