ABSTRACT
A recurring theme of the book is the decomposition of the counterparty risky price Πt of an OTC derivative contract (or portfolio of contracts) between two parties. The generic decomposition is of the form: (essentially, but see (3.12) for the precise statement)
Πt = Pt −Θt,
where Pt is the counterparty clean price of the contract and Θt is the total valuation adjustment. Throughout the text we will derive various, more specific, decompositions of the form:
Πt = Pt − ∑ i
where Ai represent various adjustments, such as the CVA, DVA, LVA, RVA and RC mentioned in the preface of the book. Thus, essentially, we will provide various decompositions of a TVA:
Θt = ∑ i
From the practical point of view, the key issue is to provide useful representations for these adjustments, as well as to compute their sensitivities with respect to relevant quantities, in order to be able to dynamically price and hedge them.
