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Determinants of the cat bond spread at issuance

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Zeitschrift für die gesamte Versicherungswissenschaft

Abstract

The contribution at hand is a short summary of a working paper presented by Alexander Braun at the annual meeting of the German Insurance Science Association (DVfVW) in Hannover in March 2012. This working paper contains empirical evidence from the primary market for cat bonds, which provides new insights concerning the prevailing pricing practice of these instruments. For this purpose, transactional information from a multitude of sources has been collected and cross-checked in order to compile a data set comprising virtually all cat bond tranches that were issued between 1997 and 2011. In order to identify the main determinants of the cat bond spread at issuance, a series of OLS regressions with robust standard errors is run. The respective results indicate that, apart from the expected loss, the covered territory, the sponsor, the reinsurance cycle, and the spreads on comparably rated corporate bonds exhibit a significant impact. Based on these findings, a multifactor pricing model for cat bonds in the primary market is then proposed. This model is applicable across all considered territories and perils, exhibits a stable fit with regard to different subsamples used for calibration, and achieves a higher in-sample and out-of-sample accuracy than several competing specifications that have been introduced in earlier work.

Zusammenfassung

Der vorliegende Beitrag stellt eine kurze Zusammenfassung eines Arbeitspapiers dar, das von Alexander Braun im März 2012 auf der Jahrestagung des Deutschen Vereins für Versicherungswissenschaft e. V. (DVfVW) in Hannover präsentiert wurde. Dieses Arbeitspapier beinhaltet empirische Evidenz aus dem Primärmarkt für Katastrophenanleihen, die neue Erkenntnisse in Bezug auf die gängige Bewertungspraxis dieser Instrumente liefert. Zu diesem Zweck wurden transaktionsspezifische Informationen aus einer Vielzahl von Quellen zusammengetragen und abgeglichen, um einen Datensatz zu generieren, der praktisch alle zwischen 1997 und 2011 emittierten Katastrophenanleihentranchen umfasst. Um die wesentlichen Determinanten der Risikoaufschläge von Katastrophenanleihen zum Zeitpunkt der Emission zu identifizieren, wird eine Serie von OLS-Regressionen mit robusten Standardfehlern durchgeführt. Die entsprechenden Ergebnisse zeigen, dass, abgesehen vom erwarteten Verlust, die abgedeckte Region, der Sponsor, der Rückversicherungszyklus sowie die Risikoaufschläge vergleichbar gerateter Unternehmensanleihen einen signifikanten Einfluss ausüben. Auf Grundlage dieser Erkenntnisse wird sodann ein Multifaktor-Bewertungsmodell für Katastrophenanleihen im Primärmarkt vorgeschlagen. Dieses Modell ist über alle betrachteten Regionen und Katastrophenrisiken hinweg anwendbar, weist hinsichtlich verschiedener zur Kalibrierung herangezogener Teilstichproben eine stabile Anpassungsgüte auf und erreicht eine höhere in- und out-of-sample Genauigkeit als etliche konkurrierende Spezifikationen, die in früheren Arbeiten vorgeschlagen wurden.

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Notes

  1. For a comprehensive discussion of cat swap contracts refer to Braun (2011).

  2. Note that both binary and proportional payouts to the sponsor are possible (see, e.g., Cummins and Weiss 2009).

  3. This is the same logic as for corporate bond spreads (see, e.g., Elton et al. 2001).

  4. The affected transactions were Ajax Re, Carillon Ltd. A-1, Newton Re 2008 A-1, and Willow Re B.

  5. See Hagedorn et al. (2009) for a more detailed discussion of the choice of trigger types.

  6. In this context, one commonly draws on the Richter Scale for earthquakes and the Saffir-Simpson Scale for hurricanes.

  7. Note that, in practice, the term “peril” is frequently used to refer to the actual combination of geographic zone and natural hazard (see, e.g., Bodoff and Gan 2009). Hence, the terminology in this regard is not entirely precise.

  8. Lane (2004) establishes a relationship between multiperil and singleperil cat bonds based on no-arbitrage considerations.

  9. A detailed description of the catastrophe modeling process can be found in Brookes (2009).

  10. The identification of relevant structures is supported by the process of geocoding, which serves to convert address information into geographic coordinates, consisting of latitude and longitude (see, e.g., Brookes 2009).

  11. Rating agencies commonly adopt a “weak-link approach” for cat bonds. Further information with regard to the corresponding methodology can be found in Standard and Poor’s (2009), Moody’s (2006), and Fitch Ratings (2011).

  12. These strands of thought underpin common theories of the term structure of interest rates (see, e.g., Cox et al. 1985).

  13. Lane and Mahul (2008) examine the impact of peril-specific expected loss on the spread of multiperil cat bonds.

  14. Unfortunately further details, such as the employed cat modeling firm, the lead underwriters, and the TRS counterparty, were only sporadically available.

  15. Please refer to the Thomson Reuters Insurance Linked Securities Community for additional information about this index, including the current calculation methodology. Since the time series available online does not date back to before 2002, we have combined it with earlier data of the long-term index of catastrophe reinsurance prices, which is based on a similar calculation methodology and has been published by Lane and Mahul (2008) in an appendix to their article. The adequacy of this approach is underlined by the fact that both indices are highly correlated during the time period between the first quarters of 2002 and 2008, in which they overlap. The resulting time series is set to start with a value of one in the fourth quarter of 1996.

  16. Sometimes the Gauss-Markov assumptions are extended by additionally requiring the errors to be normally distributed with mean zero and constant variance σ 2, i.e., ϵ∼N(0,σ 2). This complementary condition, which constitutes the classical linear model assumptions, is negligible for large enough sample sizes, since, in those cases, the central limit theorem provides for asymptotic normality (see, e.g., Wooldridge 2008). In addition, one should bear in mind that the errors need to be stochastically independent of each other. Due to the rather rare occurrence of spatial autocorrelation in financial economics, however, this assumption is typically satisfied for cross-sectional analyses. In contrast to that, it represents a common problem when running OLS regressions on time series data.

  17. The following definitions and formulae can, e.g., be found in Kianifard and Swallow (1996).

  18. The complete list of regressors comprises five continuous variables (expected loss, issue size, tenor, synthetic rate on line index, BB corporate bond spread) and nine dummy variables (trigger, wind, earthquake, multiterritory, U.S., Europe, Japan, sponsor, rating). A more detailed description can be found in the full paper by the author (see Braun 2012).

  19. Recall that 33 of the original 402 bonds have already been eliminated due to missing data. Hence, our N for this analysis equals 369, from which we subtract a total of 14 regressors plus the intercept.

  20. Note: case 183 (Successor Hurricane Ind. Class E-III) is not visible as it lies beyond the outer bounds of Fig. 3(a).

  21. An overview of these models can be found in Jaeger et al. (2010).

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Authors and Affiliations

  1. Institute of Insurance Economics, University of St. Gallen, St. Gallen, Switzerland

    Alexander Braun

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  1. Alexander Braun
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Correspondence to Alexander Braun.

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This contribution summarizes a presentation of a working paper given by the author at the annual meeting of the German Insurance Science Association (DVfVW) in Hannover in March 2012. The full working paper (see Braun, 2011), including all tables and figures, can be found at www.ivw.unisg.ch.

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Braun, A. Determinants of the cat bond spread at issuance. ZVersWiss 101, 721–736 (2012). https://doi.org/10.1007/s12297-012-0221-3

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