A bond consistent derivative fair value

Johan Gunnesson and Alberto Fernández Muñoz de Morales

Journal of Credit Risk

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.

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