Funding Strategies, Funding Costs

Christoph Burgard and Mats Kjaer

Incorporating the effects of funding derivatives into their pricing became a hot topic following the global financial crisis. Following on from earlier work by Piterbarg (2010), in Burgard and Kjaer (2011b) we established how funding costs, funding benefits and counterparty risk could be treated within one framework extending the approach of Black, Scholes and Merton. This showed that if a derivative’s issuer is able to perfectly hedge the risk of its own default, the only adjustment to the classical price is the bilateral credit valuation adjustment (CVA) inclusive of the debit valuation adjustment (DVA).

However, this would require the issuer to freely dynamically trade spread positions of different seniorities of its own bonds, and so is unrealistic. Assuming that the issuer can hedge own-default only when its derivatives position is in-the-money and so provides funding is more realistic. When it is out-of-the-money and requires funding, a post-default windfall to the issuer’s estate is generated. In that case, a funding cost adjustment (FCA) is added in to compensate.

Since the publication of Burgard and Kjaer (2011b) there has been a flurry of papers proposing alternative