Model for Central Counterparty Risk with Stochastic Default Intensities

Abstract: In this thesis we use a dynamic model to compute several margins required by a central counterparty, the central clearing house (CCP), to the participants, called clearing members (CM). These margins form the so called default waterfall. In this market only credit default swaps (CDS) are exchanged. CDS are nancial instruments that work as an insurance against counterparties default. The CCP is the main infras- tructure: it takes on counterparty credit risk between members and provides clearing and settlement services in the trading activity. The rst layer of the waterfall is the variation margin (VM). It is de ned as the value of a member's portfolio in the previous period (usually one day) and it is also needed for the next two layers computations. The second layer is the initial margin (IM), which represents an added collateral for market uctuations and has a greater time horizon, equal to 5-10 days. The third layer is the default fund (DF). It represents the last margin of interest in this work and it is used in order to cover losses deriving from defaults of one or more CM. This is the most challenging margin because there is no consensus on the way it should be computed and distributed among the members. Our nal goal is focused on nding the optimal DF=IM ratio for every CM. For the study we consider 8 CM and 4 CDS contracts. First, we compute the values of the CDS contracts, that are subsequently pooled to- gether composing the portfolios of the CM. The margins of the waterfall are computed using dynamic time consistent risk measures and, in order to take into account the risk- iness of the CDS contracts and CM, we extend the model of [Bielecki et al., 2018] to the case of stochastic default intensities, in particular using Cox-Ingersoll-Ross (CIR) processes. The results on DF=IM ratio for each CM suggest that our model is able to scale appropriately the number of members and to take into account their riskiness.