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

Abstract

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.