KVA, Mind Your P's and Q's!

20 Pages Posted: 11 Jun 2016 Last revised: 22 Jan 2018

See all articles by Shashi Jain

Shashi Jain

Indian Institute of Science (IISc) - Deptartment of Management Studies

Patrik Karlsson


Drona Kandhai

University of Amsterdam; ING Bank - Netherlands Office

Date Written: February 3, 2017


There is an increasing consensus within banks, on the need to recognize the impact of rising capital requirements on their derivative business in the form of capital valuation adjustment (KVA). However, because of varied reasons, there are still concerns over how exactly KVA should be computed, charged, and managed. The focus of our analysis here is on the numerical aspects of costs arising due to holding of counterparty credit risk (CCR) capital. CCR capital for a portfolio today under the internal model method (IMM) approach is based on its future exposure profile, usually computed by Monte Carlo methods. For the corresponding KVA, we need (outer) Monte Carlo simulation of the future capital, which ideally would then involve (inner) Monte Carlo simulation. Additionally, the measures under which the outer and inner scenarios should be simulated can be different, ideally real-world (P) in risk-neutral (Q). In this work we, first, propose the use of stochastic grid bundling method (SGBM), an American Monte Carlo based computational technique to circumvent the problem of nested simulation working under hybrid measures to efficiently solve the P-in-Q problem. Second, we demonstrate that hybrid measures can substantially affect the KVA values. Third, through a simple hedging example we demonstrate the implication of hedging KVA under various approximations and hybrid measures.

Keywords: Capital Valuation Adjustment (KVA), Hedging KVA, Hybrid Measure Monte Carlo, Internal Model Method, Valuation Adjustments (XVA)

JEL Classification: E22, G11, G12, G13, G18, G21, G28, G31, G38, H77, K23, L51, M20, M41

Suggested Citation

Jain, Shashi and Karlsson, Patrik and Kandhai, Drona, KVA, Mind Your P's and Q's! (February 3, 2017). Available at SSRN: https://ssrn.com/abstract=2792956 or http://dx.doi.org/10.2139/ssrn.2792956

Shashi Jain (Contact Author)

Indian Institute of Science (IISc) - Deptartment of Management Studies ( email )

Indian Institute of Science

Patrik Karlsson

drkarlsson.com ( email )


Drona Kandhai

University of Amsterdam ( email )

Spui 21
Amsterdam, 1018 WB

ING Bank - Netherlands Office

1102 MG Amsterdam
P.O. Box 1800
1000 BV Amsterdam

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