BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS—PART I: PRICING

TLDR

The paper and its follow‑up address valuation and hedging of bilateral counterparty risk for over‑the‑counter derivatives. It defines a no‑arbitrage price under multiple funding costs and introduces an additive, multiple‑curve extension of classical risk‑neutral pricing. Using a multiple‑curve framework that incorporates funding constraints, the authors extend the classical model to an additive, multiple‑curve risk‑neutral price and derive its dynamic hedging interpretation consistent with replication in complete markets. The method is demonstrated by a fully solved example that builds on Burgard and Kjaer’s prior work.

Abstract

This and the follow‐up paper deal with the valuation and hedging of bilateral counterparty risk on over‐the‐counter derivatives. Our study is done in a multiple‐curve setup reflecting the various funding constraints (or costs) involved, allowing one to investigate the question of interaction between bilateral counterparty risk and funding. The first task is to define a suitable notion of no arbitrage price in the presence of various funding costs. This is the object of this paper, where we develop an “additive, multiple curve” extension of the classical “multiplicative (discounted), one curve” risk‐neutral pricing approach. We derive the dynamic hedging interpretation of such an “additive risk‐neutral” price, starting by consistency with pricing by replication in the case of a complete market. This is illustrated by a completely solved example building over previous work by Burgard and Kjaer.