The German Research Foundation (DFG) funded our project "The Value of Crypto Currencies - An Asset Pricing Perspective", in which we cooperate with Prof. Dr. Erik Theissen from the University of Mannheim.

Bitcoin, the first cryptocurrency, was originally designed to be a form of electronic cash that enables online payment without intermediation by financial institutions. While Bitcoin and other cryptocurrencies still serve that purpose, they are nowadays widely considered as financial assets and are held as investments or for speculative purposes. The CME and the Cboe, two of the world's largest derivatives exchanges, trade Bitcoin futures, and some authors consider cryptocurrencies a new asset class. Despite their growing popularity cryptocurrencies are not well understood. Why is someone ready to pay a five-digit dollar amount for a piece of data representing a unit of virtual cash? Why is private money without commodity backing valuable at all? Are we simply witnessing an enormous bubble or do modern cryptocurrencies rely on unique design features that justify at least part of the demand - for instance, the cryptographic techniques inducing a high degree of counterfeit safety or the protocols that set an upper bound on cryptocurrency supply acting as commitment device not to issue too much virtual money? Are such design features crucial value drivers? What else explains a cryptocurrency’s value and volatility?

Although, at a technical level, the unique features of cryptocurrencies and the underlying blockchain (or distributed ledger) technology have been extensively discussed from a computer science and a legal perspective, there is a lack of economic research to answer the questions above. We therefore seek to deepen the understanding of cryptocurrencies from an economic and finance perspective. More specifically: We want to develop an economic model that explains, from economic primitives, why cryptocurrencies have a non-zero value at all and understand which of the various design features of cryptocurrencies affect their value. There are three sub-goals that specify the overriding question: (1) We want to provide an overview and basic understanding of the unique design features of a cryptocurrency and to identify those that are relevant for the pricing and risk profile of cryptocurrencies. At this point, we will rely on both a literature review and an own exploratory empirical analysis of the variety of cryptocurrencies traded. (2) We plan to develop an economic model that allows to formally analyze the effects of those design features that are identified in step 1 as most important for a cryptocurrency’s value and volatility. Within this modelling approach, we intend to consider two main agent groups, the consumers and the miners, and their intergroup dynamics to derive price implications. (3) We seek to empirically assess the relevance of our model predictions using the cross-sectional variation between different cryptocurrencies.

The expected outcomes are not only novel from a theoretical perspective, but also highly relevant for informing the ongoing public debate on the merits and dangers of cryptocurrencies.

• Schuster, P.; Theissen, E.; Uhrig-Homburg, M. (2020). Financial applications of block chain technology. Schmalenbach's journal for economic research, (72), 125-147.

The German Research Foundation (DFG) funded our project "The Maturity Structure of Illiquidity Premiums and their Macroeconomic Determinants".

IIlliquid bonds have a premium to compensate bond investors for the lack of liquidity. Our results from the first part of the project, however, suggest that a clear connection between illiquidity premiums and typical liquidity measures like the bid-ask spread is only significant during economic crises. Therefore, we ask the natural follow-up question, why existing liquidity measures seem to work only well in stress periods. Building on this question, we analyze how the measurement of liquidity in general should be adapted to the economic conditions. From a conceptual point of view, at least two reasons point towards a measurement of liquidity that depends on the economic context. First, typical liquidity measures calculated from completed transactions provide only an incomplete picture. The reason is that transactions that have not been executed due to extreme illiquidity do not show up in the data. Second, for bond illiquidity premiums, expected transaction costs at the future trading date are the relevant costs and not today's transaction costs. Since transaction costs increase strongly in times of economic stress, it remains unclear whether current liquidity in calm periods is a good proxy for expected future transaction costs. In the proposed second part of the project, we first want to develop a forecasting model for expected transaction costs. For that, the remaining maturity of the bond as a natural ceiling on the holding horizon plays a central role, leading to a term structure of liquidity measurement. In the second step, we use the liquidity measures derived from the forecasting model to re-assess the impact of illiquidity on bond prices. The explanatory power of the newly developed liquidity measure in this exercise also serves as a criterion to evaluate and compare different measures. Since we are not aware of an approach to measure liquidity dependent on the economic environment in any security market, we plan to extend our analysis to the stock market in the last step. We expect that our results have practical influence in at least two ways. First, our forecast model provides expected trading costs for bonds, for which there are few or no data. From a practical perspective, information on trading costs is very important for these illiquid securities. Second, our new measures allow establishing a connection between the liquidity of a security and the associated price impact at an arbitrary point during the business cycle. Financial institutions could then apply, for example, scenario analyses, to predict the impact of a deterioration of liquidity in times of crisis, which would improve risk management.

The German Research Foundation (DFG) funded our project "The Effects of Market Frictions on Option Prices", in which we cooperate with Prof. Dr. Olaf Korn from the Georg-August-University of Göttingen, from 2016 to 2020.

Classic option-pricing theory assumes that assets are traded on frictionless markets. In reality, however, different market frictions prevail, for example, asset illiquidity and funding restrictions for certain groups of market participants. Such market frictions can be substantial, as it was observed during the global financial crisis of 2008 and 2009, and can have an important impact on option prices. The goal of this project is to understand how market frictions affect option prices and option returns. A major challenge for such an investigation is that the direction of price effects depends on net end-user demand for options. If the demand is positive, i.e., end-users want to buy options, market frictions should lead to higher prices, whereas a negative demand should lead to lower prices. Unfortunately, data on end-user demand, in particular for options on individual stocks, is rarely available. Therefore, an essential idea of the project is to develop and empirically test hypotheses about the relation between market frictions and option prices which don't require any knowledge of end-user demand in a first step. This step exploits the idea that frictions should increase the variation of option prices around an appropriate reference value. If the hypotheses are supported by empirical tests for the US stock options market, we can draw conclusions about end-user demand from the difference between option prices and reference values in a second step. The project's main question about the connection between market frictions and option prices is relevant both from a scientific and socio-political perspective. In face of the controversial debate about derivatives markets a better understanding of the functioning of these markets is very important for policy recommendations concerning the design of corporate risk management strategies as well as the design and regulation of options markets. By looking at different market frictions (illiquidity, incompleteness of markets, funding restrictions) and investigating their relative importance for price formation in different market periods the project makes an important contribution in this respect.

Our project "Asset Pricing, Liquidity, and Option Returns" was funded by the Frankfurt Institute for Risk Management and Regulation (FIRM).

In risk management processes, liquid derivatives markets play an important role. At the same time, classic option-pricing theory assumes that assets are traded on frictionless markets and liquidity concerns are neglected. For the stock and bond market the interaction between liquidity and asset prices is well understood: A higher illiquidity level leads to higher expected returns. However, investigations of the effects of illiquidity in options markets are scarce. Options markets are special as they, in contrast to stock and bond markets, are in zero-net supply. Market makers absorb end-user selling or buying pressure, and hence, market makers can hold long or short positions in options. Depending on end-user demand the sign of the influence of liquidity on option prices can be positive or negative. We want to contribute to this literature by considering the effect of option liquidity level and risk depending on end-user demand in an uniform and integrated setting. In detail, we want to answer the following three main research questions: First, we want to identify the effects that the choice of (daily and intra-daily) liquidity and otion returns measures have on the asset pricing results. This includes an analysis of liquidity measures that account for the characteristics of options markets. Second, we aim to shed light on how end-user demand affects the direction of liquidity effects on option prices. Finally, we want to disentangle the influence from liquidity level and liquidity risk and determine which channel is more important. Putting everything together, the aim is to identify demand-dependent liquidity effects and to determine the importance of different measures of option liquidity and risk on expected option returns.

Our project "Size-Dependent Bond Liquidity Measures and their Asset Pricing Implications" was funded by the Fritz Thyssen Foundation from 2016 to 2018.

Due to the enormous importance of bond markets for the financing of states and companies, the functioning of these markets is very important from a social perspective. A decisive criterion here is the liquidity of bonds. It indicates how easily (or at what cost) bonds can be traded between different market participants. The recent financial crisis in particular has shown that a drying up of liquidity can lead to high losses in value. The aim of the project is to develop methods to manage the associated risks.

The first part of the research project therefore focuses on the development of a new approach to measure liquidity that takes into account the specifics of the bond market. A decisive feature - albeit neglected by existing approaches - is the strong dependence of transaction costs on the transaction volume. The use of classical liquidity measures therefore leads to an unresolved conflict of objectives. Either only very few trading transactions of comparable volume are taken into account for the calculation of liquidity measures and thus a large part of the available information is ignored. Alternatively, transactions of different volumes are used, which are ultimately not comparable in terms of their transaction costs. The approach to liquidity measurement developed by the project aims to resolve this trade-off and explicitly take into account a dependence of transaction costs on volume. Based on the newly developed volume-dependent measures, the second part of the project will reassess the dependence of the price of a bond on its liquidity. In the literature, often only individual liquidity measures are used to analyse this correlation. It is therefore to be expected that the application of the new approach to liquidity measurement and the associated coverage of further liquidity components will lead to new insights with regard to this issue which is central to risk management.

From 2007 to 2009, the German Research Foundation (DFG) funded our project "Modelling and Quantification of Credit Risks with Special Consideration of Default Dependencies".

The adequate consideration of default dependencies is one of the most crucial problems in credit risk management. Such dependencies can arise from common risk factors, learning from defaults or contagions. The aim of the project is the theoretical and empirical analysis of default dependencies. For this purpose we develop a theoretical framework that can in principle produce default dependencies in a realistic magnitude and that is furthermore consistently applicable on a large number of borrowers. Using the advantages of a top-down construction we first specify the economy-wide default intensity. Afterwards we apply the concept of random-thinning to break down the economy-wide default risk to subportfolio or single-name level. The evaluation of the models happens in two ways. Within a simulation study we analyze which dependencies can be achieved in our framework in general. We compare the derived default correlations and their consequences for the valuation of credit derivatives to the most important bottom-up approaches. An empirical verification of the model using market data of correlation sensitive credit derivatives should shed light on the question if this model can be a real-world solution.