KVA from the Beginning

Understanding the interaction between a new derivative, its financing and the wider balance sheet during pricing is critical for dealer profitability. For this purpose we extend a single period structural balance sheet model developed in Andersen, Duffie and Song to include equity financing before deriving consistent firm and shareholder break even prices. The former is given by the risk neutral expectation of the derivative cash flow in all scenarios including dealer default, discounted at the risk-free rate. The latter on the other hand is given by a dealer survival measure expectation of the derivative cash flow, including at counterparty default, discounted at the dealer weighted average rate of capital. This discounting rate is partially determined by the minimum amount to equity funding required by regulators. We next show how the shareholder break even price can be split into funding and capital valuation adjustments. All results are valid whether the dealer chooses to hedge the derivative or not.