# How to Calculate Overnight Index Swap (OIS)

by Ryan Menezes

Banks lend money over long terms at high rates, and obtain money through short-term, low-rate loans. They therefore engage in cheap, overnight borrowing, but this practice puts the bank at risk if the overnight borrowing rate rises. To minimize the risk, banks use overnight index swaps. Through such a swap, a bank exchanges the terms of its overnight loan with another institution. Rather than paying interest at the effective federal funds rate, the bank settles on a fixed daily rate throughout the loan's duration.

Multiply the overnight rate for the first day of the swap by the period for which rate applies. If the first day of the swap if Friday, the first period is three days; otherwise, it is one day. For example, if the rate is 0.005 and the first day is Wednesday the calculation would be 0.005 × 1 = 0.005.

Divide the result by 360. By convention, swap calculations treat the year as containing only 360 days. Continuing the example: 0.005 ÷ 360 = 1.388 × 10^-5.

Add 1 to this answer: 1 + (1.388 × 10^-5) = 1.0000388.

Multiply the loan's principle by this rate. For example, if the loan has a principle of \$1,000,000: \$1,000,000 × 1.0000388 = \$1,000,038.80. This is the loan's new principle.

Repeat the previous steps for each of the following days of the loan, and update the principle for each calculation. For example, if the rate varies each day, but averages at 0.504 percent, this will produce a final principle of \$1,001,439.83.

Divide the fixed rate for which the bank swaps their loan by 360. For example, if this rate is 0.0053 over 101 days: 0.0053 ÷ 360 = 1.472 × 10^-5.

Add 1 to this answer: 1 + (1.472 × 10^-5) = 1.00001472.

Raise this value to the power of the number of days of the loan: 1.00001472^101 = 1.00148781.

Multiply the principle by this figure: \$1,000,000 × 1.00148781 = \$1,001,487.81.

Subtract the sum from Step 4 from this answer: \$1,001,487.81 - \$1,001,439.83 = \$47.98. This is the value of the bank's benefit from using the overnight index swap rather than accepting the standard overnight rate.

#### About the Author

Ryan Menezes is a professional writer and blogger. He has a Bachelor of Science in journalism from Boston University and has written for the American Civil Liberties Union, the marketing firm InSegment and the project management service Assembla. He is also a member of Mensa and the American Parliamentary Debate Association.

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