Valuation and Hedging of Contracts with Funding Costs and Collateralization

Abstract

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.

A general HJM framework for multiple yield curve modelling

“…Pricing under collateral and FRA rates Let us here briefly review pricing under perfect collateralization for general derivatives which we then apply to the pricing of FRAs. For a more detailed discussion on general valuation with collateralization and funding costs, we refer to the growing literature on this topic, e.g., [3] and the references therein. We here follow closely [24, Section 2.2].…”

Arbitrage-free pricing of derivatives in nonlinear market models

“…To achieve our goals, we extend in several respects the nonlinear pricing approach developed in (El Karoui and Quenez 1997) and , which was subsequently continued in (Bielecki and Rutkowski 2015). …”

Portfolio optimization of credit swap under funding costs

“…We assume that simultaneous borrowing and lending is not efficient, i.e., φ l (t)φ b (t) = 0. We remark that similar assumptions have been made by Bielecki and Rutkowski (2015) and, by Mercurio (2015). The wealth process of a portfolio φ = (φ, φ l , φ b ) equals…”