CopulaMonteCarlo

The one-factor Gaussian copula as a recorded Monte-Carlo, so a tranche's correlation delta and its sensitivity to the pool default probability come from a single adjoint sweep — where the PortfolioLossDistribution recursion gives the price, this gives the risk.

Each path draws one systemic normal shared by every name and one idiosyncratic normal per name; a name defaults when Phi(sqrt(rho) M + sqrt(1 - rho) Z_i) < pd, monitored with a smoothed indicator so the payoff stays differentiable. The output is the discounted tranche loss to a single horizon (a protection-leg-only PV on unit tranche notional).