A PDE APPROACH TO BILATERAL COUNTERPARTY RISKS AND FUNDING COSTS

This dissertation presents a valuation framework for over-the-counter derivatives that integrates bilateral counterparty credit risk and funding costs by extending the classical Black-Scholes model through a replication-based Partial Differential Equation approach. The model captures the cost of funding required to support a self-financing hedging strategy and introduces the default risk of both counterparties by incorporating positions in each party’s own bonds within the replication portfolio. To implement the framework, a Hull-White one-factor short-rate model is used to simulate yield curves and perform the numerical evaluation of an Interest Rate Swap under different scenarios. The analysis considers multiple close-out conventions and funding scenarios, including those in which the derivative cannot be posted as collateral. Ultimately, it is discussed how this approach could be extended to incorporate climate-related risks, such as carbon pricing, by aligning the derivative valuation process with the Carbon Equivalence Principle, which supports a broader, Environmental, Social and Governance (ESG)-aligned view of derivative risk management.