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

TY - JOUR

T1 - A note on the self-financing condition for funding, collateral and discounting

AU - Brigo, Damiano

AU - Buescu, Cristin

AU - Pallavicini, Andrea

AU - Liu, Qing

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Cost of funding

KW - derivative hedging

KW - funding and discounting

KW - self-financing strategy

KW - trading strategies

UR - http://www.scopus.com/inward/record.url?scp=84928628156&partnerID=8YFLogxK

U2 - 10.1142/S0219024915500119

DO - 10.1142/S0219024915500119

M3 - Article

AN - SCOPUS:84928628156

SN - 0219-0249

VL - 18

JO - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

IS - 2

M1 - 1550011

ER -