Valuation adjusments

Specialeforsvar ved Pernille Duus

Titel: Valuation adjusments

Resume: After the financial crisis in 2007, the necessarity of adjusting the price of an uncollateralised OTC derivative contract, was no longer possible to neglect. The pricing regime based on Black-Scholes’ risk-neutral theory assumed that future cashflows could
be discounted using the risk-free rate, which was not reliable anymore. This thesis reviews the work done by Burgard and Kjaer (2013), which provide a generalised frame- work for incorporating issuer and counterparty default risk, funding costs and collateral. First, the original framework by (Black and Scholes, 1973) is presented followed by an extension where collateral is included by Piterbarg (2010). Afterwards the framework by Burgard and Kjaer (2011b), where collateral is not taken into account, is presented. Finally, a
thorough analysis of the semi-replication strategy by Burgard and Kjaer (2013), which will stand as the final generalised framework, discussed in this thesis. The analysis also includes a discussion of imposing different funding strategies, where a risk-free Black- Scholes close-out amount is assumed. This is followed by a discussion of the current debate about whether or not to include a Funding Value Adjustment. The analysis shows that it is possible to make a perfect replication of the derivative contract using the
semi-replication strategy, however, unrealistic assumptions about trading one’s own bonds have to be made. Under more applicable assumptions, a hedge error between the replicating portfolio and the derivative portfolio is present. This hedge error exists only in case of an issuer default. It is further revealed that the FVA debate can be summarised into three standpoints: Theoreticians, Traders and Accountants, and that a common shared agreement of whether or not to include FVA is still far from a conclusion.

Vejledere: Rolf Poulsen, Søren Bundgaard Brøgger, Danske Bank
Censor: Bjarne Astrup Jensen, CBS