# Derive OIS rate from IRS rate and Fed Funds/Libor basis spread

For example I have 7Y interest rate swap rate and 7Y Fed funds/Libor basis spread. What is the step-by-step procedure to derive OIS rate from these two?

• Hi andr111, welcome to Quant.SE! Please add the self-study tag if it applies. Can you tell us what you've found already and where exactly your stuck. The question in its current form would require quite a big answer. – Bob Jansen Aug 18 '15 at 20:11
• Hi Bob, I originally assumed that this can be done through a simple closed-form formula. But as I did more research I realized that this is more complex. I'll publish as I get more understanding. – andr111 Aug 19 '15 at 16:14

## 1 Answer

If you're lucky enough that the payment schedules (start/end dates, frequency, day count, business day adjustment etc.) are the same between the fixed leg of the interest rate swap and the "spread" leg of the basis swap, then you can simply use:

OIS rate (%) = IRS Rate (%) - 0.01 * (basis spread (bps))

Otherwise, to do it accurately, you'll need to do a bootstrap the two term structures (possibly simultaneously if there is mutual dependence between them).

[In fact, in the USD case, there is an added complication that comes from the OIS rate being a compounding rate, while the FedFunds rate is an arithmetic average.]

• Yes, this is what I found out. I read a bloomberg document explaining how to do the conversion. Unfortunately, I don't think I can publish it here :( – andr111 Aug 27 '15 at 14:55