## [in German only] Die Berechnung der negativen Basis anschaulich erläutert

[in German only] In einem früheren Artikel haben wir im Rahmen eines idealisierten, einfachen Kreditrisiko-Bewertungsmodells eine wissenschaftlich fundierte Definition für den Begriff der negativen Basis eingeführt. Im vorliegenden Artikel rekapitulieren wir die zugrundeliegende Logik noch einmal in einfach verständlicher Weise. Insbesondere demonstrieren wir die Mechanik des Modells anhand von einfachen Beispielen.

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## Portfolio optimization for credit-risky assets under extreme dependence

We consider power utility maximization in a multivariate Black-Scholes model that is enhanced by credit risk via the Marshall-Olkin exponential distribution. On the practical side, the model is analytically tractable, easy to interpret, and thus simple to implement. On the theoretical side, the model constitutes a well-justified and intuitive mathematical wrapping to study the effect of extreme and higher-order dependence on optimal portfolios. In particular, we show that it is rich enough to model both, situations in which diversification is beneficial and situations in which this is not the case.

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## Improved analytical proxy formulas for convertible bonds

In a previous article, we derived a sharp analytical lower bound for the price of a convertible bond. When a soft call covenant was present, a lower bound could only be derived in a simple credit-equity model, and two simplifying assumptions were made: (1) the soft call right may be executed at any time, starting at time t=0, and (2) the bond and its underlying equity are denominated in the same currency. This addendum summarizes the necessary adjustments to the formula in order to get rid of these restrictive assumptions.

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## Integrated convertibles - Investment styles and characteristics integration applied to convertible bonds

This article explores six investment styles like momentum, value, defensive and others in the niche asset class of US convertible bonds. While only carry and a characteristics integration approach yield promising results, it seems that both strategies can be explained by common equity and bond market factors. Thus, the case of characteristics investing in convertible bonds is not as strong as in other more traditional asset classes. However, convertible bond characteristics integration provides an interesting opportunity to get exposure to equity and bond markets as well as to multiple characteristics at once.

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## Geostatistical modeling of financial data

We explore how the joint modeling of financial assets can utilize methodologies from geostatistical modeling. The considered approach is essentially based on modeling data as realizations of a (Gaussian) random field. This allows for a parsimonious representation of the dependence structure by means of a covariance function taken to be a function of the distance between observations. A key beneft of this ansatz is the possibility to include new data points, i.e. to consider new companies in financial applications. Consequently, geostatistical modeling has appealing benefits in the contexts of covariance matrix estimation and missing data imputation. We thoroughly discuss the necessary adjustments when applying geostatistical methods to the high-dimensional framework that entails the modeling of financial data, instead of the 2D/3D coordinate space encountered in original applications of the method. We illustrate the two use cases of covariance matrix estimation and missing data imputation on a data set of CDS spreads of constituents of the iTraxx universe.

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