KVA is Incomplete
15 Pages Posted: 24 Feb 2020 Last revised: 22 Nov 2021
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 and is a function of unhedgeable diffusive or jump risk.
More specifically, we show that the value of a derivative can be written as the sum of an arbitrage free base value and an adjustment which is the sum of a KVA and an FVA term.
The KVA is proportional to a portfolio specific effective capital level as well as the firm's RoE. The effective capital is a function of the residual portfolio risk and the associated market price of risk.
This facilitates a rigorous framework for allocating capital to sub-portfolios and individual trades.
As an example of this approach we show that KVA for credit default risk overlaps with CVA and also estimate an appropriate return on regulatory default risk capital.
Keywords: KVA, FVA, Capital valuation adjustment, Funding valuation adjustment, Derivatives pricing, Incomplete Markets, Market price of risk
JEL Classification: G13
Suggested Citation: Suggested Citation