# Jacobian transformation

I am trying to calculate pillar-wise sensitivity of a fixed coupon bond using par rates (given pillar-wise zero coupon sensitivities). I came across the formula pv01(par) = pv01(zero) * dz/dr, where dz/dr is the rate of change of the zero rates w.r.t the par rates. I am however unable to understand how to use this formula in excel. Any help is appreciated. Thanks.

As zero rates are usually not observable, people tend to use the sensitivity with respect to par, or coupon, rates. Here, pv01(zero) is a vector, which cen be computed using the pricing formula that is usually expressed in terms of the zero rates. To compute $dz/dr$, you may need to use a finite difference scheme, for example, to shift the par rate $r$, and then re-compute the zero rates.
• @GouravPoddar, To have the Jacobian, you need the analytical expressions between $z$ and $r$. Once you have those formulas, then you can do it in Excel. – Gordon Jun 22 '15 at 21:14