# negative discount and zero rate on swap bootstraping

Hi I am writing a program to Bootstrap a EURO zero swap-curve for tenor 3M and 6M with given bid and ask. When I run the program , I get a negative zero rate and discount factor from 5Y till 30Y for both Swap 3m and 6m. Is it normal or am I doing something wrong in calculation?

For swap part, I use this formula to calculate the discount: $D_T=\frac{D_{T/N}-R_T^{par} \sum_{i=1}^{T-1}D_t}{1+R_T^{par}}$

and to calculate zero rate I use the following formula: $Z_T=((\frac{1}{D_T})^{\frac{365}{days}}-1)$

I really appreciate any tips or help. Bests

## 1 Answer

The formula seems to be correct. Negative interest rates are not impossible in these days.

http://www.bloombergview.com/quicktake/negative-interest-rates

Have you checked the algorithm with values that produce positive rates? And in what area lie the negative ones?

In the case of negative interest rates the discount factors should be greater than one, of course. Negative discount factors are (even in these days) not possible.