KVA is Incomplete
18 Pages Posted: 24 Feb 2020 Last revised: 22 Jun 2020
Date Written: February 7, 2020
In this article we derive a capital valuation adjustment for derivatives transactions due to market incompleteness. This is motivated by the fact that a return on equity (RoE) in excess of the riskless rate is the result of undiversifiable portfolio risk.The valuation adjustment represents the value of the excess return over the portfolio lifetime. More specifically, we show that the value of a derivative can be written as the sum of a risk-neutral base value and an adjustment which is the sum of a KVA and a FVA term.The KVA is proportional to the total shareholder equity as well as the RoE. We show that the RoE is function of the market price of the unhedgeable risk as well as the firms leverage. Our valuation adjustment is fundamentally risk based and has an alternative representation directly in terms of the residual diffusive and jump risk. This allows for a rigorous framework for allocating capital to sub-portfolios and individual trades.
Keywords: KVA, FVA, Capital valuation adjustment, Funding valuation adjustment, Derivatives pricing, Incomplete Markets, Market price of risk
JEL Classification: G13
Suggested Citation: Suggested Citation