Credit and liquidity risk in Lévy asset price models Zusammenfassung: In this thesis we present a new kind of asset price model. Credit risk considerations and new developments in the area of liquidity risk modelling are taken into account.In Chapter 1 essential mathematical tools such as stochastic processes and dependence modelling are reviewed.Chapter 2 presents a new asset price model which is an enhancement of the exponential Levy model. The possibility of default is modelled by a single jump to zero whereby higher probabilities for this event lead to lower asset prices. Explicit valuation formulas for European options are established by using the Fourier valuation method. The formulas can numerically be computed fast and thus allow to calibrate the model to market data.On illiquid markets the law of one price no longer prevails and the costs of holding unhedgeable risks have to be considered. This issue is incorporated in the Two Price Theory of Cherny and Madan (2010) which is discussed and applied to the considered asset price model in Chapter 3 of this thesis