A bond consistent derivative fair value

Johan Gunnesson and Alberto Fernández Muñoz de Morales

Abstract

ABSTRACT

In this paper we present a rigorously motivated pricing equation for derivatives, including cash collateralization schemes, which is consistent with quoted market bond prices. Traditionally, there have been differences in how instruments with similar cashflow structures have been priced if their definition falls under that of a financial derivative versus if they correspond to bonds, leading to possibilities such as funding through derivatives transactions. Furthermore, the problem has not been solved with the recent introduction of funding valuation adjustments (FVAs) in derivatives pricing, and in some cases has even been made worse. In contrast, our proposed equation is not only consistent with fixed income assets and liabilities, but is also symmetric, implying a well-defined exit price, independent of the entity performing the valuation, and is thus particularly suited for FVA accounting. The new ingredient which we include in the mix is the market price of providing liquidity to a given counterparty. Also, we provide some practical proxies, such as first-order approximations or basing calculations of credit valuation adjustment and debit valuation adjustment on bond curves, rather than credit default swaps.