This study includes two theoretical works. In both works, I assume that economic agents have heterogeneous beliefs. I study collateralized loan transactions among economic agents arising from the divergent beliefs. Moreover, I make collateral requirements endogenously determined, along with interest rates and loan quantities. The theme of the first work is to study private transactions in currency crises. I assume that domestic residents have different beliefs on how resilient the central bank is in defending the currency. Due to the different beliefs, domestic residents willingly borrow and lend among themselves. I show that the heterogeneity of beliefs per se brings stability to the system, but that short-term collateralized loans among domestic residents arising from the divergent opinions make an exchange rate peg vulnerable. The second work is to understand credit default swaps in general equilibrium. The model features a market for a risky asset, a market for loans collateralized by the risky asset, and a market for credit default swaps referencing these loans. I show that the introduction of credit default swaps only as insurance has no effect on the price of the risky asset. And the introduction of credit default swaps both as insurance and as tools for making side bets depresses the price of the risky asset in general but has no effect hen the majority of the economy hold bearish views on the risky asset.

Collateralization in over-the-counter (OTC) derivatives markets has grown rapidly over the past decade, and even faster in the past few years, due to the impact of the recent financial crisis and the particularly important attention to the counterparty credit risk in derivatives contracts. The addition of collateralization to such contracts significantly reduces the counterparty credit risk and allows to offset liabilities in case of default. We study the problem of valuation of OTC derivatives with payoff in a single currency and with single underlying asset for the cases of zero, partial, and perfect collateralization. We assume the derivative is traded between two default-free counterparties and analyze the impact of collateralization on the fair present value of the derivative. We establish a uniform generalized derivative pricing framework for the three cases of collateralization and show how different approaches to pricing turn out to be consistent. We then generalize the results to include multi-asset and cross-currency arguments, where the underlying and the derivative are in some domestic currency, but the collateral is posted in a foreign currency. We show that the results for the single currency, multi-asset case are consistent with those obtained for the single currency, single asset case.

The paper is concerned with counterparty credit risk management for credit default swaps in the presence of default contagion. In particular, we study the impact of default contagion on credit value adjustments such as the BCCVA (Bilateral Collateralized Credit Value Adjustment) of Brigo et al. 2012 and on the performance of various collateralization strategies. We use the incomplete-information model of Frey and Schmidt (2012) as vehicle for our analysis. We find that taking contagion effects into account is important for the effectiveness of the strategy and we derive refined collateralization strategies to account for contagion effects. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Die magnetische Blutbolusmarkierung (Spin-Labeling) ermöglicht die nichtinvasive quantitative Messung des Blutflusses im Gewebe. Beim Spin-Labeling wird arterielles Blut durch Radiofrequenzpulse magnetisch markiert und der Transport der Markierung MR-tomographisch gemessen. Am Modell einer unter physiologischen Bedingungen perfundierten extrakorporalen Schweineniere konnte die Quantifizierbarkeit der Messmethode nachgewiesen werden. In einer Studie an 36 Hirntumorpatienten wurde das Verfahren mit der kontrastmittelbasierten First-Pass-Bolus-Methode zur nicht-quantitativen Perfusionsmessung verglichen. Es zeigte sich eine sehr gute Übereinstimmung zwischen beiden Methoden, der lineare Korrelationskoeffizient des relativen Blutflusses in der Tumorregion lag bei R=0,83. Die mittels Spin-Labeling ermittelten Absolutwerte des Blutflusses spielen bei der Beurteilung des Tumorgrades eine untergeordnete Rolle, da die mittlere Perfusion individuell sehr verschieden ist. Ein zweiter Anwendungsbereich für das Spin-Labeling ist die Darstellung großer Arterien. Spin-Labeling ermöglicht die nichtinvasive dynamische Angiographie (Dynamische Spin-Labeling-Angiographie - DSLA). Analog zur digitalen Subtraktionsangiographie kann damit der Einstromvorgang des Blutes in den Gefäßbaum zeitaufgelöst gemessen werden, jedoch mit wesentlich höherer zeitlicher Auflösung und frei wählbarer Projektionsrichtung. In einer Studie an 18 Patienten mit einseitigen Carotisstenosen wurden die Zeitdifferenzen der Anflutung der zerebralen Gefäße zwischen der betroffenen und der nicht stenosierten Seite bestimmt. Die im Carotis-Siphon gemessenen Zeitdifferenzen korrelieren signifikant mit dem Stenosegrad, steigen aber erst ab einer Lumeneinengung oberhalb von 80 Prozent deutlich an. Im Vergleich zu den etablierten Methoden werden die Möglichkeiten und Grenzen der DSLA dargestellt. / Arterial spin labeling methods allow to determine quantitative tissue blood flow values noninvasively. Arterial blood is labelled by an inversion pulse and the distribution of this intrinsic tracer is measured using magnetic resonance imaging. Experiments using an extra corporal in-vitro porcine kidney in a MR compatible set-up were carried out to determine the accuracy of blood flow values calculated from arterial spin labeling measurements. In a study of 36 brain tumor patients, spin labeling was compared to non-quantitative contrast-enhanced dynamic susceptibility-weighted perfusion imaging. Relative blood flow values determined with both methods were in good agreement, the linear regression coefficient in the tumor region was R=0.83. Due to the variable individual perfusion state, quantitative blood flow values determined using spin labeling play a minor role in the assessment of tumor grade. Application of spin labeling to angiography of major arteries was investigated. Dynamic spin labeling angiography (DSLA) sequences were implemented and tested on a clinical scanner. This technique allows time-resolved depiction of blood flow in large vessels with very high temporal resolution. As opposed to digital subtraction angiography, the method allows arbitrary projection directions. In a study, 18 patients with one-sided carotid stenoses were examined. In these patients the time differences of blood bolus arrival at both hemispheres were determined. Time differences measured in the carotid siphon show a significant correlation with the degree of stenosis. However, a clear increase is not seen until 80% narrowing of a carotid. Possibilities and limitations of the DSLA method are discussed in comparison to established techniques.