Before the 2008 financial crisis, most research in financial mathematics focused on the risk management and the pricing of options without considering effects of counterparties’ default, illiquidity problems, systemic risk and the role of the repurchase agreement (Repo). During the 2008 financial crisis, a frozen Repo market led to a shutdown of short sales in the stock market. Cyclical interdependencies among financial corporations caused that a default of one firm seriously affected other firms and even the whole financial network. In this dissertation, we will consider financial markets which are shaped by financial crisis. This will be done from two distinct perspectives, an investor’s and a regulator’s. From an investor’s perspective, recently models were proposed to compute the total valuation adjustment (XVA) of derivatives without considering a potential crisis in the market. In our research, we include a possible crisis by apply an alternating renewal process to describe a switching between a normal financial status and a financial crisis status. We develop a framework for pricing the XVA of a European claim in this state-dependent framework. We represent the price as a solution to a backward stochastic differential equation and prove the existence and uniqueness of the solution. To study financial networks from a regulator’s perspective, one popular method is the fixed point based approach by L. Eisenberg and T. Noe. However, in practice, there is no accurate record of the interbank liabilities and thus one has to estimate them to use Eisenberg - Noe type models. In our research, we conduct a sensitivity analysis of the Eisenberg - Noe framework, and quantify the effect of the estimation errors to the clearing payments. We show that the effect of the missing specification of interbank connection to clearing payments can be described via directional derivatives that can be represented as solutions of fixed point equations. We also compute the probability of observing clearing payment deviations of a certain magnitude.

Le risque systémique menaçant le système financier est une préoccupation majeure pour les régulateurs. Les indicateurs adéquats de risque systémique devraient vraiment les aider à accomplir les lois réglementaires appropriées. La thèse propose un modèle dynamique du système bancaire pour calculer un indicateur de risque systémique de deux composantes :La probabilité d'un évènement déclencheur qui provient de la baisse des prix des actifs, et les pertes correspondantes dans le système Financier.La thèse prouve également l'existence et l'unicité de deux modèles d'équilibre de compensation : Le premier avec un modèle de différentes hiérarchies de dette et le second modèle avec plusieurs stratégies de liquidation / Systemic risk threatening the financial system is a major concern for regulators. Adequate indicators of systemic risk would help them perform appropriate regulatory laws.The thesis proposes a dynamic model of banking system to calculate a systemic risk indicator of two components : The probability of a triggering event originated from external asset price decline, and the corresponding losses through the financial system. The thesis also proves the existence and uniqueness of two clearing equilibrium: the first deals with a model of différent debt seniorities, the second with a model of several illiquid asset following a proportional liquidation strategy.