ABSTRACT
We describe here in mathematical, but model-free terms all the basic elements of the pricing and hedging framework that are relevant with regard to counterparty risk. We will represent a TVA process in terms of CVA and DVA components, as well as in terms of specific measures of counterparty exposures such as the exposure at default, the expected positive exposure and the expected negative exposure. In this chapter we focus on a classical setting of a single funding curve (single-curve set up); that is, we assume that all positions are funded (and discounted) using the same (risk-free) interest rate. We call this setting the “classical" setup, as it was prevalent prior to the financial crisis of the year 2007-2009 in the sense that bases between Libor rates and rates such as OIS or Eonia were negligible. Consequently, the funding issue, i.e. the issue of funding positions using various rates, was not really consequential. The funding issue becomes relevant in case of multiple and significantly different funding rates. This issue (in the case of bilateral counterparty risk in particular) will be added to the discussion in the next chapter.
