The Fair Basis: Funding and Capital in the Reduced Form Framework

Abstract

A negative basis trade enters a long bond position and buys protection on the issuer of the bond through credit default swap (CDS), aiming at arbitrage profit due to the bond-CDS basis. To better understand the trade’s economics and to predict the fair level of the basis, this article incorporates hedge funding cost and capital cost into the reduced form credit modeling framework. Employing a bond continuously hedged by CDS under a dynamic spread model with bond repo financing, we find that there is unhedged and unhedgeable residual jump to default risk that can’t be diversified because of credit correlation. An economic capital approach has to apply and a charge on the use of capital via capital value adjustment (KVA) follows. A 2-D non-linear partial differential equation for defaultable bond valuation is obtained. Numerical results show that realistic funding and KVA can produce the same magnitude of the bond-CDS basis consistently observed in the post-crisis market.