Illustrating a Problem in the Self-Financing Condition in Two 2010-2011 Papers on Funding, Collateral and Discounting

8 Pages Posted: 10 Jul 2012 Last revised: 17 Jul 2012

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Cristin Buescu

King's College London, Department of Mathematics

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Qing Liu

Imperial College London-Department of Mathematics

Date Written: July 10, 2012

Abstract

We illustrate a problem in the self-financing condition used in the papers "Funding beyond discounting: collateral agreements and derivatives pricing" (Risk Magazine, February 2010) and "Partial Differential Equation Representations of Derivatives with Counterparty Risk and Funding Costs" (The Journal of Credit Risk, 2011). These papers state an erroneous self-financing condition. In the first paper, this is equivalent to assuming that the equity position is self-financing on its own and without including the cash position. In the second paper, this is equivalent to assuming that a subportfolio is self-financing on its own, rather than the whole portfolio. The error in the first paper is avoided when clearly distinguishing between price processes, dividend processes and gain processes. We present an outline of the derivation that yields the correct statement of the self-financing condition, clarifying the structure of the relevant funding accounts, and show that the final result in "Funding beyond discounting" is correct, even if the self-financing condition stated is not.

Keywords: Funding cost, cost of funding, funding and discounting, self-financing strategy, trading strategies, hedging

JEL Classification: G12, G13

Suggested Citation

Brigo, Damiano and Buescu, Cristin and Pallavicini, Andrea and Liu, Qing, Illustrating a Problem in the Self-Financing Condition in Two 2010-2011 Papers on Funding, Collateral and Discounting (July 10, 2012). Available at SSRN: https://ssrn.com/abstract=2103121 or http://dx.doi.org/10.2139/ssrn.2103121

Damiano Brigo (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Cristin Buescu

King's College London, Department of Mathematics ( email )

Strand
London, WC2R 2LS
United Kingdom

Andrea Pallavicini

Banca IMI ( email )

Largo Mattioli 3
Milan, MI 20121
Italy
+39 02 7261 (Phone)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

Qing Liu

Imperial College London-Department of Mathematics ( email )

South Kensington Campus,Imperial College
LONDON, SW7 2AZ
United Kingdom

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