Discounting Revisited: Valuation Under Funding, Counterparty Risk and Collateralization

34 Pages Posted: 17 May 2010 Last revised: 14 Mar 2011

Christian P. Fries

LMU Munich, Department of Mathematics; DZ Bank AG

Date Written: August 30, 2010

Abstract

Looking at the valuation of a swap when funding costs and counterparty risk are neglected (i.e. when there is a unique risk free discounting curve), it is natural to ask "What is the discounting curve of a swap in the presence of funding costs, counterparty risk and/or collateralization?".

In this note we try to give an answer to this question. The answer depends on who you are and in general it is "There is no such thing as a unique discounting curve (for swaps)." Our approach is somewhat axiomatic, i.e., we make very few basic assumptions. We shed some light on the use of own credit risk in mark-to-market valuations, where the mark-to-market value of a portfolio increases as the owner's credibility decreases.

We present two different valuations. The first is a mark-to-market valuation which determines the liquidation value of a product, excluding our own funding cost. The second is a portfolio valuation which determines the replication value of a product including funding costs.

We will also consider counterparty risk. If funding costs are present, i.e. if we use a replication strategy to value a portfolio, then counterparty risk and funding are tied together:
1) In addition to the default risk with respect to our exposure we have to consider the loss of a potential funding benefit, i.e. the impact of default on funding.
2) Buying protection against default has to be funded itself and we account for that.

The valuation naturally accounts for wrong-way-risk (i.e., the correlation between counterparty default and counterparty exposure).

Keywords: Discounting, Valuation, Counterparty Risk, Collateral, Netting, CVA, DVA, Bond, Swap, Credit Risk, Own Credit Risk, Wrong Way Risk

JEL Classification: C15, G13

Suggested Citation

Fries, Christian P., Discounting Revisited: Valuation Under Funding, Counterparty Risk and Collateralization (August 30, 2010). Available at SSRN: https://ssrn.com/abstract=1609587 or http://dx.doi.org/10.2139/ssrn.1609587

Christian P. Fries (Contact Author)

LMU Munich, Department of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

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