CVA, FVA (and DVA?) with stochastic spreads. A feasible replication approach under realistic assumptions.

In this paper we explore the components that should be incorporated in the price of an uncolateralized derivative. We assume that one counterparty will act as the derivatives hedger while the other will act as the investor. Therefore, the derivative's price will reflect the replication costs from the hedger's perspective, which will not be equal to the replication price from the investor's perspective. We will also assume that the hedger only has the incentive to hedge the changes in value that the derivative experiences while the hedger remains not defaulted. We assume that both the investor's and the hedger's credit curves are stochastic, so that the hedger is not only concerned with the default event of the investor (but not of his own), but also with spread changes of both counterparties. We conclude that CVA and FVA (funding value adjustment, which include both funding cost and benet) are the only components to be incorporated in the price of financial derivatives. Of course, since we will follow pure hedging arguments, every pricing term can be hedged under reasonable assumptions. The hedging of both components will not only leave the hedger immune to both spread changes and the default event of the investor, but also to spread changes of the hedger. The latter will imply that the debt structure of the hedger will remain unchanged when the new derivative transaction is traded.