ABSTRACT
In this chapter we develop a reduced-form backward stochastic differential equations (BSDE) approach to the problem of pricing and hedging the TVA, in a general framework of bilateral counterparty risk under funding constraints. The end results of Sect. 5.3.3 and 5.3.4 yield concrete recipes for risk-managing the contract or its TVA according to the following objective of the bank: minimizing the (risk-neutral) variance of the cost process (which is essentially the hedging error) of the contract or of its TVA, subject to various hedging policies for the jump-to-default exposure. The results of this chapter also shed more light on the structure of the TVA and on the debate about unilateral versus bilateral counterparty risk.
