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The authors analyze the practical consequences of the bilateral counterparty risk adjustment. They point out that past literature assumes that, at the moment of the first default, a risk-free closeout amount will be used. They argue that the legal (ISDA) documentation suggests in many points that a substitution closeout should be used. This would take into account the risk of default of the survived party. They show how the bilateral counterparty risk adjustment changes strongly when a substitution closeout amount is considered.
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