I was looking at different methods of calculating delta for Interest Rate Swaps(IRS) and came across the words par delta and zero delta.

I am not sure of the difference between the both and when to use a particular delta.

Need some guidance on this.


Delta is a linear approximation of the change in price due to a small move of the relevant interest rate. Typically a parallel move of the whole interest curve is assumed here. This applies to all kind of fixed income instruments, in particular IRS.

Interest rates can be given as coupon rates (these are the so called par rates, based on prices observable in the market) or zero rates (as a result of a so called bootstrapping process). Both can be used to calculate the price of an instrument so for both types a delta can be calculated. So, if you use zero rates for your linear approximation the result is a zero delta. Same is true for coupon/spot rates.

  • $\begingroup$ For slightly more detail see this wilmott.com/messageview.cfm?catid=10&threadid=49898 $\endgroup$
    – noob2
    Jan 25 '16 at 16:14
  • $\begingroup$ I just want to note that par rates that are not always observable. Actual coupon bonds rarely trade at par, and their yields are not par yields. In fact, it's customary to estimate the zero coupon curve and then construct the par yield curve from it. The swap market is different, where par swap rates are indeed easily observable. $\endgroup$
    – Helin
    Jan 25 '16 at 21:40
  • $\begingroup$ when to use par delta and when to use zero delta? $\endgroup$
    – lakshmen
    Jan 26 '16 at 1:27
  • $\begingroup$ Depends on your environment (available market data) and for what you want to use the delta. If, for example, your intention is to compare the risk of a fixed instrument with a benchmark bond (Treasury, Bund,..) it might be adequate to use par rates. On the other hand, taking the comment from @haginile into account, you might have a zero curve anyway. It would say using the zero rates is the usual way. $\endgroup$
    – Dr_Be
    Jan 26 '16 at 7:27
  • $\begingroup$ In practice, the convention is almost always to shock the par curve, despite the many flaws of this approach... $\endgroup$
    – Helin
    Jan 26 '16 at 14:27

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