Tuesday January 29 2013
Scuola Normale Superiore
We revisit the problem of general no-arbitrage pricing of derivatives including the funding component. We show that, by adopting the no-arbitrage approach based on replication, PDE, and Feynman-Kac theorem, an appropriate treatment of the self-financing conditions allows straightforward and consistent proofs of the relevant pricing formulas covering a broad range of cases. In particular, we firstly recover the basic results for single currency funding of derivatives including, step by step, perfect or partial collateral, repo, and dividends. Next, we generalize the analysis to the case of multiple currency funding, and we examine the special case of interest rate derivatives. These results are useful to provide a simple and consistent framework of modern pricing formulas, fostering a broader understanding of the current market practice of CSA discounting, and to set solid theoretical grounds supporting further generalizations to include other risk factors, counterparty risk (CVA and DVA) in particular.