A Subordinated CIR Intensity Model with Application to Wrong-Way Risk CVA

28 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: January 17, 2018

Abstract

Credit Valuation Adjustment (CVA) pricing models need to be both flexible and tractable. The survival probability has to be known in closed form (for calibration purposes), the model should be able to fit any valid Credit Default Swap (CDS) curve, should lead to large volatilities (in line with CDS options) and finally should be able to feature significant Wrong-Way Risk (WWR) impact. The Cox-Ingersoll-Ross model (CIR) combined with independent positive jumps and deterministic shift (JCIR++) is a very good candidate: the variance (and thus covariance with exposure, i.e. WWR) can be increased with the jumps, whereas the calibration constraint is achieved via the shift. In practice however, there is a strong limit on the model parameters that can be chosen, and thus on the resulting WWR impact. This is because only non-negative shifts are allowed for consistency reasons, whereas the upwards jumps of the JCIR++ need to be compensated by a downward shift. To limit this problem, we consider the two-side jump model recently introduced by Mendoza-Arriaga & Linetsky, built by time-changing CIR intensities. In a multivariate setup like CVA, time-changing the intensity partly kills the potential correlation with the exposure process and destroys WWR impact. Moreover, it can introduce a forward looking effect that can lead to arbitrage opportunities. In this paper, we use the time-changed CIR process in a way that the above issues are avoided. We show that the resulting process allows to introduce a large WWR effect compared to the JCIR++ model. The computation cost of the resulting Monte Carlo framework is reduced by using an adaptive control variate procedure.

Suggested Citation

Mbaye, Cheikh and Vrins, Frederic Daniel, A Subordinated CIR Intensity Model with Application to Wrong-Way Risk CVA (January 17, 2018). Available at SSRN: https://ssrn.com/abstract=3366808 or http://dx.doi.org/10.2139/ssrn.3366808

Cheikh Mbaye

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

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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