# How to find OIS discounting factors from OIS swap rates. Please explain with example

Suppose I have the following OIS Swap rates:

1 year OIS Swap: 0.36% 2 year OIS Swap: 0.37% 3 year OIS Swap: 0.38% 4 year OIS Swap: 0.40%

From these, how do I get the OIS Discounting factors for these respective years?

Could someone please explain with a proper formula that can be applied for this?

The discount factor is just 1 divided by the interest rate, if you want a quick proxy and don't want to Bootstrap the OIS Swap curve.

1y Swap rate = 0.38% => the effective interest rate is 1.0038. Therefore the discount factor is:

$$DF(1y) = \frac{1}{1.0038}=0.99621$$.

For the second year, you need to square the annualized rate and for the third year, you need to cube it, etc:

$$DF(2y) = \frac{1}{1.0037^2}=0.0.992640868$$

$$DF(4y) = \frac{1}{1.0040^4}=0.0.0.984158729$$

• Sorry to be blunt but that is just plain wrong. The question clearly states that OP is trying to convert OIS swap rates to discount factors, not discount rates to discount factors. The latter is indeed trivial, as per your answer, whereas the former is done through bootstrapping, similar to the bootstrapping of LIBOR IR Swaps. Your answer would be correct if the OIS swaps quoted had zero-coupon compounded legs but that is not the case. – Marcino Jul 6 '20 at 20:56
• Pls feel free to update my answer or provide a different answer. In my experience, practitioners use the fixed rate on the OIS swap as a proxy to discount rates. – Jan Stuller Jul 7 '20 at 5:41

It depends on the discounting index of your OIS swaps : we recently switch from the standard OIS discounting for standard swaps to SOFR discounting. As the basis between OIS and SOFR is small, the effective impact is minimal.

The methodology is the following :

DF(1y) = 1/(1+0.0036) = 0.996413 DF(2y) = DF(1y)*DF(1y1y) DF(3y) = DF(2y)*DF(2y1y) DF(4y) = DF(3y)*DF(3y1y)

and to compute those forwards DFs, if you assume OIS discounting, you would get, by rewriting the definition of the swap fixed rate :

(2Y_fixrate)*(DF(1Y)+DF(2Y)) = (1Y_fixrate)*DF(1Y) + (1Y1Y_fixrate)*DF(2Y) ... DF(1Y1Y) = 0.996214