Computing credit valuation adjustment solving coupled PIDEs in the Bates model
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Computing credit valuation adjustment solving coupled PIDEs in the Bates model Ludovic Goudenège1 · Andrea Molent2 · Antonino Zanette3 Received: 10 October 2019 / Accepted: 10 April 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Credit Value Adjustment is the charge applied by financial institutions to the counterparty to cover the risk of losses on a counterpart default event. In this paper we estimate such a premium under the Bates stochastic model (Bates in The Review of Financial Studies 9(1): 69–107, 1996), which considers an underlying affected by both stochastic volatility and random jumps. We propose an efficient method which improves the Finite-Difference Monte Carlo (FDMC) approach introduced by de Graaf et al. (Journal of Computational Finance 21, 2017) In particular, the method we propose consists in replacing the Monte Carlo step of the FDMC approach with a finite difference step and the whole method relies on the efficient solution of two coupled partial integrodifferential equations which is done by employing the Hybrid Tree-Finite Difference method developed by Briani et al. (arXiv:1603.07225 2016;IMA Journal of Management Mathematics 28(4): 467–500, 2017;The Journal of Computational Finance 21(3): 1–45, 2017). Moreover, the direct application of the hybrid techniques in the original FDMC approach is also considered for comparison purposes. Several numerical tests prove the effectiveness and the reliability of the proposed approach when both European and American options are considered. Subject classification numbers as needed. Keywords Credit value adjustment · Hybrid methods · PIDE · Monte Carlo · Bates model
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Ludovic Goudenège [email protected] Andrea Molent [email protected] Antonino Zanette [email protected]
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Féderation de Mathématiques de CentraleSupélec - CNRS FR3487, Gif-sur-Yvette, France
2
Università degli Studi di Udine, Udine, Italy
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Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Udine, Udine, Italy
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L. Goudenège et al.
Mathematics Subject Classification 11K45 · 35R09 · 45K05 · 65M06 · 65M75 · 65Y20
1 Introduction Financial institutions suffer several risks, one of them is the counter-party credit risk (CCR). This risk arises from the possibility that the counter-party of a financial contract may default. This risk was often overlooked, but in the last decades, after the financial crisis of 2007 and the Lehman Brothers failure in 2008, it gained more and more interest by practitioners and academics. In particular, according to the Basel III framework of 2010, financial institutions must charge a premium to their counter-party according to its credit reliability in order to compensate for a possible counter-party default. Also IFRS 13 in 2013 requires the fair value of financial products to be measured based on counter-party credit risk. For these reasons, financial institutions charge to the counter-party a premium called Credit Valuation Adjustment (CVA), which is the difference betwee
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