How does the funding spread adjustment work for uncollateralized derivatives, and why is FVA controversial?

The funding valuation adjustment (FVA) captures the cost (or benefit) of funding an uncollateralized derivative position at a rate above (or below) the risk-free rate. It represents the spread between the dealer's actual borrowing cost and the OIS rate, applied to the expected funding requirements of the derivative over its life.\n\nFVA Mechanics:\n\nFor a derivative with positive expected exposure (the dealer is owed money), the dealer must fund the uncollateralized receivable at their borrowing rate rather than the risk-free rate. The FVA is:\n\nFVA = -integral from 0 to T of s_F(t) x EE(t) x DF(t) dt\n\nwhere s_F is the dealer's funding spread, EE(t) is the expected exposure at time t, and DF(t) is the discount factor.\n\n`mermaid\ngraph TD\n A[\"Collateralized Trade\"] --> B[\"Post cash collateral
Earn OIS rate\"]\n B --> C[\"Funding cost = 0
No FVA needed\"]\n \n D[\"Uncollateralized Trade\"] --> E[\"No collateral posted
Dealer funds at SOFR + spread\"]\n E --> F[\"Positive MTM:
Dealer funds receivable
FVA cost (negative)\"]\n E --> G[\"Negative MTM:
Dealer invests payable
FVA benefit (positive)\"]\n F --> H[\"FVA = spread x exposure x time\"]\n G --> H\n`\n\nWorked Example:\nHartfield Bank enters a 5-year uncollateralized interest rate swap with a mid-market value of $1.5 million (in Hartfield's favor). Hartfield's unsecured borrowing spread is 95 basis points over SOFR.\n\nSimplified FVA calculation:\n- Average expected positive exposure over 5 years: $1.8 million\n- Funding spread: 0.95%\n- Duration-weighted FVA approximately equals $1.8M x 0.95% x 3.2 years (weighted average life) = $54,720\n\nHartfield would quote the swap at $1,500,000 - $54,720 = $1,445,280 to the client, passing through the funding cost.\n\nThe Academic Controversy:\n\nPro-FVA (practitioner view):\n- Funding costs are real: the bank's treasury charges desks for unsecured funding\n- Not charging FVA means the desk subsidizes the client's lack of collateral\n- Every major dealer incorporates FVA into pricing (ignoring it means losing money)\n\nAnti-FVA (academic view):\n- FVA conflates the bank's credit risk with the derivative's value\n- In a Modigliani-Miller framework, funding costs should not affect asset valuation\n- DVA (debit valuation adjustment) already captures the dealer's own default risk\n- Adding FVA on top of DVA double-counts the dealer's credit spread\n\nThe Resolution in Practice:\n\nMost dealers include FVA in their internal pricing and P&L but may not always disclose it as a separate line item in financial statements. Accounting standards (IFRS 13, ASC 820) allow but do not mandate FVA recognition, creating inconsistency across institutions.\n\n| Adjustment | What It Captures | Applied When |\n|---|---|---|\n| CVA | Counterparty default risk | Always |\n| DVA | Own default risk | Always |\n| FVA | Funding cost/benefit | Uncollateralized only |\n| ColVA | Collateral rate mismatch | Different CSA terms |\n\nExplore valuation adjustments in depth in our FRM course.