# DV01 of Zero Coupon Bond

Can someone please explain me the concept of DV01 for Zero Coupon Bonds and how to calculate it??The formula is very tedious and I am unable to grasp the logic behind it.There are many questions given in past mock papers regarding this concept.Any help will be greatly appreciated…

Having never studied for the FRM, I’m not sure what DV01 means; if you can give me a definition, I’m sure that I can help.

Sure…It is basically equivalent to Price Value of a Basis Point(PVBP).Its the absolute value of change in price of the bond for one basis point change in yield.This concept is simple but for calculating this DV01 for zero coupon bonds they are using this formula- T/100(1+y/2)^2T+1). I don’t have any clue where it is coming from and how it is being calculated.

I take it that this is a formula per dollar of par value.

The Macaulay duration of a zero is its time to maturity: T. Modified duration is:

Dmod = Dmac / (1 + YTM)

where YTM is measured for the period between coupon payments: the compounding period. In this case, the compounding is semiannual, so YTM = y/2, where y is the annual (BEY) yield. Thus, the modified duration of a zero is:

Dmod = Dmac / (1 + YTM) = T / (1 + y/2).

The dollar duration is the modified duration times the price; for a zero, the price is:

Price = par / (1 + y/2)^(2_T_),

so the dollar duration is:

\$Dur = Dmod × Price

= T / (1 + y/2) × par / (1 + y/2)^(2_T_)

= (T × par) / (1 + y/2)^(2_T_ + 1).

Finally, the price value of a basis point is the dollar duration divided by 100, so

PVBP = \$Dur / 100

= (T × par) / [100(1 + y/2)^(2_T_ + 1)].

If DV01 is the PVBP per dollar of par, then,

DV01 = PVBP / par

= {(T × par) / [100(1 + y/2)^(2_T_ + 1)]} / par

= T / [100(1 + y/2)^(2_T_ + 1)].

U are a genius…!!!..Thanx a ton for ur simplification…:)…U made it look so easy…

You’re very kind.

It was my pleasure.