# Pricing IRS: bootstrapping zero rate (spot rate) from the swap curve

I would like to ask about swap zero curve calculation algorithm used by Bloomberg. Below is a plain vanilla EUR IRS. I want to calculate >= 2 year spot rates from the market rates. I don't know how to bootstrap them for the valuation date = 04/14/2019. The swap pays twice a year on Jan 19 and Jul 19. Below I have attached screenshots of the swap yield curve (with Bloomberg zero rates that I'm trying to replicate) and swap details.

It seems you are using the same curve for forward and discounting.

The EUR Vanilla Swaps vs 6M actually have yearly payments, so to obtain the discount factors, and after having the DF for year 1, you can sequentially solve for them just using the par swap Rates.

$$DF_n = \frac{1-par_n \times \sum^{n-1}_{i=1} DF_i}{1+par_n}$$

So the DF for year 2 would be:

$$DF_2 = \frac{1-(-0.0019925)\times 1.002337 }{ 1 + (-0.0019925) } = 1.003998$$

• Thanks, David. Maybe this is a trivial question, but why this swap has actually yearly payments?
– Bart
Commented Apr 11, 2020 at 18:35
• That just happens to be the market convention for EUR swaps vs 6M. Fixed leg is yearly 30/360 and Euribor 6M leg is obviously half-yeraly, Act/360. So to bootstrap your curve from the par rates, you have to take into account the convention of the instruments you are using. Commented Apr 12, 2020 at 8:49
• What is a par rate ? In layman terms Commented Aug 25, 2021 at 16:32