A High-Performance Monte Carlo Framework for Credit Derivatives Pricing, Implied Dependence, and Model Risk

Abstract

We develop a high-performance Monte Carlo framework for pricing credit derivatives, including single-name Credit Default Swaps (CDS) and multi-name basket structures such as First-to-Default and Nth-to-Default products.

The framework combines reduced-form hazard rate modelling with latent dependence captured via a one-factor Gaussian copula, and introduces a structural decomposition in which combinatorial default aggregation is separated from simulation. This enables the construction of an effective basket hazard curve prior to Monte Carlo valuation, significantly reducing computational complexity while remaining fully consistent with calibrated single-name CDS term structures.

The implementation is designed for scalability and numerical efficiency, leveraging quasirandom Sobol sequences, OpenMP parallelisation, and a flattened memory architecture that ensures cache-efficient path evaluation. In the single-name case, pricing reduces to a single uniform draw per path, yielding linear complexity in the number of simulations.

We interpret Monte Carlo pricing as a structural mapping from model primitives-hazard rates, dependence structure, and higher-order features such as jumps or regime shifts-to observable market prices. Within this framework, dependence parameters such as Gaussian copula correlation are not structural constants, but reduced-form objects that absorb multiple sources of systemic risk and model misspecification.

Extensions such as jump dynamics and regime-dependent intensities do not introduce independent pricing signals, but instead reshape the implied dependence structure required to match market prices.

The resulting framework serves both as a production-grade pricing engine and as a research platform for analysing calibration instability, model risk, and the regime dependence of implied credit correlations in multi-name credit markets.