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Real Data Empirical Applications

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Counting Statistics for Dependent Random Events

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Abstract

The goal of this chapter is to display a number of empirical applications of some of the new aggregation techniques discussed in the book. We give details of several examples, from risk management to portfolio selection, where market data are used to properly calibrate the dependence structure and to identify the more suitable approach to the problem at hand.

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Notes

  1. 1.

    We consider eleven maturities totally: eight of these come from real market data, while the other corresponding to a maturity of 6, 7, and 8 years are interpolated prices.

  2. 2.

    Given the anomalies on the CDSs’ prices of the Greece during the analyzed period, we assume a flat structure of CDS price equal to the asset swap spread of the Hellenic Republic step-up coupon bond (isin: GR0128011682) at the 24th of January 2013 and with 12 years maturity.

  3. 3.

    We need to fix a bound to allow for the classification of small group. Coherently with Schönbucher [15], we set a bound of 20.

  4. 4.

    The acronym stands for self-organizing map which refers to a particular type of artificial neural network proposed by Kohonen [11].

  5. 5.

    All data are drawn from Thomson Reuters Datastream.

  6. 6.

    The data regarding spot rates have been provided from IRS Agency. The IRS is a bureau of the Department of the Treasury and one of the world’s most efficient tax administrators. The website is the following: “http://www.irs.gov/Retirement-Plans/Monthly-Yield-Curve-Tables”.

  7. 7.

    The 1-year and 5-year transition matrixes were derived from CreditMetrics paper issued by J.P. Morgan. Ratings are provided by the Agency Standard & Poor’s issued in 2014.

  8. 8.

    A CDS is a proper credit derivative product designed to transfer the credit exposure of fixed income products between parties, protecting the buyer against credit events that typically are defaults.

  9. 9.

    LGD is an attribute of any exposure and represents the share of an asset that is lost when borrower defaults. LGD is facility-specific because such losses depend on several characteristic such as the presence of collateral and the degree of subordination. Nevertheless Basel II requirements prescribe fixed LGD ratios (from 0.45 to 0.75) for classes of unsecured exposures; our portfolio can be assumed to belong to. Obviously the chosen value is not restrictive for our procedure.

  10. 10.

    The couples of variables are ordered such to have a decreasing dependence parameters. The couples are Banco Santander-Intesa San Paolo, Deutsche bank-Nordea bank, Credit Suisse Group-DNB bank, KBC-Banco Espirito Santo, and Lloyds bank-BNP Paribas.

  11. 11.

    The sampling from the hierarchical Archimedean structures has been done with the algorithm proposed in Savu and Trede [14]. This algorithm, based on the conditional inversion method, is computationally intensive especially in high dimensional problems. For a better performing sampling, see Hofert and Mächler [10].

  12. 12.

    This is done by the rnacopula function in R.

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Authors and Affiliations

  1. Department of Statistical Sciences “Paolo Fortunati”, University of Bologna, Bologna, Italy

    Enrico Bernardi & Silvia Romagnoli

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  1. Enrico Bernardi
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  2. Silvia Romagnoli
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Bernardi, E., Romagnoli, S. (2021). Real Data Empirical Applications. In: Counting Statistics for Dependent Random Events. Springer, Cham. https://doi.org/10.1007/978-3-030-64250-1_6

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