Price change of a bond towards yield and YTM

Question

I have been trying to get a good picture of PV01 and DV01(PVBP). I was going through below link.

This measure is the absolute value of the change in price of a bond for a one basis point change in yield. It is another way to measure interest-rate risk.

I find Price Value of Basis Point explanation from Fabozzi Hand Book is clearer.

PVBP is measure of the price volatility of a bond to quantify
interest-rate risk—the price value of a basis point (PVBP). 
This measure, also called the dollar value of an 01 (DV01), 
is the absolute value of the change in the price of a bond 
for a 1 basis point change in yield. That is,
**PVBP = | initial price − price if yield is changed by 1 basis point |**

To me it sounds like YTM than the current yield. Isn't it YTM it is referring to? I understand the calculations and relationship between Price and Interest Rate in terms of a bond. Price of a bond is affected by a change in interest rate and yield remains the same. So in my understanding such changes in interest rate only matters for YTM and not current yield.

So what yield is this article really referring to?

On a latter note, can someone direct me to a good material for PV01 calcualtion?

Answer 1

This can actually get quite confusing. Some people use them to mean different things, but many use them to mean exactly the same thing.

There's typically no ambiguity in DV01. It is a $dP/dy$ calculation and represents the change in price when the yield of a bond changes by 1 basis point. I need to emphasize that you're changing the bond's own yield (typically yield to maturities for government bonds) and you're NOT changing the yield CURVE!

If you shock the entire yield curve in a parallel way by 1 basis point and computes the change in price based on the new yield CURVE, we typically refer to that as the "effective DV01" or "effective '01". In practice, the curve shocked is typically the par yield curve (a theoretic curve representing the yields of bonds trading at $100). As a result, the effective DV01 tends to be higher than DV01.

PVBP is a terminology used more frequently in the swap/swaption world (although Lehman and JPM use "PVBP" on their reports, even though they mean "DV01"). Strictly speaking, it is the present value of a stream of 1bp coupon payments – this is why it's also called the "annuity factor." For example, if you have a 1-year swap and its fixed side has two cash flows, 6m from today and 1y from today. Then the PVBP of the fixed side is literally just $$d(0.5) + d(1),$$ where $d(t)$ is the discount factor for time $t$. Similar computations can be done for the floating leg. When people talk about the PVBP of a swap without specifying which leg it is, it refers to the fixed leg.

The DV01 of a swap is different. It is the change in the value of a swap when we bump the entire swap curve (some houses bump the par swap curve, some houses bump the instruments going into the curve construction). In reality, a lot of people use the PVBP of a swap instead of the "true" DV01 because the former is much easier to compute (just summing up discount factors). For par swaps, the two are pretty much the same anyways.

Finally, PV01 typically refers to PVBP, but again, some use it to mean DV01, and yet others use it to mean effective DV01. It's a crazy world out there...