TY - THES A1 - Riedel, Robby T1 - Die 'Too Big to Fail'-Problematik - Quantitative Regulierung zur Reduzierung der Interbankenverflechtung und damit systemischen Risikos - T1 - 'Too Big to Fail' - Quantitative Regulation of Interconnectedness and Systemic Risk - N2 - Im Rahmen dieser Arbeit wird ein Modell entwickelt, welches auf Basis von länderübergreifenden Forderungs- und Verbindlichkeitsstrukturen die internationale Vernetzung der Banken abbildet. Die Analyse offenbart, dass systemische Risiken im Allgemeinen von wenigen Instituten ausgehen. Zudem wird aufgezeigt, dass solche Risiken vornehmlich in Banken aus Volkwirtschaften auftreten, in denen die Finanzindustrie eine exponierte Stellung einnimmt. Auf der anderen Seite sind die Institute aus diesen Ökonomien auch überproportional anfällig gegenüber systemischen Schocks und somit erhöhten Ansteckungsgefahren ausgesetzt. Systemische Risiken gehen nicht nur von Großbanken aus, sondern auch der Ausfall mittelgroßer oder gar kleiner Institute kann erhebliche Konsequenzen für das Gesamtsystem nach sich ziehen. Darüber hinaus ist ersichtlich, dass höhere systemische Risiken von Banken ausgehen, die einen hohen Verflechtungsgrad innerhalb des Bankensystems haben. Die potentiellen Schäden für das Gesamtsystem sind umso höher, je mehr signifikante Geschäftsbeziehungen eine Bank zu anderen Banken aufweist. Systemische Risiken können nicht grundsätzlich innerhalb eines nationalen Bankensystems isoliert werden, denn ein Großteil der Folgeausfälle erfolgt länderübergreifend. Die Analyse bringt zudem zu Tage, dass seit dem Jahr 2006 systemische Risiken im Allgemeinen zurückgingen. In der vorliegenden Arbeit werden zunächst regulatorische Instrumente zur Reduzierung systemischer Risiken für alle Banken vorgestellt. Es lässt sich konstatieren, dass Eigenkapitalerhöhungen die Widerstands- und Verlustabsorptionsfähigkeit der Banken maßgeblich stärken würden. Auch können durch geeignete Großkreditvorschriften Risiken für das Gesamtsystem reduziert werden. Um das System entscheidend zu stabilisieren, müssten diese Instrumente allerdings erheblich von den aktuellen Bestimmungen abweichen. Die Untersuchungen zeigen, dass eine Eigenkapitalausstattung der Banken von 12% der risikoungewichteten Bilanz (Leverage Ratio) oder Großkreditvorschriften für Exposures zu einzelnen Gegenparteien von höchstens 18% des haftenden Eigenkapitals maßgeblich zu einer adäquaten bzw. notwendigen Finanzmarktstabilität beitragen können. Diese Arbeit befasst sich ferner mit möglichen regulatorischen Ansätzen zur Reduzierung systemischer Risiken speziell für systemrelevante Banken. Eine mögliche regulatorische Alternative könnte eine Kombination sowohl höherer Eigenkapitalvorschriften als auch verschärfter Großkreditvorschriften darstellen. Durch eine Leverage Ratio von mindestens 9% für nicht-systemrelevante Institute und eine höhere Quote von 11% für systemrelevante Banken, kombiniert mit einem maximalen Exposure zwischen zwei Vertragsparteien von 23% sowie zu systemrelevanten Banken von maximal 18%, ließe sich das systemische Risiko im Bankensystem entscheidend senken. N2 - For this paper, a model has been educed, depicting the international network of banks on the basis of transnational receivable and liability structures. The analysis reveals that systemic risk originates from few institutions only. In addition, it is demonstrated that those risks mainly occur in banks of economies having a financial industry that occupies a prominent position. On the other hand, financial institutions within those economies are disproportionately vulnerable to systemic shocks and thus have increased risk of infection. Systemic risks can not only spring from major banks, but even the failure of medium-sized or small institutions may have substantial consequences for the entire system. Moreover, it is evident that higher systemic risks are caused by banks that have a large degree of entanglement within the banking system. The more significant the relations of a certain bank are to other banks, the greater the potential damage is for the entire system. Systemic risks cannot always be isolated within a national banking system. The analysis also brings to light that systemic risk has decreased in general since 2006. First, in this work some regulatory instruments to reduce systemic risk for all banks are derived. It can be stated that capital increases is an appropriate tool to strengthen the resistance and loss absorption capacity of banks considerably. A reduction of risk can also be achieved by suitable large exposures regimes. In order to stabilize the system sufficiently, these instruments should however be substantially different from the current regulations. The investigations show that a capital adequacy of banks from 12% of riskunweighted balance (leverage ratio) as well as large exposures restrictions to individual counterparties by less than 18% of the liable capital can contribute significantly to achieve adequate and necessary financial stability. This work also deals with possible regulatory approaches that are cut out for systemically important banks in particular. A possible regulatory alternative could be a combination of both higher capital requirements and stricter large exposures regime. A leverage ratio of at least 9% for non-systemically important institutions and a higher rate of 11% for systemically important banks is advisable. That should be combined with a maximum exposure between two parties of 23% as well as exposures to systemically important banks by at most 18%. Altogether those measures would lead to a vast reduction of systemic risk in the banking system. KW - Systemisches Risiko KW - Bankenregulierung KW - Basel III KW - Interbankenmarkt KW - Finanz- und Wirtschaftskrise KW - Interconnectedness KW - Geldmarkt KW - Bank KW - Unternehmensgröße KW - Insolvenz KW - Bankenaufsicht KW - Großbank KW - Strukturreform Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-138319 ER - TY - THES A1 - Karl, Sabine T1 - Firm Values and Systemic Stability in Financial Networks T1 - Firmenwerte und systemisches Risiko in finanziellen Netzwerken N2 - Based on the work of Eisenberg and Noe [2001], Suzuki [2002], Elsinger [2009] and Fischer [2014], we consider a generalization of Merton's asset valuation approach where n firms are linked by cross-ownership of equities and liabilities. Each firm is assumed to have a single outstanding liability, whereas its assets consist of one system-exogenous asset, as well as system-endogenous assets comprising some fraction of other firms' equity and liability, respectively. Following Fischer [2014], one can obtain no-arbitrage prices of equity and the recovery claims of liabilities as solutions of a fixed point problem, and hence obtain no-arbitrage prices of the `firm value' of each firm, which is the value of the firm's liability plus the firm's equity. In a first step, we consider the two-firm case where explicit formulae for the no-arbitrage prices of the firm values are available (cf. Suzuki [2002]). Since firm values are derivatives of exogenous asset values, the distribution of firm values at maturity can be determined from the distribution of exogenous asset values. The Merton model and most of its known extensions do not account for the cross-ownership structure of the assets owned by the firm. Therefore the assumption of lognormally distributed exogenous assets leads to lognormally distributed firm values in such models, as the values of the liability and the equity add up to the exogenous asset's value (which has lognormal distribution by assumption). Our work therefore starts from lognormally distributed exogenous assets and reveals how cross-ownership, when correctly accounted for in the valuation process, affects the distribution of the firm value, which is not lognormal anymore. In a simulation study we examine the impact of several parameters (amount of cross-ownership of debt and equity, ratio of liabilities to expected exogenous assets value) on the differences between the distribution of firm values obtained from our model and correspondingly matched lognormal distributions. It becomes clear that the assumption of lognormally distributed firm values may lead to both over- and underestimation of the “true" firm values (within the cross-ownership model) and consequently of bankruptcy risk, too. In a second step, the bankruptcy risk of one firm within the system is analyzed in more detail in a further simulation study, revealing that the correct incorporation of cross-ownership in the valuation procedure is the more important, the tighter the cross-ownership structure between the two firms. Furthermore, depending on the considered type of cross-ownership (debt or equity), the assumption of lognormally distributed firm values is likely to result in an over- resp. underestimation of the actual probability of default. In a similar vein, we consider the Value-at-Risk (VaR) of a firm in the system, which we calculate as the negative α-quantile of the firm value at maturity minus the firm's risk neutral price in t=0, i.e. we consider the (1-α)100%-VaR of the change in firm value. If we let the cross-ownership fractions (i.e. the fraction that one firm holds of another firm's debt or equity) converge to 1 (which is the supremum of the possible values that cross-ownership fractions can take), we can prove that in a system of two firms, the lognormal model will over- resp. underestimate both univariate and bivariate probabilities of default under cross-ownership of debt only resp. cross-ownership of equity only. Furthermore, we provide a formula that allows us to check for an arbitrary scenario of cross-ownership and any non-negative distribution of exogenous assets whether the approximating lognormal model will over- or underestimate the related probability of default of a firm. In particular, any given non-negative distribution of exogenous asset values (non-degenerate in a certain sense) can be transformed into a new, “extreme" distribution of exogenous assets yielding such a low or high actual probability of default that the approximating lognormal model will over- and underestimate this risk, respectively. After this analysis of the univariate distribution of firm values under cross-ownership in a system of two firms with bivariately lognormally distributed exogenous asset values, we consider the copula of these firm values as a distribution-free measure of the dependency between these firm values. Without cross-ownership, this copula would be the Gaussian copula. Under cross-ownership, we especially consider the behaviour of the copula of firm values in the lower left and upper right corner of the unit square, and depending on the type of cross-ownership and the considered corner, we either obtain error bounds as to how good the copula of firm values under cross-ownership can be approximated with the Gaussian copula, or we see that the copula of firm values can be written as the copula of two linear combinations of exogenous asset values (note that these linear combinations are not lognormally distributed). These insights serve as a basis for our analysis of the tail dependence coefficient of firm values under cross-ownership. Under cross-ownership of debt only, firm values remain upper tail independent, whereas they become perfectly lower tail dependent if the correlation between exogenous asset values exceeds a certain positive threshold, which does not depend on the exact level of cross-ownership. Under cross-ownership of equity only, the situation is reverse in that firm values always remain lower tail independent, but upper tail independence is preserved if and only if the right tail behaviour of both firms’ values is determined by the right tail behaviour of the firms’ own exogenous asset value instead of the respective other firm’s exogenous asset value. Next, we return to systems of n≥2 firms and analyze sensitivities of no-arbitrage prices of equity and the recovery claims of liabilities with respect to the model parameters. In the literature, such sensitivities are provided with respect to exogenous asset values by Gouriéroux et al. [2012], and we extend the existing results by considering how these no-arbitrage prices depend on the cross-ownership fractions and the level of liabilities. For the former, we can show that all prices are non-decreasing in any cross-ownership fraction in the model, and by use of a version of the Implicit Function Theorem we can also determine exact derivatives. For the latter, we show that the recovery value of debt and the equity value of a firm are non-decreasing and non-increasing in the firm's nominal level of liabilities, respectively, but the firm value is in general not monotone in the firm's level of liabilities. Furthermore, no-arbitrage prices of equity and the recovery claims of liabilities of a firm are in general non-monotone in the nominal level of liabilities of other firms in the system. If we confine ourselves to one type of cross-ownership (i.e. debt or equity), we can derive more precise relationships. All the results can be transferred to risk-neutral prices before maturity. Finally, following Gouriéroux et al. [2012] and as a kind of extension to the above sensitivity results, we consider how immediate changes in exogenous asset values of one or more firms at maturity affect the financial health of a system of n initially solvent firms. We start with some theoretical considerations on what we call the contagion effect, namely the change in the endogenous asset value of a firm caused by shocks on the exogenous assets of firms within the system. For the two-firm case, an explicit formula is available, making clear that in general (and in particular under cross-ownership of equity only), the effect of contagion can be positive as well as negative, i.e. it can both, mitigate and exacerbate the change in the exogenous asset value of a firm. On the other hand, we cannot generally say that a tighter cross-ownership structure leads to bigger absolute contagion effects. Under cross-ownership of debt only, firms cannot profit from positive shocks beyond the direct effect on exogenous assets, as the contagion effect is always non-positive. Next, we are concerned with spillover effects of negative shocks on a subset of firms to other firms in the system (experiencing non-negative shocks themselves), driving them into default due to large losses in their endogenous asset values. Extending the results of Glasserman and Young [2015], we provide a necessary condition for the shock to cause such an event. This also yields an upper bound for the probability of such an event. We further investigate how the stability of a system of firms exposed to multiple shocks depends on the model parameters in a simulation study. In doing so, we consider three network types (incomplete, core-periphery and ring network) with simultaneous shocks on some of the firms and wiping out a certain percentage of their exogenous assets. Then we analyze for all three types of cross-ownership (debt only, equity only, both debt and equity) how the shock intensity, the shock size, and network parameters as the number of links in the network and the proportion of a firm's debt or equity held within the system of firms influences several output parameters, comprising the total number of defaults and the relative loss in the sum of firm values, among others. Comparing our results to the studies of Nier et al. [2007], Gai and Kapadia [2010] and Elliott et al. [2014], we can only partly confirm their results with respect to the number of defaults. We conclude our work with a theoretical comparison of the complete network (where each firm holds a part of any other firm) and the ring network with respect to the number of defaults caused by a shock on a single firm, as it is done by Allen and Gale [2000]. In line with the literature, we find that under cross-ownership of debt only, complete networks are “robust yet fragile" [Gai and Kapadia, 2010] in that moderate shocks can be completely withstood or drive the firm directly hit by the shock in default, but as soon as the shock exceeds a certain size, all firms are simultaneously in default. In contrast to that, firms default one by one in the ring network, with the first “contagious default" (i.e. a default of a firm not directly hit by the shock) already occurs for smaller shock sizes than under the complete network. N2 - Basierend auf den Arbeiten von Eisenberg und Noe [2001], Suzuki [2002], Elsinger [2009] und Fischer [2014] wird ein Netzwerk aus n≥2 Firmen betrachtet, die über Fremd- und/oder Eigenkapitalverflechtungen miteinander verbunden sind. Dabei wird angenommen, dass jede Firma eine Klasse von exogenen Assets sowie eine Klasse von Schulden mit Fälligkeitszeitpunkt T besitzt. Der Wert der Schulden und des Eigenkapitals jeder Firma zum Fälligkeitszeitpunkt kann dann mit Hilfe des Fixpunktalgorithmus von Fischer [2014] bestimmt werden, was auch den ‚Firmenwert‘ (Gesamtwert der Assets einer Firma) liefert. Ausgehend von lognormalverteilten Assetwerten wird in einer Simulationsstudie für den Zwei-Firmen-Fall die Verteilung des Firmenwerts mit einer angepassten Lognormalverteilung verglichen, ebenso die daraus resultierenden Ausfallwahrscheinlichkeiten. Für extrem hohe Verflechtungsgrade werden theoretische Ergebnisse bezüglich Über- und Unterschätzung der tatsächlichen Ausfallwahrscheinlichkeit durch die Lognormalverteilung hergeleitet. Anschließend wird der lower und upper tail dependence coefficient der Firmenwerte zweier Firmen bei ausschließlich Fremd- bzw. Eigenkapitalverflechtungen bestimmt. Für Netzwerke beliebiger Größe wird nach einer Sensitivitätsanalyse des Werts der Schulden, des Werts des Eigenkapitals und des Firmenwerts in Abhängigkeit der vorliegenden Verflechtungsgrade und des nominellen Schuldenwerts untersucht, unter welchen Bedingungen sich Schocks auf die exogenen Assetwerte einer oder mehrerer Firmen innerhalb des Netzwerks verbreiten und möglicherweise zum Ausfall anderer, nicht direkt vom Schock betroffenen Firmen im System führen. KW - Finanzmathematik KW - Systemisches Risiko KW - finanzielles Netzwerk KW - Kapitalverflechtungen KW - cross-ownership KW - financial network KW - systemic risk KW - structural model KW - firm valuation KW - Firmwert Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-115739 ER - TY - THES A1 - Hain, Johannes T1 - Valuation Algorithms for Structural Models of Financial Networks T1 - Algorithmen zur Bestimmung von Gleichgewichtslösungen in Finanzsystemen mit Kapitalverflechtung N2 - The thesis focuses on the valuation of firms in a system context where cross-holdings of the firms in liabilities and equities are allowed and, therefore, systemic risk can be modeled on a structural level. A main property of such models is that for the determination of the firm values a pricing equilibrium has to be found. While there exists a small but growing amount of research on the existence and the uniqueness of such price equilibria, the literature is still somewhat inconsistent. An example for this fact is that different authors define the underlying financial system on differing ways. Moreover, only few articles pay intense attention on procedures to find the pricing equilibria. In the existing publications, the provided algorithms mainly reflect the individual authors' particular approach to the problem. Additionally, all existing methods do have the drawback of potentially infinite runtime. For these reasons, the objects of this thesis are as follows. First, a definition of a financial system is introduced in its most general form in Chapter 2. It is shown that under a fairly mild regularity condition the financial system has a unique existing payment equilibrium. In Chapter 3, some extensions and differing definitions of financial systems that exist in literature are presented and it is shown how these models can be embedded into the general model from the proceeding chapter. Second, an overview of existing valuation algorithms to find the equilibrium is given in Chapter 4, where the existing methods are generalized and their corresponding mathematical properties are highlighted. Third, a complete new class of valuation algorithms is developed in Chapter 4 that includes the additional information whether a firm is in default or solvent under a current payment vector. This results in procedures that are able find the solution of the system in a finite number of iteration steps. In Chapter 5, the developed concepts of Chapter 4 are applied to more general financial systems where more than one seniority level of debt is present. Chapter 6 develops optimal starting vectors for non-finite algorithms and Chapter 7 compares the existing and the new developed algorithms concerning their efficiency in an extensive simulation study covering a wide range of possible settings for financial systems. N2 - Die vorliegende Dissertation hat die Unternehmensbewertung in Finanzsystemen mit Fremd- und Eigenkapitalverflechtung zum Thema. Die zentrale Eigenschaft dieser Modelle ist, dass zur Bestimmung der Firmenwerte eine Gleichgewichtslösung ermittelt werden muss. Die Zahl der Veröffentlichungen mit dem Schwerpunkt des Nachweises von Existenz- und Eindeutigkeitsaussagen der Gleichgewichte steigt zwar stetig an, allerdings ist die Fachliteratur in diesem Bereich teilweise noch sehr inkonsistent. Beispielsweise existieren je nach Autor unterschiedliche Vorgehensweisen, das zugrunde liegende Finanzsystem zu definieren. Darüber hinaus schenken nur wenige Fachartikel der Frage Beachtung, wie die Lösungsgleichgewichte genau bestimmt werden können. Zuletzt weisen die bereits entwickelten Verfahren den Nachteil auf, dass Sie womöglich unendlich viele Iterationsschritte benötigen bis die gesuchte Lösung exakt erreicht wird. Aus diesen Gründen beinhaltet die vorliegende Dissertation folgende Themen. Im ersten Schritt wird in Kapitel 2 eine möglichst allgemeine Definition eines Finanzsystems eingeführt. Es wird gezeigt dass unter nicht allzu strengen Voraussetzungen die Gleichgewichtslösung dieses Systems eindeutig bestimmt ist. In Kapitel 3 werden in der Fachliteratur zu diesem Thema zu findende Erweiterungen und abweichende Definitionen des Systems vorgestellt und wie diese in das allgemeine Modell aus dem vorherigen Kapitel eingebettet werden können. Danach wird in Kapitel 4 ein Überblick über bereits entwickelte Lösungsverfahren gegeben, wobei die existierenden Prozeduren in ihrem Vorgehen verallgemeinert und deren zugehörige mathematische Eigenschaften aufgezeigt werden. Des weiteren wird im gleichen Kapitel eine komplett neue Klasse von Lösungsverfahren entwickelt, die noch die zusätzliche Information verarbeiten, ob eine Firma für einen gegebenen Zahlungsvektor solvent oder insolvent ist. Als Folge dieses Ansatzes sind diese Algorithmen in der Lage, die exakte Gleichgewichtslösung des Systems in endlich vielen Schritten zu finden. In Kapitel 5 werden die entworfenen Konzepte dann für Finanzsysteme angewendet, in denen mehr als nur eine Schulden-Seniorität berücksichtigt wird. Kapitel 6 leitet optimale Startvektoren der nicht-endlichen Verfahren her und Kapitel 7 vergleicht die bereits existierenden und alle neu entwickelten Lösungsverfahren bezüglich ihrer Laufzeiteffizienz im Rahmen einer ausführlichen Simulationsstudie. KW - Risikomanagement KW - Finanzmathematik KW - Financial Networks KW - Counterparty Risk KW - Numerical Asset Valuation KW - Systemic Risk KW - Structrual Model KW - Unternehmensbewertung KW - Kapitalverflechtung KW - Finanzielle Netzwerke KW - Systemisches Risiko Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-128108 ER -