XVA Framework: CVA, DVA & FVA

Before 2008, derivative pricing ignored the credit quality of the counterparty. The crisis showed that this was not a theoretical idealisation but a material mispricing — one that destroyed billions of dollars of value on uncollateralised books. Credit Value Adjustment, Debit Value Adjustment and Funding Value Adjustment are the industry's answer: they are the adjustments that bring counterparty risk, own-default risk and funding cost into the fair value of every derivative trade.

This course builds a complete XVA engine for an interest rate swap from first principles. You simulate the swap's mark-to-market across 10,000 paths under the Hull-White model, compute the expected positive exposure and negative expected exposure profiles across the trade's 5-year life, and translate those profiles into CVA, DVA and FVA using the industry-standard discrete-time formulas. Every component is built transparently so you understand exactly what assumptions are driving each adjustment.

CVA is now a regulatory capital line item, reported quarterly by every bank under IFRS 13. DVA is controversial — it is a gain from own-default risk, which raises uncomfortable accounting questions — and FVA divides academic opinion but is universally charged in practice. This course gives you the technical foundation to compute, stress and challenge these numbers, whether your role is in XVA trading, model validation, risk oversight or quant research.

The project is structured around a single 5-year interest rate swap. You first build an exact Hull-White simulation: using the analytical conditional mean and variance of the short rate, you generate 10,000 paths on a monthly time grid without Euler approximation error, calibrate the model to the current market term structure, and reconstruct the full discount curve on each path at each time step.

With the exposure simulation running, you value the IRS on each path at each future date, compute the expected positive exposure profile EE(t) = E[max(V(t),0)] and the negative expected exposure profile NEE(t) = E[max(-V(t),0)], and compute the 95th-percentile peak exposure PFE(t). You visualise the exposure profiles and verify they peak near the midpoint of the trade's life — a standard sanity check for an at-market swap.

The final component translates exposure into XVA. You compute CVA using the discrete sum LGD × Σ P(0,t_i) × EE(t_i) × ΔPD_B(t_i), and DVA symmetrically for own-default probability and NEE. You compute bilateral CVA, then add FVA for the uncollateralised funding cost. You analyse the impact of a zero-threshold CSA on CVA, compute spread sensitivities, and present the results in a unified XVA decomposition table.