OIS Mechanics Example
- 03:40
How an OIS rate is set in practice.
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Glossary
overnight index swapTranscript
Let's walk through a concrete step-by-step example to illustrate how this works. Suppose we are calculating the compounded SOFR over a seven day period as shown in the table. On Monday SOFR is 5.25%, which gives an adjusted notional of 1.000145833 calculated by dividing 5.25% by 360 days, and then adding on one. On Tuesday SOFR increases slightly to 5.26%. Bringing an adjusted notional to 1.000291966 calculated by multiplying the 1.000145833 from Monday by one plus 5.26% divided by 360. This process continues with Wednesday's adjusted notional rising to 1.000438397, and so on. By Friday with a SOFR at 5.25% and a day weight of three for the weekend. The final adjusted notional reaches 1.0001022328, calculated as 1.000584573 multiplied by in brackets or parentheses, one plus 5.25% divided by 360 times by three. Using this adjusted notional, we can now calculate the effective seven day rate. All we have to do is to rearrange the simple interest rate formula. Future value equals present value multiplied by one plus interest rate times, days over basis and rearrange to solve for i or the interest rates. Which gives us interest rate equals future value over present value minus one times by basis over days. Using the values on screen and an actual 360 day count convention as it applies for SOFR, that gives us 1.001022328 divided by one and then all minus one, which is the interest earned in seven days, then multiplied by 360 over seven to annualize the rates. Meaning we get an effective annualized rates of 5.25769%. This is slightly higher than the arithmetic weighted average, Which would've been 5.25571% in this case, compensating the floating rate payer for the fact that they aren't receiving daily payments. And just to double check that the formula gives us the same result as our intuitive approach, let's apply it for our example as well. As we can see, the formula gives us the same result. It's important to note that while most OIS swaps will use this daily compounded calculation methodology, in some cases an arithmetic average might be used instead.