Monte Carlo exposure & CVA

A browser version of the workbench's core idea. It simulates the mark-to-market of a swap-like trade, applies a CSA threshold, and computes Expected Exposure (EE), 95% Potential Future Exposure (PFE), and unilateral CVA.

Illustrative only · synthetic data · simplified model, not a pricing tool

Volatility of MtM (σ, % of notional / √yr)20

Trade tenor (years)10

CSA threshold H (% of notional; 30 = no CSA)30

Counterparty hazard rate λ (% / yr)2

Notional 100 · 2,000 paths · LGD 60% · discount rate 3% · 5-day margin period of risk ignored for clarity.

CVA (% of notional)

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Peak EE

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Peak PFE 95%

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Default prob. over tenor

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━ sample MtM paths━ EE━ PFE 95%┅ CSA threshold H░ default-weighted EE (drives CVA)

Model

MtM(t) = σ·W(t)·(T−t)/T·N, a Brownian driver with linear amortization (the classic swap "hump"). Collateral posted C(t) = max(MtM(t) − H, 0), so exposure E(t) = min(max(MtM(t), 0), H). EE(t) = mean E(t); PFE(t) = 95th percentile of E(t). CVA = LGD · Σ DF(tᵢ) · EE(tᵢ) · [e^(−λtᵢ₋₁) − e^(−λtᵢ)].