Can someone explain CVA (Credit Valuation Adjustment) intuitively and show how it's calculated?

CVA is indeed one of the more challenging FRM Part II topics, but it becomes intuitive once you see the logic. Let me build from the simple case to the general formula.

Intuition: What Is CVA?

Imagine you enter an interest rate swap with Bridgewater Pacific Bank. If the swap is in your favor (positive mark-to-market) and the bank defaults, you lose that value. CVA is the expected present value of that potential loss — it's the cost of counterparty credit risk.

Think of it as the price of a contingent CDS: you lose money only if (a) the counterparty defaults AND (b) the derivative has positive value to you at that moment.

Simplified CVA Formula:

$$\text{CVA} = \text{LGD} \times \sum_{i=1}^{T} \text{EE}_i \times \text{PD}_i \times \text{DF}_i$$

Where:

• LGD = Loss Given Default of the counterparty (1 − Recovery Rate)
• EE_i = Expected Exposure (expected positive mark-to-market) in period i
• PD_i = Marginal probability of default in period i (derived from CDS spreads)
• DF_i = Discount factor for period i

Worked Example (3-Period):

You hold a 3-year interest rate swap with Crestline Capital. Assume:

• Recovery Rate = 40% → LGD = 60%
• Risk-free rate = 3% (flat curve for simplicity)

Calculation:

• Year 1: 0.60 × $2.4M × 0.020 × 0.9709 = $27,962
• Year 2: 0.60 × $3.1M × 0.018 × 0.9426 = $31,537
• Year 3: 0.60 × $1.8M × 0.016 × 0.9151 = $15,819

Total CVA = $75,318

This means the fair value of counterparty credit risk on this swap is approximately $75,318. You would subtract this from the risk-free value of the swap to get the credit-adjusted value.

Key Concepts for the Exam:

1. Expected Exposure profile — For a swap, EE typically rises then falls (hump-shaped) because early on rates haven't moved much, and near maturity the remaining cash flows shrink.
2. Wrong-way risk — When exposure and default probability are positively correlated (e.g., you hold an FX forward with a bank whose creditworthiness deteriorates when its domestic currency falls), CVA is higher than the standard formula suggests.
3. CVA vs. DVA — DVA (Debit Valuation Adjustment) is the mirror image: the value to you of your own potential default. Under accounting standards, your total credit adjustment is CVA − DVA.
4. Marginal PD — Always use marginal (not cumulative) default probabilities in each bucket.

For the full multi-period treatment with netting sets and collateral, check out AcadiFi's FRM Part II Credit Risk module — we have step-by-step video walkthroughs of CVA under Basel III requirements.