The inclusion of DVA in the fair-value of derivative transactions has now become standard accounting practice in most parts of the world. Furthermore, some sophisticated banks are including an FVA (Funding Valuation Adjustment), but since DVA can be interpreted as a funding benefit the oft-debated issue regarding a possible double-counting of funding benefits arises, with little consensus as to its resolution. One possibility is to price the derivative by replication, by constructing a portfolio that completely hedges all risks present in the instrument, guaranteeing a consistent inclusion of costs and benefits. However, as has recently been noted, DVA is (at least partially) unhedgeable, having no exact market hedge. Furthermore, current frameworks shed little light on the controversial question, raised by Hull (2012), of whether the effect a derivative has on the riskiness of an institution's debt should be taken into account when calculating FVA.In this paper we propose a solution to these two problems by identifying an instrument, a fictitious CDS written on the hedging counterparty which, although not available in the market for active hedging, is implicitly contained in any given derivatives transaction. This allows us to show that the hedger's unhedged jump-to-default risk has, despite not being actively managed, a well-defined value associated to a funding benefit. Carrying out the replication including such a CDS, we obtain a price for the derivative consisting of its collateralized equivalent, a CVA contingent on the survival of the hedger, a contingent DVA, and an FVA, coupled to the price via the hedger's short-term bond-CDS basis.The resulting funding cost is non-zero, but substantially smaller than what is obtained in alternative approaches due to the effect the derivative has on the recovery of the hedger's liabilities. Also, price agreement is possible for two sophisticated counterparties entering a deal if their bond-CDS bases obey a certain relationship, similar to what was first obtained by Morini and Prampolini (2010).
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 cash flow 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 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. Also, we provide some practical proxies, such as first-order approximations or basing calculations of CVA and DVA on bond curves, rather than Credit Default Swaps.
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 cash flow 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 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. Also, we provide some practical proxies, such as first-order approximations or basing calculations of CVA and DVA on bond curves, rather than Credit Default Swaps.
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