Default risk and funding costs in derivatives valuation

Amanda Langgaard-Sørensen & Nicoline Maibomm Nielsen

Student thesis: Master thesis


The financial crisis and regulation following the crisis led institutions to consider the impact of counterparty credit risk, funding costs and collateral in the derivatives valuation. This thesis aims to examine these changes to practice when valuing a single derivative on a single underlying asset. We will examine credit and debt value adjustments (CVA and DVA) to the value of a derivative and show how the original Black Scholes and Merton arguments can be extended to incorporate counterparty credit risk. Furthermore we show that the OIS rate is the best proxy currently available for the risk-free interest rate, both when valuing collateralized and non-collateralized derivatives. We also examine whether a bank should make a funding value adjustment (FVA) when valuing derivatives. We show how and when making an adjustment leads to double counting and arbitrage opportunities. We conclude that whether to make a FVA depends on if the funding costs is only due to default risk or not. Finally we will look into the regulatory changes and how they incentivise and require the use of collateral and clearing through central counterparties. Furthermore we will show how to make a collateral rate adjustment to the value of a derivative, using the Black Scholes and Merton arguments.

EducationsMSc in Business Administration and Management Science, (Graduate Programme) Final Thesis
Publication date2014
Number of pages115