A note on the self-financing condition for funding, collateral and discounting

Damiano Brigo*, Cristin Buescu, Andrea Pallavicini, Qing Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We present the derivation of the self-financing condition used in a derivative pricing framework with funding, collateral and discounting. This is done in a way that clarifies the structure of the relevant funding accounts. This clarification is achieved by properly distinguishing between price processes, dividend processes and gains processes. Without this explicit distinction, the resulting self-financing condition can be erroneous, as we illustrate in the case of two papers: Piterbarg (2010) and Burgard & Kjaer (2011a). In these papers, the self-financing condition is equivalent to assuming that a subportfolio is self-financing on its own and without including the cash position. We show that the final result in Piterbarg (2010) is correct, even if the related self-financing condition is not. In the process, we raise a further question on the supplementary source of randomness in the funding rate dynamics that has no hedging counterpart in the replicating portfolio.

Original languageEnglish
Article number1550011
JournalInternational Journal of Theoretical and Applied Finance
Issue number2
Early online date25 Mar 2015
Publication statusPublished - 2015


  • Cost of funding
  • derivative hedging
  • funding and discounting
  • self-financing strategy
  • trading strategies


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