Funding Value Adjustment (FVA) in Simple Terms

Funding valuation adjustment (FVA) reflects the funding cost of uncollateralized derivatives above the risk-free rate of return, typically benchmarked against rates like €STR or OIS in Europe.

Understanding FVA through an Example

Consider a scenario involving an uncollateralized swap between a bank and a client. In this agreement, the bank exchanges cash flows with the client based on differing interest rates. Crucially, neither party posts collateral to secure the future obligations under this swap.

To mitigate the associated risks, the bank enters a second, collateralized swap with another financial institution. Here, both parties post collateral to cover future obligations.

Suppose initially the swap with the client has a positive value for the bank, denoted as:

Consequently, the hedging swap (collateralized) in the market has a negative value for the bank:

Impact of Collateral and Funding Costs

Under the collateralized market swap agreement, if its value decreases further (becomes more negative) for the bank, the bank must post additional collateral remunerated at a benchmark rate, such as the Euro short-term rate (€STR), to secure this hedging swap.

If the client swap were collateralized, the bank would have a symmetrical arrangement, where it would receive a margin call if the client swap decreases in value and need to pay margin if its value increases. However, since the client swap is uncollateralized, the bank must finance this margin call at its internal funding rate, typically higher than €STR:

Calculating Funding Valuation Adjustment (FVA)

The difference between the internal funding rate and the collateral rate (e.g., €STR) generates a cost known as FVA. Mathematically, FVA for a given period can be expressed as:

Where:

• \( \lambda(t) \) is the funding spread (cost of funding over the risk-free rate).
• \( E_t \) is the expected exposure at time \( t \).
• \( r(s) \) is the risk-free discount rate.
• \( T \) is the maturity of the derivative contract.

This cost leads to an accounting loss, recorded as a negative FVA.

Funding Benefit Adjustment (FBA)

Conversely, if the client derivative has a negative value and remains uncollateralized, while the market derivative is collateralized and holds positive value for the bank, the bank gains a funding advantage. This is recorded as a positive FVA, also known as Funding Benefit Adjustment (FBA).

Understanding Benchmark Rates: €STR and OIS

To clarify, two benchmarks are frequently referenced:

• OIS (Overnight Index Swap): Reflects the overnight interbank rate through derivatives contracts.
• €STR (Euro Short-Term Rate): Based on actual overnight borrowing costs within the euro area.

Typically, a bank's internal funding rate is higher than these benchmarks due to additional risk premiums.

The Funding Valuation Adjustment is crucial for accurately pricing derivatives and managing financial risk effectively. Understanding and managing FVA helps banks and financial institutions avoid unanticipated losses and optimize their funding strategies.