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Journal of Financial Services Research

Erschienen in:

01.05.2018

Credit Value Adjustment with Market-implied Recovery

verfasst von: Pascal François, Weiyu Jiang

Erschienen in: Journal of Financial Services Research | Ausgabe 2/2019

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Abstract

We present a model for CVA calculation in which the recovery rate is inferred from the term structure of CDS spreads. The negative relation between recovery rates and default probabilities induces a substantial underestimation of the CVA when constant recovery is assumed. That underestimation prevails for both unilateral and bilateral CVA as well as for the CVA capital charge. The underestimation gets more severe as the horizon of the position increases. Our CVA model with market-implied recovery also offers a way to capture correlation effects between the level of exposure and counterparty risk.

Vorheriger Artikel Can the Book-to-Market Ratio Signal Banks’ Earnings and Default Risk? Evidence Around the Great Recession

Nächster Artikel Observables and Residuals: Exploring Cross-Border Differences in SME Borrowing Costs

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The Bank for International Settlements regularly reports the notional amount outstanding on the OTC derivatives market. It was estimated at 544 trillions of USD by the end of 2016, interrupting a 20-year steady growth that peaked with USD 696 trillions in 2013. The proportions of notional amount across the three major types of derivatives have been relatively stable over time: Roughly two-thirds for swaps, one quarter for forwards, and one tenth for options.

The credit risk literature provides strong evidence documenting the negative correlation between recovery rates and default probabilities. See, among others, the works of Altman et al. (2005), Das(2007) and Bastos (2014).

In a different context but relying on a similar argument, Chambers et al. (2010) show that the assumption of constant recoveries led to overestimating the ratings of mortgage-backed securities during the subprime crisis.

On the U.S. segment for instance, the first quarter 2017 review of the Office of the Comptroller of the Currency reports that the top four banks account for almost 90% of all OTC derivatives notional amount and the top 25 banks account for 99% of it (Office of the Comptroller of the Currency (OCC) 2017, Table 1).

In this section we focus on the basic unilateral CVA. Hull and White (2012) refine the CVA calculation to account for collateral and cure period. In Section 4.6 we extend the model to account for the bilateral CVA, that is, for the fact that the holder of the position can also default.

We opt for the logistic specification for the recovery rate. Alternatively, Das and Hanouna (2009) examine a probit and an arctan specification, and obtain similar results.

A common practice is to set the constant recovery on OTC derivatives close to the historical average recovery rate of senior unsecured debt.

They find a downward bias of about 15% of the bond price (which represents a smaller fraction of par) and mostly attribute it to a liquidity premium.

Before September 2010, the data was provided by CMA via Datastream. After that date, the data is provided by Thomson Reuters. We have combined the data from the two providers on 525 firms by using the function “SPLC” of Datastream. For the 214 firms left, we only have data from January 2008.

During the sample period, we note that there are only 12 firms with a default record on senior unsecured debt, according to the Fixed Investment Security Database (FISD). The impact of survivorship bias on our results should therefore be limited.

There is strong evidence that recovery rates are cyclical. See in particular Düllmann and Trapp (2004), Altman et al. (2005), or Bruche and Gonzalez-Aguado (2010).

The convexity bias refers to the fact that credit spreads are usually convex functions of default risk determinants (such as the rating, the leverage, or the solvency ratio). Thus, the average spreads are larger than the spreads evaluated at the average value of the determinant.

We only report the CVA term structures for the long position in the forward. Results for the short position are qualitatively similar and available upon request.

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Titel: Credit Value Adjustment with Market-implied Recovery
verfasst von: Pascal François
Weiyu Jiang
Publikationsdatum: 01.05.2018
Verlag: Springer US
Erschienen in: Journal of Financial Services Research / Ausgabe 2/2019
Print ISSN: 0920-8550
Elektronische ISSN: 1573-0735
DOI: https://doi.org/10.1007/s10693-018-0298-5