2014/10/02 by Giovanni Mottola, Mottola, Giovanni
Economics, Econometrics and Finance · Decision Sciences · #Economic theories and models #Stochastic processes and financial applications #Game Theory and Applications
paper · pdf · doi:10.48550/arxiv.1410.0594
We study the solution's existence for a generalized Dynkin game of switching\ntype which is shown to be the natural representation for general defaultable\nOTC contract with contingent CSA. This is a theoretical counterparty risk\nmitigation mechanism that allows the counterparty of a general OTC contract to\nswitch from zero to full/perfect collateralization and switch back whenever she\nwants until contract maturity paying some switching costs and taking into\naccount the running costs that emerge over time. In this paper we allow for the\nstrategic interaction between the counterparties of the underlying contract,\nwhich makes the problem solution much more tough. We are motivated in this\nresearch by the importance to show the economic sense - in terms of optimal\ncontract design - of a contingent counterparty risk mitigation mechanism like\nour one. In particular, we show that the existence of the solution and the game\nNash equilibrium is connected with the solution of a system of non-linear\nreflected BSDE which remains an open problem. We then provide the basic ideas\nto numerically search the game equilibrium via an iterative optimal stopping\napproach and we show the existence of the solution for our problem under strong\ncondition, in the so called symmetric case.\n