# Introduction / Background / Definitions

Since the 2008 financial crisis, an increasing number of derivative trades have been collateralized.

The collateral payments usually earn interest, paid to the owner of the collateral, at a rate that is often perceived to be a risk free rate, such as the overnight index swap (OIS) rate in the US.

There are still transactions that are not fully collateralized.

In these situations, the CFs associated with the uncollateralized derivative trade may be different than the CFs that would arise under a fully collateralized trade.

Given the potentially different CFs, some market participants have chosen to recognize a difference in the economic value between a collateralized and an uncollateralized trade with a term known as the Funding Valuation Adjustment (FVA).

Simple Example:

Assumptions:

- trading desk entered into uncollateralized USD IRS with A and hedged it with offsetting collateralized USD IRS with B.

- both swaps were done at par --> Swap A and Swap B had value of \$0 when they were done.

After some time, IRs have moved such that the market value of Swap A to the firm is \$1,000,000.

As Swap B is identical and offsetting, the value of Swap B then is -\$1,000,000 to the firm.

In such a case the firm will have to deposit \$1,000,000 in collateral to Counterparty B.

To obtain the funds, the trading desk will need to borrow from the firm’s treasury.

The resulting set of cash flows from this trade is now:

- receives interest on the \$1,000,000 collateral deposit

- pays interest on its loan from the treasury at the firm's funding rate.

The funding rate is sometimes higher than the rate earned on the collateral --> additional interest cost --> FVA calculation.

To compute FVA in this example:

- (Funding rate - collateral IR) * value of collateral each year until maturity.

- FVA then substracted from value of Swap B.

A Closer Look

An actual FVA computation is not as straightforward as the one laid out above, because the charge may depend on many factors such as:

1. The expected duration of Swap A, which in part depends on the likelihood that Counterparty A defaults.
2. The funding and liquidity strategy of the firm.
3. The role of other derivative trades in the trading desk’s book.
4. The interaction of CVA and DVA with the FVA charge.

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