6,428 research outputs found
Central Clearing Valuation Adjustment
This paper develops an XVA (costs) analysis of centrally cleared trading,
parallel to the one that has been developed in the last years for bilateral
transactions. We introduce a dynamic framework that incorporates the sequence
of cash-flows involved in the waterfall of resources of a clearing house. The
total cost of the clearance framework for a clearing member, called CCVA for
central clearing valuation adjustment, is decomposed into a CVA corresponding
to the cost of its losses on the default fund in case of defaults of other
member, an MVA corresponding to the cost of funding its margins and a KVA
corresponding to the cost of the regulatory capital and also of the capital at
risk that the member implicitly provides to the CCP through its default fund
contribution. In the end the structure of the XVA equations for bilateral and
cleared portfolios is similar, but the input data to these equations are not
the same, reflecting different financial network structures. The resulting XVA
numbers differ, but, interestingly enough, they become comparable after scaling
by a suitable netting ratio
Central Limit Results for Jump-Diffusions with Mean Field Interaction and a Common Factor
A system of weakly interacting particles whose dynamics is given in terms
of jump-diffusions with a common factor is considered. The common factor is
described through another jump-diffusion and the coefficients of the evolution
equation for each particle depend, in addition to its own state value, on the
empirical measure of the states of the particles and the common factor. A
Central Limit Theorem, as , is established. The limit law is
described in terms of a certain Gaussian mixture. An application to models in
Mathematical Finance of self-excited correlated defaults is described
Sample-path Large Deviations in Credit Risk
The event of large losses plays an important role in credit risk. As these
large losses are typically rare, and portfolios usually consist of a large
number of positions, large deviation theory is the natural tool to analyze the
tail asymptotics of the probabilities involved. We first derive a sample-path
large deviation principle (LDP) for the portfolio's loss process, which enables
the computation of the logarithmic decay rate of the probabilities of interest.
In addition, we derive exact asymptotic results for a number of specific
rare-event probabilities, such as the probability of the loss process exceeding
some given function
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