Arbitrage-Free Pricing in Nonlinear Market Models

We proposed a nonlinear arbitrage-free pricing theory, which arises in a natural way when accounting for salient features of real-world trades such as: trading constraints, differential funding costs, collateralization,... [ view full abstract ]

We proposed a nonlinear arbitrage-free pricing theory, which arises in a natural way when accounting for salient features of real-world trades such as: trading constraints, differential funding costs, collateralization, counterparty credit risk and capital requirements. We introduce the notion of regular market models, and within this class of models, we propose several notions of no-arbitrage, and several definitions of fair prices. Finally, we will discuss the BSDEs approach to the proposed valuation and hedging methodology, and we will consider several illustrative examples.