Model-free bounds on bilateral counterparty valuation

In the last years, counterparty default risk has experienced an increased interest both by academics as well as practitioners. This was especially motivated by the market turbulences and the financial crises over the past years which have highlighted the importance of counterparty default risk for uncollateralized derivatives. The following paper focuses on the pricing of derivatives subject to such counterparty risk. After a succinct introduction to the topic, a brief review of state-of-the-art methods for the calculation of bilateral counterparty value adjustments is presented. Due to some weaknesses of these models, a novel method for the determination of model-free tight lower and upper bounds on these adjustments is presented. It will be shown in detail how these bounds can be easily and eciently calculated by the solution of a corresponding linear optimization problem. It will be illustrated how usual discretization methods like Monte Carlo methods allow to reduce the calculation of bounds to an ordinary finite dimensional transportation problem, whereas a continuous time approach will lead to a general mass transportation problem. The paper is closed with several applications of these model-free bounds, like stress-testing and estimation of model reserves.