Approximate XVA for European Claims

24 Pages Posted: 17 Aug 2020

See all articles by Fabio Antonelli

Fabio Antonelli

Sapienza University of Rome

Alessandro Ramponi

Dept. Economics and Finance, University of Rome Tor Vergata

Sergio Scarlatti

University of Rome Tor Vergata

Date Written: July 15, 2020

Abstract

We consider the problem of computing the Value Adjustment of European contingent claims when default of either party is considered, possibly including also funding and collateralization requirements.

As shown in Brigo et al. ({BLPS}, BFP}), this leads to a more articulate variety of Value Adjustments ({XVA}) that introduce some nonlinear features. When exploiting a reduced-form approach for the default times, the adjusted price can be characterized as the solution to a possibly nonlinear Backward Stochastic Differential Equation (BSDE). The expectation representing the solution of the BSDE is usually quite hard to compute even in a Markovian setting, and one might resort either to the discretization of the Partial Differential Equation characterizing it or to Monte Carlo Simulations. Both choices are computationally very expensive and in this paper we suggest an approximation method based on an appropriate change of numeraire and on a Taylor's polynomial expansion when intensities are represented by means of affine processes correlated with the asset's price. The numerical discussion at the end of this work shows that, at least in the case of the CIR intensity model, even the simple first-order approximation has a remarkable computational efficiency.

Keywords: Credit Value Adjustment, Defaultable Claims, Counterparty Credit Risk, Wrong Way Risk, XVA; Affine Processes

JEL Classification: C02, C63

Suggested Citation

Antonelli, Fabio and Ramponi, Alessandro and Scarlatti, Sergio, Approximate XVA for European Claims (July 15, 2020). Available at SSRN: https://ssrn.com/abstract=3652443 or http://dx.doi.org/10.2139/ssrn.3652443

Fabio Antonelli

Sapienza University of Rome ( email )

Piazzale Aldo Moro 5
Roma, Rome 00185
Italy

Alessandro Ramponi (Contact Author)

Dept. Economics and Finance, University of Rome Tor Vergata ( email )

Via Columbia, 2
Rome, Lazio 00133
Italy

Sergio Scarlatti

University of Rome Tor Vergata ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

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