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Credit Value Adjustment (CVA) is the difference between the value of thedefault-free and credit-risky derivative portfolio, which can be regarded asthe cost of the credit hedge. Default probabilities are therefore needed, asinput parameters to the valuation. When liquid CDS are available, then impliedprobabilities of default can be derived and used. However, in small markets,like the Nordic region of Europe, there are practically no CDS to use. We studythe following problem: given that no liquid contracts written on the defaultevent are available, choose a model for the default time and estimate the modelparameters. We use the minimum variance hedge to show that we should use thereal-world probabilities, first in a discrete time setting and later in thecontinuous time setting. We also argue that this approach should fulfil therequirements of IFRS 13, which means it could be used in accounting as well. Wealso present a method that can be used to estimate the real-world probabilitiesof default, making maximal use of market information (IFRS requirement).

Credit Value Adjustment for Counterparties with Illiquid CDS