KVA as a Transfer of Wealth

In this article we derive the shareholder loss due to a capital requirement associated to a derivatives transaction. This is a result of a transfer of wealth between shareholders and creditors of the firm. The charge required to negate this loss can be regarded as a capital valuation adjustment which we refer to as KVA2. Our approach does not assume a fixed hurdle rate on equity required by shareholders. Instead we derive the economic return on capital for a marginal derivatives trade. We provide two complementary derivations of the valuation adjustment. The first is based on a Merton single-period balance sheet model and the second on continuous time no-arbitrage arguments.

Our resulting KVA expression is similar in structure to those proposed in the literature. We find however that the effective rate on capital that a shareholder should demand in a derivatives transaction is a junior funding rate as opposed to the return on equity. This is a consequence of the fact that the only risk a shareholder faces once a derivatives transaction is fully hedged is the default of the firm itself.