Valuation and Hedging of Contracts with Funding Costs and Collateralization

The research presented in this work is motivated by recent papers by Brigo et al. [5, 6], Burgard and Kjaer [7, 8, 10], Crépey [14, 15], Fujii and Takahashi [21], Piterbarg [38] and Pallavicini et al. [37]. Our goal is to provide a sound theoretical underpinning for some results presented in these papers by developing a unified framework for the non-linear approach to hedging and pricing of OTC financial contracts. The impact that various funding bases and margin covenants exert on the values and hedging strategies for OTC contracts is examined. The relationships between our research and papers by other authors, with an exception of Pallavicini et al. [37] and Piterbarg [38], are not discussed in this part of our research. More detailed studies of these relationships, as well as the issue of the counterparty credit risk, are examined in the follow-up paper.