Credit contingent interest rate swap pricing

Area of Science:

• Quantitative Finance
• Financial Risk Management
• Computational Finance

Background:

• Credit Value Adjustment (CVA) pricing currently assumes default-free replacement contracts post-counterparty default.
• This assumption is often unrealistic, as trades are typically reassigned, introducing potential defaults in replacement contracts.
• Ignoring these secondary defaults can lead to inaccurate CVA estimations.

Purpose of the Study:

• To investigate the impact of counterparty defaults in replacement contracts on CVA pricing.
• To compare the accuracy of CVA estimations under different default assumptions.
• To analyze the pricing of credit contingent interest rate swaps (CCIRS) and credit contingent default swaps (CCDS) as CVA hedges.

Main Methods:

• Derived partial differential equations (PDEs) for approximated CVA under no-default and finite-default scenarios for replacement contracts.
• Developed an analytical solution framework applicable to both no-default and two-default cases.
• Calibrated the model using market data for empirical validation.

Main Results:

• The study derived PDEs for CVA considering a finite number of counterparty defaults in replacement contracts.
• No-default and two-default CVA cases were shown to be solvable within the same analytical framework.
• Model calibration and computation revealed that CVA values converge for highly-rated counterparties but diverge significantly for lower-rated ones.

Conclusions:

• Current CVA practices may lead to under or overestimation of risk due to the assumption of default-free replacement contracts.
• The derived two-default CVA model provides a more accurate risk assessment, especially for counterparties with lower credit ratings.
• The findings highlight the importance of incorporating potential defaults in replacement contracts for robust CVA calculations.