Bilateral counterparty risk under funding constraints. I: Pricing. (English) Zbl 1314.91207
Summary: 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.
For part II, cf. [ibid. 25, No. 1, 23–50 (2015; Zbl 1314.91208)].
For part II, cf. [ibid. 25, No. 1, 23–50 (2015; Zbl 1314.91208)].
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
Keywords:
counterparty risk; funding costs; nonlinear pricing and hedging; arbitrage; backward stochastic differential equationCitations:
Zbl 1314.91208References:
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