How to Calculate Overnight Index Swap (OIS)

An overnight index swap (OIS) is a very common financial contract where two parties agree to exchange payment at the contract's end. The rate for the payment is based on the difference between a fixed and overnight index rate. This is an arrangement that is used every single day in the banking and lending industries. Take a peek behind the curtain to see how OIS is calculated.

As you may know, banks lend money at high rates while also obtaining money to fund those loans through short-term, low-rate loans. This means they use very inexpensive "overnight" borrowing to fund their operations. The risk for banks is that overnight borrowing rates could spike suddenly.

To insulate themselves from risk, banks use overnight index swaps. The terms of these swaps can be set for periods lasting from ​three months to more than 12 months​. Here's how it works:

• A bank exchanges terms of its "overnight" loan with another company.
• Regular interest at the federal rate is waived.
• The bank settles on a fixed daily rate through the life of the loan.

There's a specific formula for calculating an overnight index swap (OIS). It starts with setting an overnight rate. Next, you multiply the overnight rate for the first day of the swap by the loan duration.

There are five pieces of information needed before you can calculate OIS. They are the notional amount, start date, end date, underlying referenced overnight index and which party will be paying fixed versus floating. Here's a sample OIS agreement:

• A rate is 0.005.
• The first day of the loan begins on a Wednesday.
• The formula is 0.005 × 1 = 0.005.
• Next, you divide the result that you get by 360 to figure out the daily charge. Note that OIS calculations treat a year as having 360 days instead of the standard 365 days.
• The formula now looks like 0.005 ÷ 360 = 1.388 × 10^-5.
• You will now add 1 to the answer that you got in the previous step for a formula that looks like this: 1 + (1.388 × 10^-5) = 1.0000388.
• Finally, it's time to multiply the loan's principal by the rate you've determined. A loan with a principal of $1,000,000 will have an equation that looks like this: $1,000,000 × 1.0000388 = $1,000,038.80.
• $1,000,038.80 is now your new principal.
• You will repeat steps one through eight for each of the subsequent days of the loan while updating your principal for each calculation.

Note when you are doing calculations that any swap done on a Friday will have an initial period lasting three days. Swaps done on other days will be a single day. You will also notice that OIS calculations consider a year as lasting for ​360 days ​instead of ​365 days​. This isn't an error in your calculations; this is simply the industry's standard practice that should be applied every time you do an OIS calculation.

Banks stand to gain substantially by using the overnight index swap instead of simply taking the standard overnight rate. In fact, the average person can thank the OIS for their ability to finance a mortgage or loan because this arrangement is what makes lending feasible for banks. Banks also see overnight index swaps as being good indicators of credit markets within the "interbank" world. This option also poses much less risk than traditional spreads of interest rates.