# Overnight Index Swap

## What is an 'Overnight Index Swap'

An overnight index swap is an interest rate swap involving the overnight rate being exchanged for a fixed interest rate. An overnight index swap uses an overnight rate index, such as the overnight federal funds rate, as the underlying rate for its floating leg, while the fixed leg would be set at an assumed rate.

## BREAKING DOWN 'Overnight Index Swap'

Overnight index swaps are popular among financial institutions because the overnight index is considered to be a good indicator of the interbank credit markets and less risky than other traditional interest rate spreads. Generally short-term, the interest of the overnight rate portion of the swap is compounded and paid at reset dates, with the fixed leg being accounted for in the swap's value to each party. The floating leg's present value is determined by either compounding of the overnight rate or by taking the geometric average of the rate over a given period. Like other interest rate swaps, an interest rate curve must be produced to determine the present value of any cash flows.

## Overnight Index Swap Calculation Example

There are 10 steps involved in calculating a bank's dollar benefit from using an overnight index swap. The first step is to multiply the overnight rate for the period which the swap applies. If the swap begins on a Friday, the swap's period is three days because transactions don't settle on the weekends. If the swap begins on any other business day, the swap's period is one day. For example, if the overnight rate is 0.005% and the swap is entered into on a Friday, the effective rate to use would be 0.015%, otherwise, it's 0.005%.

Step two of the calculation is divide the effective overnight rate by 360. Industry practice dictates that overnight swap calculations use 360 days in a year instead of 365. Using the above rate, the calculation in step two is: 0.005% / 360 = 1.3889 x 10^-5.

For step three, simply add one this result: 1.3889 x 10^-5 + 1 = 1.00003889.

For step four, multiply this new rate by the total principal of the loan. For example, if the overnight loan has a principal of \$1 million, the resulting calculation is: 1.00003889 x \$1,000,000 = \$1,000,013.89. Step five requires that the above calculations be made for each of the days of the loan, with the principal being updated for each day. This is done for multi-day loans in case the rate varies.

Step six and seven are similar to two and three. The fixed rate the bank swaps use must be divided by 360 and added to 1. For example, if this rate is 0.0053% the result is: 0.0053% / 360 + 1 = 1.00001472. In step 8, raise this rate the power of the number of days in the loan and multiply by the principal: 1.00001472^1 x \$1,000,000 = \$1,000,014.72.

Lastly, subtract the two to find the dollar value the bank gains from using the swap: \$1,000,014.72 - \$1,000,013.89 = \$0.83