Bivariate Probability Density Function (Normal Distribution)

Bivariate Probability Density Function (Normal Distribution) | Gaussian Copula

Enter probability-of-default (PD) for each asset and the correlation. The tool computes the threshold implied by PD and shows the joint CDF P(X < threshold1, Y < threshold2) using a numeric integral and a Monte‑Carlo estimate. The joint PDF is shown as an interactive 3D surface. Means and standard deviations are assumed 0 and 1 by default.

Asset parameters

Probability of default PD1 (0..1) Probability of default PD2 (0..1)

Correlation ρ (between -0.999 and 0.999) 0.30 Monte‑Carlo samples Surface grid size (max 120 — larger = slower)