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The recursive nature of KVA: KVA mitigation from KVA

García Muñoz, Luis Manuel and Palomar Burdeus, Juan Esteban and de Lope Contreras, Fernando (2016): The recursive nature of KVA: KVA mitigation from KVA.

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Abstract

KVA represents the extra cost being charged by banks to clients in order to remunerate banks’ shareholders for the mandatory regulatory capital provided by them throughout the life of the deal. Therefore, KVA represents earnings charged to clients that must be retained in the bank’s balance sheet and not be immediately paid out as dividends. Since retained earnings are part of core TIER I capital, future KVAs imply a deduction in today’s KVA calculation. In this paper we propose a KVA formula that is consistent with his idea and in line with full replication of market, ounterparty and funding risks. Although the formula might seem cumbersome at first sight due to its recursive nature, we show how calculate it in a Montecarlo XVA engine without any approximation. Finally, we provide a numerical example where the KVA obtained under this new formula is compared with other approaches yielding significantly lower adjustments.

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